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... There are many different approaches and criterions leading to solution of timetable synchronization problem. Basic overview of approaches published in time 1989-2015 is provided by [7]. Conclusion is that there is not one approach and one universal solution of this problem only. ...

... This can have also serious influence on needed dwell (sojourn) time DTi. Three different 'passenger types' are defined by [7]: transferring (interchanging), through and boarding passenger. This division is necessary for correct evaluation of time loss. ...

... Researched task belongs to the scope of 'timetable synchronization problem'. In general, there are several ways how this problem can be solved [7]. Local conditions, specifics and requirements must be reflected. ...

The article is focused on timetable synchronization problem. Interconnection of urban public transport and long-distance transport in busy hubs is researched. Intension is to find adequate time positions of urban public transport arrivals and departures with an effort to minimize passengers’ time loss related to this interchange. Timetable of long distance transport is considered as constant (given). Timetable of urban public transport is result of optimization (and presupposed to be periodic). Nonlinear integer mathematical programming model is formulated. Model is implemented in Microsoft Excel Solver. Parallel way based on exhaustive-search algorithm is introduced as well. This algorithm provides extended set of output data able to be used in transport planning. Two different criterions are proposed. Each interchange (pair of vehicles) has the same weight in the case of uniform approach. Intensity approach considers interchanges as weighted by numbers of interchanging passengers. Some additional modifications of proposed model are mentioned for possibility to regard some important technological aspects and to reach more individualized solution. Model is illustrated by the case study located to Pardubice main station as a hub of passenger railway transport. Interface with urban public transport is mentioned as an illustrational example of synchronization.

... The latter body of works is closer to our work which uses historical AVL and APC data to generate robust timetables. One example of such works is the work of Wu et al. (2015) which assumed stochastic bus travel times to calculate slack times at transfer stops and improve the synchronization of timetables. Studies on operational control have also considered stochastic travel times. ...

... The incremental contribution(s) of this work to the state-of-the-art are: (a) the consideration of in-vehicle times as a problem objective to avoid prolonging trip travel times that appear in other works (see Fu and Yang (2002)); (b) the development of a timetable optimization model that uses (bounded) uncertainty sets of travel times and passenger demand, instead of typical probability distributions (Hickman, 2001;Wu et al., 2015); and (c) the inclusion of practical, regulatory constraints in the generation of the timetable such as the resting times of bus drivers, the required deadheading times and the maximum dispatching headway limits. ...

... In future research, the proposed robust timetabling approach can be applied to other problems such as the timetable synchronization problem which is typically solved with deterministic approaches (Wu et al., 2015). Moreover, our approach can be applied to the optimal slack time problem. ...

Timetables are typically generated based on passenger demand and travel time expectations. This work incorporates the travel time and passenger demand uncertainty to generate robust timetables that minimize the possible loss at worst-case scenarios. We solve the resulting minimax problem with a genetic algorithm that uses sequential quadratic programming to evaluate the worst-case performance of each population member. Our approach is tested on a bus line in Singapore demonstrating an improvement potential of 5% on service regularity and excessive trip travel times.

... Ein der Serviceregularität entgegengesetztes Gütekriterium ist Synchronisation (siehe z.B. [20], [34], [46], [75], [103]). Sie ist ein Maß für die Zahl der (nahezu) gleichzeitig stattfindenden Ankünfte/Abfahrten an den Haltepunkten des Verkehrssystems und soll für Passagiere komfortable Umsteigeverbindungen zwischen Fahrzeugen verschiedener Linien sicherstellen. ...

... Sind nur spezifische Komponenten des Streckennetzes (bspw. wichtige Umsteigeknoten) Ziel der Optimierung, können zur Abbildung auch Graphen mit reduzierter Knoten-und Kantenmenge verwendet werden (siehe z.B. [20], [34], [75], [103]). Eine häufig angewendete Repräsentierung mit stärkerer Abstrahierung vom zu untersuchenden System basiert auf Ereignis-Aktivitäts-Netzwerken (engl. ...

Until recently the project Computer Aided Traffic Scheduling (CATS) was only concerned with the design and implementation of methods and software tools that enable transport providers to generate, simulate and evaluate tram schedules, assisting them during the tactical planning phase. During the work on the project the desire for a simulation software arose, which would be able to represent multi modal public transit systems and could assist transport planners not only during the tactical planning phase but also during daily operations. This thesis deals with three main goals: At first, an optimization software for the generation of timetables with high service regularity for multi modal public transit systems is developed, which is also able to consider interdependencies within and between different modes of transportation, e.g. transfer connections. In addition, the software can incorporate other economic, operative, and political requirements during the optimization to assure feasibility of the resulting timetables during daily operations. The correctness and efficiency of the optimization model is demonstrated by applying it to models of artificial transit networks as well as to a model of the bus network of Cologne from 2001. Furthermore, a new event-based, mesoscopic simulation software for multi modal public transit systems is developed, which can be used to evaluate timetable quality. The individual components of the software are designed in such a way that future extensions of the model, e.g. new modes of transportation, can be incorporated easily. The correctness and plausibility of the simulation model, even when using sparse data sets, is proven through theory and function based validation, using models of an artificial bus network as well as the tram network of Cologne from 2001. The efficiency of the simulation software is demonstrated via exemplary runtime analyses. Thereupon, the simulation software is extended with capabilities to autonomously initiate rule-based traffic management measures, enabling transport planners to evaluate different traffic management strategies. The correctness of the implemented measures is demonstrated exemplarily by applying them to models of artificial and real-world transit networks. Lastly, the applicability of the complete software package is demonstrated via its application to a typical use case of the complete public transit network of Cologne from 2001. The thesis begins with an introduction to context, motivation and aims (chapter 1), followed by an introduction to the domain of public transit timetable generation as well as a review of selected existing literature (chapter 2). Afterwards, a new optimization model for the generation of timetables for multi modal public transit systems is presented, which is based on two models reviewed beforehand (chapter 3). The correctness and efficiency of the optimization software designed to solve the optimization model is proven via sample applications. After this, some general simulation techniques as well as existing simulation models specific to public transit systems are discussed (chapter 4), before a new simulation model for multi modal public transit systems is presented (chapter 5). Its correctness and efficiency is demonstrated by applying it to models of artificial and real-world transit networks. Then the simulation model is extended with capabilities to autonomously initiate rule-based traffic management measures. To this end a short introduction to the domain of traffic management for short- and long- distance transit systems as well as a review of selected existing literature is given (chapter 6), before the actual extensions of the model are presented (chapter 7). The correctness of selected extensions is demonstrated via sample applications. After completion of the analyses of single components of the software package, its applicability is demonstrated by applying it to a typical use case of the complete public transit network of Cologne from 2001 (chapter 8). The thesis concludes with a short summary and some thoughts on further research (chapter 9).

... Although a well-planned synchronized scheme can considerably improve the level of service by providing seamless transfer solutions ( Ceder et al., 2001 ), in practice, there exist a large number of stochastic attributes in the public transport system: travel time, dwell time, adverse weather, demand, etc., which affects the materialization of the planned synchro-nized timetable ( Yu et al., 2012;Yao et al., 2014;Wu et al., 2015;Wu et al., 2016 ). Such stochastic events cause arrival delay to transfer stations and missed connection for passengers. ...

... The design variables to be optimized include the vehicle size, headways and slack times. Thereafter, Wu et al. (2015) investigated a timetabling model by adding slack times to mitigate the travel time variability. They built upon the original work of Ceder et al. (2001) and developed a stochastic integer programming model where decision variables consist of slack times and departure times. ...

Schedule coordination is a proven strategy to improve the connectivity and service quality for bus network, whereas current research mostly optimizes schedule design using the a priori knowledge of users’ routings and ignores the behaviour reactions to coordination status. This study proposes a novel bus stochastic schedule coordination design with passenger rerouting in case of transfer failure. To this end, we develop a bi-level programming model in which the schedule design (headways and slack times) and passenger route choice are determined simultaneously via two travel strategies: non-adaptive and adaptive routings. In the second strategy, transfer passengers would modify their paths in case of missed connection. In this way, the expected network flow distribution is dependent on both the transfer reliability and network structure. The upper-level problem is formulated as a mixed integer non-linear program with the objective of minimizing the total system cost, including both the operating cost and user cost, while the lower-level problem is route choice (pre-trip and on-trip) model for timed-transfer service. A more generalized inter-ratio headways scenario is also taken into account. A heuristic algorithm and the method of successive averages are comprehensively applied for solving the bi-level model. Results show that when the rerouting behaviour is considered, more cost-effective schedule coordination scheme with less slack times can be achieved, and ignoring such effect would underestimate the efficacy of schedule coordination scheme.

... It was found that the model based on mixed buses was superior to the other two based on the small and large buses in terms of passenger total travel time and public transit expenditure [21]. Wu et al. developed a bus schedule optimization method that incorporated slack time to increase the transfer efficiency with the consideration of the stochastic bus travel time [22]. Using plentiful boarding and alighting data, Wang et al. introduced a time-related passenger demand model and determined the departure time of every bus by minimizing passenger waiting time [23]. ...

... The second-type passengers can only choose one route to travel at a stop, even the stop is in the overlapping area. The waiting time for the second-type passengers is denoted by 2 t and it is shown in (22). ...

Bus routes overlapping would lead to more than one bus entering the stop simultaneously, which may trigger bus bunching. Focusing on high frequency routes with common stops, this paper proposes a mixed scheduling method combining the all-stop service and the stop-skipping service. The method optimizes scheduling strategies for multiple routes by minimizing total passenger travel time. The optimization variables are binary variables reflecting whether the stops in the overlapping area are skipped. Three exciting bus routes are employed for case study. Results show that the proposed method reduces total passenger travel time by 21.4% compared with the current scheduling strategy.

... Introducing long slack times though requires more buses to maintain the same service frequency, leading to the under-utilization of resources. Wu et al. [15] scheduling (offline) integer program Yes genetic algorithm heuristic Adamski and Turnau [7] rescheduling multiple programs No sub-optimal, simulation-based control Eberlein et al. [18] periodic bus holding non-convex quadratic program No heuristic Hickman [3] single-vehicle holding control convex quadratic program in a single variable ...

... However, such models do not consider the travel time variations during the actual operations and cannot react to real-time changes in the travel conditions (Fayyaz et al. [13] ). Another distinct line of works models the scheduling problem as a stochastic optimization one incorporating the travel time and passenger demand variability when determining the dispatching times of the daily trips at the tactical planning stage (Xuan et al. [14] , Wu et al. [15] ). Despite the above, solving such stochastic models during the actual operations is not computationally feasible. ...

We model the problem of dispatching time control in rolling horizons following a periodic optimization approach reactionary to travel time and passenger demand disturbances. This model provides more flexibility to transport planners allowing them to adjust the bus schedules during the daily operations. We prove that our periodic optimization model is a convex quadratic program, guaranteeing the global optimality of its solution. To reduce the computational burden, we introduce an iterative algorithm that uses gradient approximations
to obtain an approximate dispatching solution. The proposed solution method is found to be significantly faster than exact optimization approaches for quadratic programming and maintains an (almost) negligible optimality gap in realistic bus operation scenarios. Finally, we show that our periodic optimization method outperforms myopic
methods that adjust the dispatching time of each bus trip in isolation using operational data from bus line 302 in Singapore.

... The scheduling problem is usually based on maximization of the number of synchronized vehicles arriving at the transfer station or minimization of the total waiting time at the station. For solving the latter problem, a genetic algorithm with local search is used in [20]. The model is applied to a small bus network and the cost of the waiting time is reduced by 9.5%. ...

... • [11,20], [21,30], [31,40], [41, 50], [51, 60]. Table 4 presents the combined results of the proposed method using MOPSO algorithm and the results from the literature. ...

Determining the best timetable for vehicles in a public transportation (PT) network is a complex problem, especially because it is just necessary to consider the requirements and satisfaction of passengers as the requirements of transportation companies. In this paper, a model of the PT timetabling problem which takes into consideration the passenger waiting time (PWT) at a station and the vehicle occupancy ratio (VOR) is proposed. The solution aims to minimize PWT and maximize VOR. Due to the large search space of the problem, we use a multiobjective particle swarm optimization (MOPSO) algorithm to arrive at the solution of the problem. The results of the proposed method are compared with similar results from the existing literature.

... However, the waiting time of transfer passengers is not mentioned in that article. Wu, Tang et al. [16] designed a genetic algorithm with local search to solve a bus timetabling problem with stochastic travel times. They added slack time into timetable to reduce transfer failure greatly, as the total waiting time cost was reduced by 9.5%, in which waiting time for transfer passengers by 11.8%. ...

... Equations (12) and (13) ensure that the departure time and the arrival time of the trains adjusted fall within the reasonable time range respectively. Equations (14)(15)(16)(17) ensure that reasonable time range cannot lead to train conflicts at adjacent stations. Equations (18) and (19) ensure that the departure time and the arrival time of the trains adjusted belongs to one optimized period time respectively. ...

As one kind of highest hierarchy node on the network, the transfer scheme of high-speed railway hub timetable should be studied at priority. After defining the problem that optimizing transfer scheme of timetable at high-speed railway hub, this paper proposes time adjusting strategy and platform adjusting strategy to optimize the problem, of which the first strategy introduces a FUZZY set of reasonable time range to reduce the possible train conflicts at adjacent stations on the network, and the second strategy helps to use different transfer time to match the arrival and departure of trains. Then, an optimization model of timetable based on passenger transfer is established with the minimized invalid transfer waiting time for passenger and train conflicts at adjacent stations as the objective function. The model is solved by the above two strategies in MATLAB software. Finally, the rationality and effectiveness of this model are verified, taking Shanghai Hongqiao Station as an example.

... Models and optimisation methods for the synchronisation are presented in many articles of foreign authors [5][6][7][8][9][10]. Although the authors consider some characteristics of subprocesses as random variables [8][9][10], a functional dependence of the impact of their parameters on the waiting time is not studied. ...

... Models and optimisation methods for the synchronisation are presented in many articles of foreign authors [5][6][7][8][9][10]. Although the authors consider some characteristics of subprocesses as random variables [8][9][10], a functional dependence of the impact of their parameters on the waiting time is not studied. An investigation of the influence of random variables of vehicles arrival and departure time on the passenger transfer waiting time at a transfer node requires a special research for the designing synchronised schedules of UPT with minimal waiting time. ...

... Moreover, genetic algorithms in the conditions of public transport are also used by authors of [25], who explore solutions of the coordination problem of individual lines, for which irregular travel times among individual stops are expected. e objective is to minimize the total waiting time cost for three types of passengers (i.e., transferring passengers, boarding passengers, and through passengers). ...

... When it is necessary to solve passing between train connections i and j, the incidence matrix shows value a ij � 1; in the opposite case, the value is 0. Passing of the train connections in their initial nodes (train stations) is not considered since in these situations train units could accumulate in the given initial train stations. 13 4 7 10 17 12 1 7 20 16 18 23 20 0 24 8 9 18 1 9 2 13 14 21 Number of transfer passengers in the direction CB > Cesky Krumlov 15 9 19 1 23 6 19 0 17 0 20 18 20 20 20 9 6 12 12 3 3 3 11 3 24 10 2 20 6 1 8 18 21 18 21 11 21 10 12 5 21 13 4 7 10 17 12 1 7 20 16 18 23 20 0 24 8 9 18 1 9 2 13 14 21 3 3 24 23 25 Number of transfer passengers in the direction Vimperk > Strakonice > Razice 6 15 13 5 1 12 20 6 19 7 20 3 4 7 0 10 23 7 12 24 13 19 22 21 12 12 19 9 8 23 14 22 17 1 3 22 16 1 3 13 3 17 4 Number of transfer passengers in the direction Prachatice > Cicenice > Divcice 12 25 14 2 11 18 4 12 25 3 20 17 4 21 11 5 21 19 7 6 3 22 2 17 14 Number of transfer passengers in the direction Cicenice > Prachatice 19 21 5 15 3 12 9 1 6 18 19 6 13 19 18 12 18 10 2 22 11 17 24 16 8 9 9 0 4 6 6 24 13 Upon substituting the input values to the proposed mathematical model, the following results were achieved, see Table 11. ...

The article addresses creation of a mathematical model for a real problem regarding time coordination of periodic train connections operated on single-track lines. The individual train connections are dispatched with a predefined tact, and their arrivals at and departures to predefined railway stations (transfer nodes) need to be coordinated one another. In addition, because the train connections are operated on single-track lines, trains that pass each other in a predefined railway stations must be also coordinated. To optimize the process, mathematical programming methods are used. The presented article includes a mathematical model of the given task, and the proposed model is tested with real data. The calculation experiments were implemented using optimization software Xpress-IVE.

... Closer to our work, [28], [19], [29] and [30] have con- sidered the stochastic nature of the trip travel times during the daily operations. However, [28] was focused on the bus line synchronization problem, [29] on the reliable frequency settings problem and [30], [19] on the bus holding problem during the actual operations without addressing the dispatch- ing time planning problem. ...

... Closer to our work, [28], [19], [29] and [30] have con- sidered the stochastic nature of the trip travel times during the daily operations. However, [28] was focused on the bus line synchronization problem, [29] on the reliable frequency settings problem and [30], [19] on the bus holding problem during the actual operations without addressing the dispatch- ing time planning problem. Focusing specifically on the problem of planning robust dispatching times for all daily trips, this work contributes to the state-of-the-art by: (i) incorporating the observed uncertainty of the bus travel times using historical AVL and AFC data; (ii) developing a model for timetable optimization which can handle uncertainty; (iii) introducing a Genetic Al- gorithm coupled with Monte Carlo evaluations for addressing the NP-hardness of the robust timetabling problem; and (iv) analyzing the performance of robust timetables in scenarios with low and high travel time variability. ...

Bus operators plan the dispatching times of their daily trips based on the average values of their travel times. Given the trip travel time uncertainty though, the performance of the daily operations is different than expected impacting the service regularity and the expected waiting times of passengers at stops. To address this problem, this work develops a model that considers the travel time uncertainty when planning the dispatching times of trips. In addition, it introduces a minimax approach combining Monte Carlo evaluations with a Genetic Algorithm for computing dispatching times which are robust to travel time variations. This approach is tested in a circular bus line of a major bus operator in Asia Pacific (APAC) using 4 months of Automated Vehicle Location (AVL) and Automated Fare Collection (AFC) data for analyzing the travel time uncertainty and computing robust dispatching times. In addition, 1 month of data is used for validation purposes demonstrating a potential service regularity improvement of 5.5% in the average case and ≃22% in worst-case scenarios.

... The research results presented in these publications do not provide recommendations for reducing the passengers waiting time carrying out transfers. Models and optimisation methods for the synchronisation are presented in many articles of foreign authors [5][6][7][8][9][10]. Although the authors consider some characteristics of subprocesses as random variables [8][9][10], a functional dependence of the impact of their parameters on the waiting time is not studied. ...

... Models and optimisation methods for the synchronisation are presented in many articles of foreign authors [5][6][7][8][9][10]. Although the authors consider some characteristics of subprocesses as random variables [8][9][10], a functional dependence of the impact of their parameters on the waiting time is not studied. An investigation of the influence of random variables of vehicles arrival and departure time on the passenger transfer waiting time at a transfer node requires a special research for the designing synchronised schedules of UPT with minimal waiting time. ...

... That microscopic deterministic approach can calculate the maximum curable delay of a bus. In certain research the slack is allocated to the trip as an aggregate (Wu et al. 2015) and then use this slack to reduce randomness in transit nodes. The stochastic optimisation model suggested by Wu et al. (2016) for designing the transit network timetable considered the slack time at the transfer node of the synchronised route to avoid the missing of the connection bus. ...

... The mean of the running time and the dwell time along with their degree of deviation are used for fixing the scheduled times. Wu et al. (2015) signifies the slack time as the allowance given in the schedule for adjusting the variation of bus operation. This paper estimates this measure by Eq. (7) keeping the objective of getting an optimal value of slack to catch up with the schedule. ...

Bus bunching in public transport is the concentration of similar buses having different schedules to a common time point. The reason for this phenomenon is variations existing in the bus operation as earliness and lateness. Bus bunching has the consequence of reduced service reliability concerning both passengers and operators. A zero bunching state is vital for enhancing the usage of public transport where the buses operate with utmost schedule adherence. Two generally adopted strategies for solving bus bunching are a schedule-based strategy which provides slack time in a timetable to address late running and fixed departure time for the early operations, and a headway-based strategy that maintains headway between buses. Bus bunching due to multiple origins is a special case in which common tactics cannot effectively control a bunching tendency that arises at the entry point. The operation schedules of multiple origins must be so designed that a state of zero bus bunching can be ensured while buses from different origins reach the entry points. This article presents a model of a multiple-origins public transport network as a combination of origins, routes and entry points, developed in the search for achieving a zero bunching state in the operation beyond an entry point. The origins are modelled based on the entry-point variables. The routes are modelled based on the running time, departure time, arrival time, and dwell time. The entry points are modelled based on route and entry-point variables. Redesigning route schedules based on the entry-point characteristics and an appropriate slack time implementation are proposed and observed to be suitable for overcoming bunching in a multiple-origins bus operation.

... Parbo et al. [12] studied a bilevel timetable optimization problem, aimed at minimizing the weighted transfer waiting time. Wu Y. et al. [13] studied a stochastic version of SBT. Slack time was inserted into the timetable to mitigate the randomness of travel times to reduce the rate of transfer failures. ...

... Proof. Without considering small timetable modifications, Wu Y. H. et al. [25] and Ibarra-Rojas et al. [8] have derived the departure time window of as (13). We thus obtain expression (14). ...

Bus timetabling is a subproblem of bus network planning, and it determines departure time of each trip of lines to make vehicles from different lines synchronously arrive at transfer stations. Due to the well-designed coordination of bus timetables, passengers can make a smooth transfer without waiting a long time for connecting buses. This paper addresses the planning level of resynchronizing of bus timetable problem allowing modifications to initial timetable. Timetable modifications consist of shifts in the departure times and headways. A single-objective mixed-integer programming model is proposed for this problem to maximize the number of total transferring passengers benefiting from smooth transfers. We analyze the mathematical properties of this model, and then a preprocessing method is designed to reduce the solution space of the proposed model. The numerical results show that the reduced model is effectively solved by branch and bound algorithm, and the preprocessing method has the potential to be applied for large-scale bus networks.

... Ceder et al. (2001) devised a method for minimizing passengers' waiting time at the transfer nodes, by establishing a model to maximize the synchronization of a given network of buses. Wu et al. (2015) considered a bus optimization problem to minimize the total waiting time cost for transferring passengers, boarding passengers and carrying through passengers. Based on the above literature review, it is clear that timetable optimization from either bus carriers' perspectives or passengers' perspectives has drawn great attention and become a much sought after topic in recent years. ...

... Since genetic algorithm first proposed by Holland (1975), it has been widely studied, experimented and applied by many researchers (Pillai et al. 2017;Ting et al. 2017). Owing to the robustness and success of GA in providing good solutions to many complex optimization problems, the algorithm has been widely applied to solve various scheduling problems in the field of public transit (Liu et al. 2013;Zuo et al. 2015;Huang et al. 2016), including the application of GA to solve timetable optimization problems (Niu and Zhou 2013;Wu et al. 2015). Following this trend, this paper designs a genetic algorithm with variable-length chromosomes in the attempt to resolve the proposed fuzzy bi-objective model. ...

Timetable optimization is an important step for bus operations management, which essentially aims to effectively link up bus carriers and passengers. Generally speaking, bus carriers attempt to minimize the total travel time to reduce its operation cost, while the passengers attempt to minimize their waiting time at stops. In this study, we focus on the timetable optimization problem for a single bus line from both bus carriers’ perspectives and passengers’ perspectives. A bi-objective optimization model is established to minimize the total travel time for all trips along the line and the total waiting time for all passengers at all stops, in which the bus travel times are considered as fuzzy variables due to a variety of disturbances such as weather conditions and traffic conditions. A genetic algorithm with variable-length chromosomes is devised to solve the proposed model. In addition, we present a case study that utilizes real-life bus transit data to illustrate the efficacy of the proposed model and solution algorithm. Compared with the timetable currently being used, the optimal bus timetable produced from this study is able to reduce the total travel time by 26.75% and the total waiting time by 9.96%. The results demonstrate that the established model is effective and useful to seek a practical balance between the bus carriers’ interest and passengers’ interest.

... Vansteenwegen and Van Oudheusden proposed a standard linear programming model to improve passenger service with a waiting cost function that weighted different types of waiting times and late arrivals; they then applied the programming model to a small part of the Belgian railway network (8). Wu et al. considered a bus timetabling problem with stochastic travel times and added slack time to mitigate randomness in bus travel times (9). They also developed a stochastic integer programming model to minimize total waiting time cost for three passenger types (i.e., transferring, boarding, and through passengers). ...

In an urban subway network, a synchronized and optimized timetable can provide a good service to all passengers. Therefore, the timetable is typically the most important factor for an operator. This study builds a time-dependent passenger demand-driven timetable synchronization and optimization (TDTSO) model as a mixed-integer programming model to minimize passenger total travel time in an urban subway network by adjusting departure times, running times, stopping times, and headways of all trains on each line. To solve the model, a binary variable determination (BVD) method is developed to calculate the binary variables of the TDTSO model, and a genetic algorithm based on the BVD method is proposed. The proposed TDTSO model is applied to the Beijing subway network in a case study. Several performance indicators are presented to verify the efficiency of the proposed model. The results can provide the operator of an urban subway network with additional options to produce a synchronized and optimized timetable for real-world situations.

... The timetable problem is usually based on the maximization of the number of synchronized vehicles arriving at the transfer station or on the minimization of the total PWT at the station for the vehicle with which the passenger continues his journey [25]. The authors have proposed a stochastic integer programming model to minimize the cost of the total PWT for three types of passengers: transferring passengers, boarding passengers and through passengers. ...

One of the greatest challenges in the public transportation network is the optimization of the passengers waiting time, where it is necessary to find a compromise between the satisfaction of the passengers and the requirements of the transport companies. This paper presents a detailed review of the available literature dealing with the problem of passenger transport in order to optimize the passenger waiting time at the station and to meet the requirements of companies (maximize profits or minimize cost). After a detailed discussion, the paper clarifies the most important objectives in solving a timetabling problem: the requirements and satisfaction of passengers, passenger waiting time and capacity of vehicles. At the end, the appropriate algorithms for solving the set of optimization models are presented.

... A large case study is solved using a genetic algorithm approach and reductions of 11.5% of transfer waiting times are reported. Wu et al. (2015) present a timetabling model that minimizes the total waiting time costs for three classes of passengers: transferring, boarding, and through passengers. They consider stochastic travel times and allow the addition of slack time to benefit the passenger transfer feasibility. ...

Long transfer times often add unnecessary inconvenience to journeys in public transport systems. Synchronizing relevant arrival and departure times through small timetable modifications could reduce excess transfer times, but may also directly affect the operational costs, as the timetable defines the set of feasible vehicle schedules. Therefore better results in terms of passenger service, operational costs, or both, could be obtained by solving these problems simultaneously.
This paper addresses the tactical level of the integrated timetabling and vehicle scheduling problem as a bi-objective mixed integer programming problem that minimizes transfer costs and operational costs. Given an initial non-cyclical timetable, and time-dependent service times and passenger demand, the weighted sum of transfer time cost and operational costs is minimized by allowing modifications to the timetable that respect a set of headway constraints. Timetable modifications consist of shifts in departure time and addition of dwell time at intermediate stops with transfer opportunities.
A matheuristic is proposed that iteratively solves the mathematical formulation of the integrated timetabling and vehicle scheduling problem allowing timetable modifications for a subset of timetabled trips only, while solving the full vehicle scheduling problem. We compare different selection strategies for defining the sub-problems. Results for a realistic case study of the Greater Copenhagen area indicate that the matheuristic is able to find better feasible solutions faster than a commercial solver and that allowing the addition of dwell time creates a larger potential for reducing transfer costs.

... Service time is also is useful for bus operations such as headway control (3) and schedule planning (4). In addition, bus service time functions play an important role in transit network design (5,6) and transit assignment analysis (7,8). For such reasons, it is quite often necessary to estimate bus service time. ...

Bus queuing occurs frequently at the entry and exit areas of curbside stops. Formed queues can induce extra delays for bus operations. Conventional regression-based models to analyze bus service time cannot capture such delays because of their limitations in addressing interactions between buses and arriving passengers. To capture the extra delays, this paper proposes a new approach to estimate bus service time on the basis of the Monte Carlo method. The proposed models account for interactions between arriving buses as well as the numbers of boarding and alighting passengers. The models were established for curbside stops with both one and two berths. Case studies were implemented to show the effectiveness of the proposed approach. Archived data from the automatic vehicle location system and the automatic fare collection system were used to calibrate and validate the models. With the established models, the impact of passenger arrivals on bus service time was further demonstrated.

... Recently, Wu, Tang, Yu, and Pan (2015) facilitated a bus timetable with stochastic travel time by determining the departure time of each trip. Slack time was added to mitigate the randomness, and a genetic algorithm with local search was proposed to solve this stochastic optimization model. ...

This study provides a novel solution for the synchronized and coordinated railway scheduling optimization (SCSO) problem by the determination of the departure times of a public transit network. Railway timetable optimization is dealt with maximizing the number of synchronized meetings to allow for smooth transfers at interchanges. The developed model uses binary variables to record the number of synchronized meetings considering the importance of transfer stations and rail lines without the need to apply the modeling of passenger assignments. The model allows for a permissible and flexible transfer waiting time for making a connection between rails instead of the commonly used and assumed values. The solution of the mixed-integer programing problem of larger-sized railway networks is based on a synchronized and coordinated scheduling optimization genetic algorithm (SCSO-GA) with a local search strategy (LSS). This solution method is proved to be more efficient and accurate than the CPLEX solver. In addition it is proven to be a periodic event-scheduling problem (PESP) solver. The model is tested computationally on the Beijing urban rail transit network. The results demonstrate the advantage of the novel approach over other methods.

... Urban bus planning process is very complicated and requires many interdependent decisions to make. According to [2][3][4][5][6][7][8], the process can be divided into four basic steps; (1) network route design, (2) frequency and timetable setting, (3) vehicle scheduling, and (4) crew assignment. Each step is a complicated process and consists of several operations; therefore, they are usually performed in sequence, and the output of one step is the input for the next one. ...

Nowadays public transportation plays an important role in people's lives. One of the most important steps of public transportation planning is timetable setting. In timetable setting, the coordination of timetables of different lines should be considered in order to reduce passenger waiting times at transfer nodes. In this paper, a mathematical programming model for timetable setting is proposed, whose objectives are to maximize the simultaneous arrival of vehicles at transfer stops and to minimize the number of required vehicles. Due to the complexity of the developed model, the recommended solving methods are metaheuristic approaches that can provide high quality solutions within a reasonable time.

... Urban bus planning process is very complicated and requires many interdependent decisions to make. According to [2][3][4][5][6][7][8], the process can be divided into four basic steps; (1) network route design, (2) frequency and timetable setting, (3) vehicle scheduling, and (4) crew assignment. Each step is a complicated process and consists of several operations; therefore, they are usually performed in sequence, and the output of one step is the input for the next one. ...

Public transit plays an important role in economics and quality of life of citizens. It improves the quality of life by reducing traffic congestion and air pollution and also providing an easy way to travel. Among the different modes of public transportation, bus is the most common mode due to its flexibility, accessibility, and inexpensiveness. One of the most important steps of public transportation planning is scheduling and timetable setting. Since there is no direct link between every single origin and destination in a transit network, passengers often need to make a transfer at some point during their trip; consequently, facing an extra waiting time that needs to be minimized through timetable synchronization. In this study, a mixed integer nonlinear programming (MINLP) model is developed to find the optimal departure times. The main goal of the proposed model is to efficiently synchronize the timetables of different bus lines by maximizing the number of simultaneous arrivals at transfer points so that the waiting time for passengers who want to transfer between lines is minimized. Also, a fleet size constraint is considered to maintain the balance between the scheduled headways and the total number of required vehicles. The proposed model is solved using the General Algebraic Modeling System (GAMS) on a sample transit network and the results are reported.

... ILP-formulation is proposed that minimizes the total duty time. An interesting approach is synchronization of the movement of buses in the city, taking into account the random travel time [7]. ...

Abstract
One of the main directions of increasing the efficiency of the operating model of the railways functioning is the reduction of
logistics costs in the transportation of wagon and group shipments due to the improvement of the technology for accelerating the
passage of low-capacity railcar traffic on the basis of the organization of the circulation of grouped trains of operational purpose,
taking into account the synchronization of the plan for the formation of grouped trains with a schedule of traffic. In order to
provide the railway system with the properties of adaptive control of low-capacity railcar traffic at the networks of large
dimensions, an optimization mathematical model has been developed. To optimize this mathematical model, it is proposed to use
a real coded genetic algorithm. The coding and decoding process of the chromosome of the genetic algorithm has been formed,
which reflects the technological features of the implementation of the train formation plan of the grouped trains of operational
purpose. This approach will allow to increase the level of organization of transportations and to accelerate the delivery of cargoes
and to increase the competitiveness of railways in the market of transport services.

... Illustration of the potential gains obtained from adjusting tram trajectories and signal timings simultaneously: (a) Optimizing trajectories with fixed signal timings; (b) adjusting tram trajectories and signal timings simultaneously without considering timetable adherence; (c) adjusting tram trajectories and signal timings simultaneously considering timetable adherence. transit agency often adds slack times when determining scheduled travel times between time points (Furth and Muller, 2009;Wu et al., 2015). Insufficient slack times would result in a tight timetable. ...

Modern trams run on exclusive rail lanes along urban streets, but they usually share the right of way with general traffic at intersections and often get interrupted by traffic signals. To improve tram operation reliability, this paper develops a methodology to optimize a multi-period tram timetable by simultaneously adjusting bidirectional scheduled tram trajectories and traffic signal timings. The objective balances the operational priorities of minimizing tram running time and maximizing timetable adherence. The scheduled trajectories depict tram movements along the roads and dwell processes at stations. Arterial signal timings are resynchronized to favor tram movements. The proposed methodology was evaluated in a simulation of a real-world tram line. Compared with a traditional approach, the proposed methodology reduced tram running time, number of stops at intersections and schedule delay by 11.1%, 82.4% and 37.5%, respectively. The impact on general traffic could be assumed neutral since cycle lengths, green splits and vehicular bandwidths were kept unchanged.

... Constraint (8) de nes the binary variable y introduced in Table 2. It compares all the arrival times calculated by Constraint (7). In case the interval between two arrivals from di erent lines at a transfer point is shorter than the maximum allowable time window ( lk tp ), y takes 1; otherwise, it remains equal to 0. Eq. (9) calculates the minimum number of the required vehicles on each line which is equal to the maximum number of the required vehicles in each period on the same line. ...

The quality of public transportation service has major effects on people’s quality of life. During frequency and timetable setting, as an important step of the public transportation planning process, there is an important and complicated issue of synchronization which can directly influence the utility and attractiveness of the system; thus, it should be taken into account during the whole planning process, especially during the frequency timetable setting step. In this paper, a mixed-integer nonlinear programming model is proposed that aims at setting timetables on a bus transit network with the maximum synchronization and the minimum number of fleet size. The proposed model is shown to be applicable for both small and large-scale transit networks by employing it for setting timetables on two samples of both sizes. A simple problem is solved by GAMS Software where the obtained timetable is substantially reasonable. Moreover, the proposed model is used to set timetables through the genetic algorithm on Tehran BRT networks as a real-life instance; then the NSGA-II is used to obtain the Pareto optimal solutions of the problem for five different scenarios. The overall results show that the proposed model is efficient for setting timetables on transit networks of different sizes.

... With the rapid development of Internet technology, artificial intelligence technology has been applied in various industries. Especially in the fields of transportation, it solves of the problem of our country highway construction and management of related difficulties, but it is because of the involved area is relatively more, mutual penetration and cross between disciplines, in the actual operation not only have the transportation expert, expert, also have artificial intelligence technology for intelligent traffic system is based on 5 g network technology in the new system, and traffic development is of vital significance for the future [10][11]. In combination with the characteristics of the current network information technology, the intelligent transportation system must establish its emergency mechanism and safety protection measures, in order to build its perfect service system, so as to scientifically and ...

With the continuous development of urbanization in China, urban traffic problems are gradually highlighted. In the future, intelligent transportation system will be the most important method to solve the demand of urban traffic. The realization of intelligent transportation system requires real-time perception and monitoring of road traffic conditions. Fortunately, with the continuous development of mobile communication, satellite positioning, Internet of Things, big data and other technologies, GNSS, RFID, microwave, geomagnetic, video and other acquisition methods have been widely used in information perception in the field of urban traffic. Based on the concept of intelligent transportation, this paper constructs an intelligent transportation system based on Internet network technology, which has a certain guiding significance for the construction of intelligent transportation under computer network technology.

... The prediction accuracy of dwell time is important not only because of its contribution to the bus journey time, but also for its role in several other important aspects related to bus service (Tirachini 2013a). A better prediction of boarding and alighting times is useful for accurate estimates of bus stop capacity (Bian et al. 2015), efficient design of transit networks (Szeto et al. 2011;Wu et al. 2015), transit assignment and schedule reliability analysis (Leurent et al. 2014;Aashtiani and Iravani 2002), providing signal priority for buses (Oliveira-Neto et al. 2009;Bhattacharyya et al. 2019), and better estimation of service time for planning and evaluation of bus systems (Ceder 2007). ...

A majority of the past studies on bus dwell time have been carried out in the context of developed countries and the dwell time prediction models established in literature adopted the fixed parameter assumption. The variations due to human factors such as passenger and driver behavior are not reflected under a fixed parameter framework. This paper presents a methodology for rational estimation of passenger boarding and alighting time in the context of an emerging country using both fixed parameter and random parameter models. The methodology is demonstrated with reference to a case study in the Kolkata metro city, India. The results establish that the boarding and alighting time varies significantly across bus type, in-vehicle crowding, and size of the passenger group. In this context, random parameter models were found to out-perform fixed parameter models towards capturing the heterogeneity in bus and demand characteristics. The models were also validated successfully with statistically acceptable errors.
Keywords: bus dwell time, fixed parameter model, random parameter model, boarding dynamics, alighting dynamics, bus service.

... The most important criteria from the passengers' perspective related to timetables are synchronization at interchange nodes, operational reliability, information availability and supplementary services [60]. There are many different approaches and criteria leading to solutions for the timetable synchronization problem available in the literature [61]. Based on the overview of the proposed solutions, it can be concluded that there is not only one approach and one universal solution to this problem. ...

Intermodal and multimodal door-to-door journeys refer to the usage of various transport modes (air, rail, bus, road or maritime) by the traveler to complete a single journey. The main difference between these two approaches is that multimodal transport is executed under a single transport contract (a single ticket) between the passenger, on the one hand, and transport operators, on the other hand. The benefits of this type of service are reflected in the potential to save time and money. Such systems would make the transport sector greener and more sustainable, promote growth and reduce carbon emissions. The purpose of this paper is to define the concept of an air passenger multimodal transport system, identify factors and challenges that determine such a system’s development within Europe and to provide recommendations and directions for future research. The research carried out so far has indicated that market segmentation and transport system characteristics, as well as economic, social and political factors, have direct impacts on system development. This paper provides the basis for introducing single ticket, timetable synchronization and data sharing services, as well as the need to update the related regulations in order to move towards air passenger multimodality in both research and practice.

... Xiao processed the historical GPS of the bus, analyzed the running characteristics of the bus, and established the bus departure time model to alleviate the phenomenon of bus bunching and large interval [25]. Wu et al. aim to minimize the total waiting time of transfer passengers, waiting for passengers and direct passengers, and add redundant time in the bus timetable to adapt to the randomness of bus travel time [26]. A reasonable timetable can effectively improve the stability of the bus system from the root and reduce the trouble of later dispatching. ...

Improving the sharing rate of public transportation is an important content for the sustainable development of urban transportation. However, bus bunching, a common phenomenon during transit operation, makes negative effects on reliability and service level of the bus system. In most urban centers in China, many bus lines usually serve in a corridor. Different buses may interact with each other in the corridor, which may aggravate the bus bunching. However, previous studies on bus bunching focused on single bus service. In addition, with the popularization of bus data acquisition and the maturity of data processing methods, the accuracy of bus bunching research meets more opportunities. In this paper, we proposed a holding strategy based on two-bus cooperative control. A simulation was carried out after preliminarily processing and analyzing the bus operation data of Foshan, Guangdong City. In the simulation, we compared the performance of three different scenarios, which are before control strategy, under the strategy for a single bus line and under the coordinated strategy for multiple bus lines. We contrastively analyze the results of the two strategies from different aspects. The results show that in aspects, such as holding a frequency, holding time, the total running time and the influence on the other bus line, the cooperative holding strategy manifests better. It illustrates that it is meaningful to do such a research on the effect of corridor service on bus bunching and add this effect into traditional holding strategy to build a multi-bus cooperative control strategy. The results have important theoretical significance for enriching and completing existing theory and methods of transit system and practical value for improving the service level and attractiveness of buses, increasing the share rate of public transportation, and thus, promoting the sustainable development of cities.

... problems. In ( Wu et al. 2015), a bus timetable problem involving stochastic travel times (BTP-STT) was 108 considered and slack time was added into the timetable to mitigate the randomness of bus travel times. A 109 stochastic integer programming model was developed to minimize the total waiting time cost for three 110 types of passenger activities, including transferring passengers, boarding passengers, and through 111 passengers. ...

20 This paper investigates bus bunching issues encountered with a single bus line. A real-time speed control 21 model was proposed with the objective of minimizing variations in bus headway. Three cases of a typical 22 road infrastructure for bus lines were studied. Two main factors that influence the stability of bus service, 23 namely, signalized intersection delays and heterogeneous roadway conditions, were studied in the 24 modeling process. In addition, other common variables were considered, including the time required for 25 passengers to board a bus and alight from it. Compared with findings from prior literature, that frequently 26 assumed homogeneous roadway infrastructure conditions and ignored intersection delays, the built model 27 outputted the degree of speed adjustment required in accordance with different roadway configurations 28 and the congestion level at each road section. A case study was designed to test the performance of the 29 proposed model, based on the data collected from 40 bus stops, on Bus Route No. 600, in Xi'an, China. 30 Results showed that the proposed model could effectively restrain the problems posed by headway 31 deviations and reduce travel time for the passengers. 32

... Wu considered the relaxation time and established a stochastic model of timetable synchronization to minimize passenger waiting time. A genetic algorithm with local search was proposed to solve the model (Wu, Tang, Yu, & Pan, 2015). Guo optimized the timetable of the first train to minimize the total transfer waiting time (Guo, Wu, Sun, Liu, & Gao, 2016). ...

... dynamic rescheduling problems [43]). Wu et al. [44] assumed stochastic travel times to calculate slack times at transfer stops to improve the synchronisation of timetables. Stochastic travel times have also been considered for operational control in [32], who used bus holding to improve the adherence of the operations to the planned schedule, and Chen et al. [45] who developed a model for the optimal stopping design considering the vehicle capacity. ...

Bus scheduling is a well-known NP-hard problem, and it is addressed with the use of heuristic solution methods or graphical approaches. In this study, the author proposes an improved formulation of the bus scheduling problem that considers the vehicle availability, the vehicle capacity and the allowed headway variability among successive trip dispatches. His formulation expands the classic bus scheduling model formulation by including the aforementioned features. In his study, the bus scheduling problem is understood as the problem of setting the optimal dispatching times for a set of pre-determined daily trips of a particular bus line. His model facilitates the search of solutions that can improve the waiting times of passengers while meeting the operational requirements and avoiding overcrowding. His proposed mathematical program is proved to be non-convex, and it is solved with heuristic solution methods because numerical optimisation approaches cannot guarantee a globally optimal solution. The performance of his approach is tested in a case study using real operational data from bus line 302 in Singapore. A simulation-based evaluation demonstrates potential gains of up to 20% on average passenger waiting times and a major reduction in refused passenger boardings because of overcrowding.

... As shown above, although a variety of studies have focused on the Train Timetable Rescheduling (TTR) problem and the Timetable Synchronization Problem (TSP), the problem of rescheduling URT trains to serve passengers from delayed HSR trains is still neglected. Moreover, few researchers [1,8,[10][11][12][13][44][45][46] pay attention to the uncertain and stochastic factors of real-world operations in rescheduling the timetable. ...

This paper develops a multi-objective mixed-integer linear programming model for the problem of robust rescheduling for capacitated urban rail transit (URT) trains to serve passengers from delayed high-speed railway (HSR) trains. The capacity of each extra train is not assumed to be unlimited in this paper. Robust passenger assignment constraints are developed to ensure that delayed passengers can board the URT trains under different random delay scenarios of HSR operations. Robust dispatching constraints of URT trains are designed for a stable disrupting number of URT trains across different scenarios. The multi-objective model is used to maximize the number of expected transported passengers and minimize the number of extra trains and operation-ending time of all extra trains. An iterative solution approach based on a revised version of the epsilon-constraint method combined with the weighted-sum method is designed for the computation of the multi-objective model. Computational experiments are performed on the Beijing URT lines and the Beijing-Shanghai HSR line. We evaluate the impact of the robustness constraints of passenger assignment and the number of extra trains to ensure that the number of trains are maintained and the passengers can successfully take the trains during different delayed scenarios.

... Using multisource bus data, Wen-zhou et al. [6] proposed a new time division method based on minimizing fleet operation time cost, established an optimization model with the goal of minimizing the cumulative fleet operation time cost throughout the day, and used GA to optimize the operation time division scheme. Wihartiko et al. [7], Wu et al. [8], and Tang and Yang [9] improved the GA by combining the integer programming model with the GA, setting the GA with local search and setting the quantum GA with penalty strategy to optimize the timetable for passengers and the generalized cost of bus companies. Bao-yu et al. [10] and Wang [11], respectively, designed the timetable optimization using K shortest path idea and max-min ant colony algorithm from the perspective of adding different types of buses to the operation line. ...

The aim of this study was to explore the bus operating state of the city bus passenger corridor, taking the minimum bus operating cost and passenger travel cost as the objective function, taking passenger flow demand and operating income as the constraint, and considering the average speed change of the bus line in the bus corridor at different times. This paper proposes a dynamic optimization model of bus route schedule based on bus Integrated Circuit Card (IC Card) data. The optimization variable is the departure frequency of the candidate lines. To solve the model, a dynamic departure interval optimization method based on improved Genetic Algorithm (GA) was designed under different decision preferences. The method includes the calibration of generalized cost functions for passengers and bus companies and grasps the characteristics of bus operating speed changes and the design of departure strategies under different decision preferences. The validity and applicability of the proposed method are verified by a numerical example. We mainly carried out the following work: (1) Dynamic analysis of the time dimension of the bus departure interval takes into account the changes in passenger time characteristics during peak periods. (2) Seven schemes of weight ratio of passenger waiting time cost and bus operation cost were designed, and the departure intervals with different benefit orientations of passengers and operators were discussed, respectively, so as to select the corresponding departure schemes for decision makers under different decision preferences. The results show that (1) the total cost of the 7 different weighting schemes is lower than the actual value by 6.90% to 18.20%; (2) when decision makers need to bias the weight to the bus company, the weight ratio α : β between passengers and bus company is 0.25 : 0.75 which works best. The frequency of departures has been reduced by 6, and at the same time, the total optimized cost is reduced by 18.2%; (3) when decision makers need to bias the weight to the passengers, the weight ratio α : β between the passengers and bus company is 0.75 : 0.25 which works best. The frequency of departures has been increased by 19, and at the same time, the total optimized cost is reduced by 17.7%; and (4) when decision makers consider passengers and bus companies equally, the weight ratio α : β between passengers and bus companies is 0.5 : 0.5, the optimization cost is the closest to the actual cost, the optimization cost is reduced by 6.9%, and the frequency of departures has been increased by 5. The results show that the model in this paper provides a new idea for the information mining of bus routes in the research based on the bus IC Card data and provides an effective tool for the management of different operation decision preferences.
1. Introduction
Improper setting of bus line schedules will cause social and economic losses and potential safety hazards. Short departure intervals will waste resources and increase the financial pressure of the bus company. Too long intervals between departures will result in longer waiting times for passengers, a waste of time for passengers, and even the accumulation of people in public places, which may cause safety accidents [1]. The bus line optimization problem includes bus line path, line length, line nonlinear coefficient, line operation timetable, vehicle capacity, and so on [2]. The research problem of this paper is the departure schedule optimization of a single bus line in the commuter corridor. Starting from the departure schedule, this problem optimizes the travel waiting time and bus operation cost of passengers on the whole line, so as to achieve the goal of improving passengers’ riding experience and the income of bus companies [3]. Many rersearchers have conducted in-depth research on the optimization of bus timetable. At present, the research directions of bus line optimization mainly include single-line timetable optimization, cooperative optimization of multiline timetable, and considering the connection between bus and rail transit.
For single-line timetable optimization problems, Ma et al. [4] and Hassold and Ceder [5] took the passenger waiting time as the generalized cost of passengers, considered the bus operation cost and bus operation emission as the bus operation cost, and used GA to optimize the timetable. Using multisource bus data, Wen-zhou et al. [6] proposed a new time division method based on minimizing fleet operation time cost, established an optimization model with the goal of minimizing the cumulative fleet operation time cost throughout the day, and used GA to optimize the operation time division scheme. Wihartiko et al. [7], Wu et al. [8], and Tang and Yang [9] improved the GA by combining the integer programming model with the GA, setting the GA with local search and setting the quantum GA with penalty strategy to optimize the timetable for passengers and the generalized cost of bus companies. Bao-yu et al. [10] and Wang [11], respectively, designed the timetable optimization using K shortest path idea and max-min ant colony algorithm from the perspective of adding different types of buses to the operation line. Jun et al. [12], Wu et al. [13], and Zhang et al. [14] started with the service reliability of public transport companies, analyzed the suitability of bus arrival punctuality rate and passenger arrival time with the current operation timetable, and optimized the operation timetable with maximizing service reliability as a constraint. Some reasearchers considered the impact of signalized intersections in public transport operation. Among them, Jing et al. [15] considered the impact of public transport advance policy on social vehicles at signalized intersections and used simulated annealing algorithm and an event-driven policy combination model to optimize the timetable under the constraints of total line operation time and the negative impact of line operation on social vehicles at intersections. Bai et al. [16] considered the impact of the green light phase of the signal intersection on the line operation and optimized the bus schedule with the constraints of the average travel time and the average punctuality rate of the bus through the simulation software. Zhang et al. [17] and Gu et al. [18] proposed, from the perspective of data, the former uses the polynomial difference method to fill in the data for the lack of bus operation data and the latter uses back propagation (BP) and Radial Basis Function (RBF) neural networks to predict the boarding data of IC Card passengers and optimize the operation timetable. Yang et al. [19] proposed, from the perspective of energy conservation and emission reduction, an evaluation system for energy conservation and emission reduction when buses are driving on the road, and the bus schedule is optimized with emission pollution as the objective function.
For cooperative optimization of multiline timetable, Xu et al. [20] proposed a method to identify the direction of passengers getting off, transferring, and running based on the relationship between station attraction right, card swiping interval, and threshold. Zhang and Cao [21] calibrated the weight of passengers with different travel purposes, considered the demand of passengers with different travel purposes for equivalent time, and used GA to optimize the timetable. Chu et al. [22] considered the travel path selection of passengers in the area and used a mixed integer linear programming model and heuristic algorithm to optimize the operation timetable and pedestrian path selection at the same time. Jiang et al. [23], Wu et al. [24], and Guo-Jiang and Jian-Bo [25] used an enumeration method, GA based on nondominated sequence, and GA to optimize the operation schedule with the minimum total waiting time of passengers as the constraint. Wang and Cao [26] converted the loss of passengers caused by early and late vehicles into equivalent operating mileage. Aiming at minimizing the total operating mileage of multiple buses, considering passengers’ station constraints, bus capacity constraints, and passengers’ travel time window, they established a customized bus scheduling optimization model. Yang et al. [27] selected three kinds of public transit modes to establish a multimode public transit network and apply dimensionality reduction algorithm and the branch boundary method to optimize the transportation network.
Considering the connection between bus and rail transit, Takamatsu and Taguchi [28] established an event activity network to give vehicle timetable and passenger behavior in the backward areas of public transport in Japan and explored the rationality of train and bus transfer with the constraint of passenger transfer waiting time. Dou and Meng [29], based on exploring the rationality of the transfer between the terminal bus and the railway station, taking the minimization of passenger transfer waiting time as the constraint, and considering the bus capacity and passenger queuing attitude, established an MINLP model to optimize the timetable. Zheng-Wu and Ming-Qun [30] built a two-stage coordinated optimization of the operation lines of the corresponding feeder bus system at multiple transfer points for the mixed demand including reservation demand and real-time demand.
In summary, researchers at this stage are mainly concerned with the impact of the setting of bus schedules on passengers and bus companies. There are few studies on the changes in operating speed caused by the influence of social vehicles during bus operation. This article focuses on the itinerary optimization of a single line in the public transportation service corridor, extracting passenger flow characteristics from IC Card data, and grasping the characteristics of the travel time between stations on the target line on the target line based on the IC Card data of the passenger on the target line. GA is used to optimize the timetable with the travel cost model of the bus company to discuss the departure interval under different decisions.
2. Methodology
2.1. Problem Description
In the optimization of a single bus line, the departure interval of the bus at different times affects the bus service level, which is expressed by the total time cost of passengers and the operating cost of the bus company. In the research on the travel of passengers on bus lines, the travel time and travel OD matrix of passengers can be calculated according to the bus IC Card data. The research objective of this paper is to determine the dynamic departure interval of bus lines in different periods of working days. According to the obtained passenger IC Card swiping data, this paper makes the following assumptions:(1)The running speed of the bus between bus stops is constant, which is calculated by the average running speed between two stations in different time periods(2)There is no passenger capacity limit during the operation of the bus, which means that passengers at all stations can be loaded by the next bus currently waiting(3)The dimensions and operating parameters of public transport vehicles are the same
Based on the abovementioned assumptions, it is determined that the main research content of this paper is the impact of passenger travel demand in different time periods and different bus speeds in different time periods on bus schedule planning.
Passenger travel demand and bus operating speed change at different times. Therefore, the research time range of this paper needs to include the peak period and peak period of passenger travel in a day, in which the passenger travel characteristics and bus operating speed are extracted through IC Card data.
The main work of this paper is shown in Table 1, problem-solving framework, which is mainly divided into three parts: Part I: basic data acquisition: it includes obtaining necessary data such as the number of passengers arriving in the time period and the running speed of buses in different periods between stations Part II: design and modeling of different decision preferences: the different weights between passenger waiting and bus company operating costs are designed, and the GA is used to solve the optimal cost and the corresponding departure schedule Part III: result analysis: the optimized timetable is compared with the existing departure timetable, and the feasibility of optimizing the timetable is discussed
Steps
Main work
Eliminating useless data of IC Card
Data preprocessing
Determining peak and off-peak periods
Determining the optimization period
Extracting card swiping time data and analyzing passenger flow characteristics of card swiping time data and bus running speed
Key factor analysis
Weighting design under different decision preferences of optimization of departure schedule by GA
Model solving
Comparison between the optimized and original departure timetable
Analysis

... A reduction in total boarding time can result in significant benefits for the aircraft industry. To reduce the idle time of aircrafts, optimizations can start at any point between arrival and departure [3]. Among all the factors, the boarding time plays an important part in the turnaround time [4]. ...

The boarding efficiency is essential for all airlines due to potential competitive financial pressure. Therefore, the turnaround time needs to be cut down for a shorter boarding time. The paper devised a feasible boarding strategy which combines the management mode decision of passenger boarding with the intelligent deployment of the operation process and will be likely to improve the efficiency of the passenger travel chain. Among which, to decrease the boarding time is an effective method. Firstly, we proposed an improved outside-in strategy, which costs shorter boarding time based on the existing outside-in strategy. However, this method requires passengers to stand in queue in advance. Secondly, we put forward a deterministic queue-ordered boarding method to improve it. Finally, we simulated and applied the strategy to a narrow-body aircraft A320 and a wide-body A380, both representative for their type of airplanes. It turns out that this strategy performs better than the current widely used method and will be able to increase boarding efficiency and thus maximize the profits of airlines.

... Moreover, designing a synchronized timetable for the AHIS is an effective way to improve the quality of transfers, but it requires cooperation between the air and HSR operators. Maximizing synchronization to optimize transfers is important for operators and passengers (Wu et al., 2015;Ke et al., 2020). ...

Air and high-speed rail (HSR) intermodal service (AHIS) breaks through the barriers of aviation and HSR, which builds a modern integrated transportation system. However, this system also poses a challenge to operators to provide satisfactory travel services for passengers. This paper aims to identify the service indicators that influence travelers' overall satisfaction with AHIS and the relationships between them based on research data acquired from a passenger behavior survey at Shijiazhuang Zhengding International Airport (SJW) in 2019. First, a Bayesian network (BN) is constructed by integrating the greedy thick thinning (GTT) algorithm with expert knowledge. Then, sensitivity analysis and overall satisfaction prediction are conducted to determine the correlation and influence effect between service indicators and overall satisfaction. The research findings are as follows: (1) Compared to a binary logit model, the Bayesian network shows high fitting and prediction accuracies. (2) Transfer time is negatively correlated with satisfaction, for AHIS with the same total travel time, travelers tend to choose services with less transfer time since this choice increases their satisfaction. Interestingly, passengers are more tolerant of the travel time of airline than HSR. (3) Service indicators such as real-time information, arrival punctuality and ticket price have the highest sensitivity values for overall satisfaction. The results can provide useful suggestions for AHIS operators.

The integrated air-bus service expands the catchment area and alleviates congestion of regional airports. To gain further insights into the unexplored potential attributes of the integrated service that generate passenger satisfaction, this paper utilizes a two-stage analysis approach to identify the key promotion factors for passengers from different constituents. Based on the survey data collected in Nanjing Lukou International Airport, this paper 1) uses k-means clustering to categorize respondents into four groups. 2) Combines the gradient boosting decision tree and impact asymmetry analysis to identify the attributes that have nonlinear influences on the overall service satisfaction for each group respectively. Results suggest that the timetable of the airport bus is critical for all passenger groups. Interestingly, there are noticeable differences in passenger satisfaction with the accessibility, cost affordability, comfort, reliability, and integration of the integrated service, providing the basis for customizing service promotion strategies among different passenger groups and airports.

Nowadays the traffic congestion is being a common problem in major cities, every time the travel time is increasing and also the number of private cars. It is urgent to take actions to solve this problem. The urban transport is becoming into the best way to fight against congestion; but to make it more attractive to users it has to be more efficient (less travel time, less waiting time, low fare). The urban transport process has four main activities: Network design, Timetabling, Vehicle scheduling and Crew scheduling. The problem presented here is about the integration of the frequency and departure time scheduled both are subactivities of the timetable construction, besides it includes multiple periods planning and multiperiod synchronization, also the authors consider uncertainty in demand and travel time using fuzzy numbers. The planners faced this problem everyday. The authors created a mathematical model including the characteristics previously mentioned, the objectives of this model are to minimize the total operation cost, to maximize the number of multiperiod synchronization between routes, and to minimize the total waiting time for passengers. The SAugmecon method is used to solve the problem, 32 instances were randomly generated based on real data, and the comparison of two defuzzification methods (k-preference and second index of Yager) is presented. Also, the comparison of the problem with uncertainty on demand and uncertainty on demand and travel time is presented.

In this paper, the design of experiment (DOE) technique is used to formulate the robust schedule for the single-direction transit route. Factors affecting transit schedule performance are classified into two categories: the controllable and the uncontrollable. With Taguchi design method, these two types of factors are crossed mutually to carry out the Monte Carlo simulation to obtain the expected and variance values of the total schedule deviation. Next, two Kriging metamodels are fitted to describe relationships between controllable factors and the total transit schedule deviation. Based on these Kriging metamodels, the Pareto-optimal solution of the robust transit schedule is obtained.

Timetable regularity, that is, equability of headways, is an important measure for service quality in high frequency public transit systems, assuring an evenly distributed passenger load as well as improving product attractiveness. However, to be feasible during daily operation a timetable may also have to adhere to other planning requirements, such as departure time coordination with other service providers or deliberately short headways to reduce the passenger load of follow‐up vehicles. In this article, a disjunctive program formulation combining aspects of two previous optimization models is proposed, to generate regular public transit timetables adhering to planning requirements. The modeled requirements not only allow for the consideration of feasibility constraints from daily operations, but also for the consideration of simultaneous departures for transfer connections, an objective traditionally opposed to regularity. To show its applicability the approach is applied to two models of artificial transit networks as well as to models of the public transit network of Cologne, Germany. The results show that the proposed formulation can be used to generate timetables for network instances of realistic size in acceptable time. For networks consisting of multiple connected components it is shown that a decomposition approach can significantly reduce run times.

Synchronizing bus arrival and departure times at transfer stations could reduce excess transfer times. This paper addresses the planning level of bus schedule coordination problem through small timetable modifications to given an initial timetable. Timetable modifications consist of shifts in initial departure times of vehicles from the depot. Headway-sensitive passenger demand is also considered in this problem. A nonlinear mixed integer-programming model is proposed for the problem to maximize the number of total transferring passengers with smalll excess transfer times. Based on the analysis of the proposed model, a genetic algorithm combining local search (GACLS) is designed to solve this model. Several numerical experiments are performed to show the utility and performance of GACLS. For small case, the proposed GACLS is highly effective, and can obtain the optimal solution with less time than enumeration method. For large real case, the GACLS also has good performances.

While transferring between public transport services has a negative impact on the level-of-service, it is an inevitable feature of public transport networks. Transfer coordination can help reduce passenger transfer waiting times and improve service connectivity. In this paper, we systematically review the literature on transfer coordination design in public transport systems. First, four solution approaches for solving the transfer coordination design problem (TCDP) are identified and reviewed in detail, namely heuristic rule-based, analytical modelling, mathematical programming , and simulation. We then identify and review three extensions of the TCDP, i.e., considering first or last train transfer optimization, integrating vehicle scheduling, and incorporating passenger demand assignment. Finally, following the synthesis of the literature, some promising future research directions are outlined. This paper provides comprehensive insights on how to better design coordinated transfers to provide a seamless travel experience and improve the service connectivity of public transport networks.

With more and more interchange stations in a large-scale metro network, passengers tend to transfer between different metro lines from origination to destination, sometimes even more than once. Passenger waiting time is one of the critical standards for measuring the quality of urban public transport services. To support high service quality, this paper proposes a mixed integer nonlinear programming (MINLP) model for the train timetable generation problem of a metro network that minimizes the transfer waiting times and access passenger waiting times. In the mathematical formulation of the model, the transfer walking times at the interchange stations between two connected lines are treated as uncertain parameters. The robust train timetable generation model is formulated to optimize timetables by adjusting arrival and departure times of each train in the metro network to reduce access and transfer passenger waiting times. A robust counterpart is further derived that transforms the formulated robust model into a deterministic one. Moreover, a generalized Benders decomposition technique based approach is developed to decompose the robust counterpart into a subproblem and a master problem. The subproblem is a convex quadratic programming problem that can be solved efficiently. Finally, two sets of numerical examples, consisting of a small case and a large-scale case based on a real-world portion of the Beijing metro network, are performed to demonstrate the validity and practicability of the proposed model and solution approach.

In film and television animation works, animated characters are the soul and core of the work. The behavior, language expression, and emotional expression of animated characters play an important role in the expression of the animation theme and content. Aiming at the problem that the mobile animation system can only add and change actions for a single virtual character, and the characters cannot interact with each other, this paper analyzes the technical principles, technical characteristics, and application scope of human–computer interaction (HCI), taking sensors as the research object. An algorithm for separating the human body from the background environment in the depth image is proposed. Through the calculation of the depth value, the calculation results are compared, and the target human body and the background are effectively separated. In the depth data processing, the algorithm of judging the pixel offset value is used to identify the body part, and a sensor‐based HCI system is designed. The depth‐of‐field data map acquired by the sensor is used to identify human body parts and determine actions, thereby realizing HCI based on action recognition. Simulation test results show that the effective rate of the system is 80%, and the design of animated characters can be put into the visualization stage. Using the algorithm in this paper, the physical signs of the animated characters can be quickly identified, so that the next action of the animation can be more clearly captured. Has a certain practical value.

Bus timetables play an important role in improving the level of service and reducing operations costs of a bus transit system. Without dedicated bus lanes, bus travel times, which are important input data for bus timetabling, are usually time-dependent due to recurrent traffic congestion. However, few studies on bus timetabling have explicitly considered such travel time time-dependency in creating timetables. This paper addresses the problem of how to optimally modify an existing single-line bus timetable by slightly shifting vehicle departure times at the departure terminal and holding vehicles at other stops taking into account time-dependent travel times. The problem is mathematically formulated as a nonlinear programming model. According to the special structure and properties of the model, a derivative-free constrained compass search algorithm with revised step-size updating rule is applied to solve it. A case study of a bus line in Beijing, China is conducted to demonstrate the effectiveness and efficiency of the proposed model and solution algorithm. The case study results show that by utilizing the proposed methodology the optimized bus timetable can significantly reduce the total passenger travel time and improve ridership comfort, while rarely increasing the average vehicle cycle time. This study offers a promising and practical methodology for optimizing single-line bus service taking into account time-dependent travel times.

The primary aim of this research is to solve the timetabling optimisation problem of bus service with multiple bus types consideration. A bus timetabling optimisation model with bi-objective functions is constructed. The first objective is to minimize the total bus dwell time for all bus stops along the route. The second objective is to minimize the total passenger waiting time for all passengers at all bus stops. Both objectives are considered simultaneously in the model by using weighted optimisation model with one objective function. Genetic algorithm is used to decide the bus departure time and type of bus used for every trip. Moreover, the passenger demand distribution is used to simulate the bus dwell time at all bus stops in the algorithm. Real-life bus passenger data such as passenger demand is used to demonstrate the efficiency of the proposed timetable and the productiveness of the timetabling optimisation model. The proposed optimal bus timetable from optimisation model is able to reduce the total dwell time by 14.88% and the total passenger waiting time by 23.55% compared with the bus timetable currently used. The result shows that the constructed bus timetabling optimisation model is effective to provide a reliable bus timetable by balancing the benefits between the bus passengers and operators.

This paper focuses on the demand-oriented passenger train scheduling problem for a congested urban rail line, simultaneously considering uneven spatial and temporal demand distributions. To account for the left-behind phenomenon and passenger selection behavior, a passenger-train interaction framework is developed to dynamically assign passengers to capacitated trains. A mixed integer nonlinear programming model that combines heterogeneous headways and short turning as an integrated strategy (HH-ST) is proposed with the aim of jointly minimizing the passenger waiting time and operational costs, and balancing train loads. A two-stage genetic algorithm based on an integer coding approach is proposed to solve this problem efficiently. To verify the effectiveness of the proposed method, the HH-ST strategy is compared with alternative strategies, namely short-turning alone, heterogeneous headways alone and regular schedule (with no strategy), through a real-world case study of Shanghai Metro Line 9. The results show that the HH-ST strategy provides a better trade-off between users’ cost and operators’ cost than other strategies, thus achieving a better match between transport capacity and passenger demand.

This study proposes a solution to the feeder bus timetabling problem, in which the terminal departure times and vehicle sizes are simultaneously determined based on the given transfer passengers and their arrival times at a bus terminal. The problem is formulated as a mixed integer non-linear programming (MINLP) model with the objective of minimizing the transfer waiting time of served passengers, the transfer failure cost of non-served passengers, and the operating costs of bus companies. In addition to train passengers who plan to transfer to buses, local passengers who intend to board buses are considered and treated as passengers from virtual trains in the proposed model. Passenger attitudes and behaviors toward the waiting queue caused by bus capacity constraints in peak hour demand conditions are explicitly embedded in the MINLP model. A hybrid artificial bee colony (ABC) algorithm is developed to solve the MINLP model. Various experiments are set up to account for the performance of the proposed model and solution algorithm.

This paper presents a global review of the crucial strategic and tactical steps of transit planning: the design and scheduling of the network. These steps influence directly the quality of service through coverage and directness concerns but also the economic profitability of the system since operational costs are highly dependent on the network structure. We first exhibit the context and the goals of strategic and tactical transit planning. We then establish a terminology proposal in order to name sub-problems and thereby structure the review. Then, we propose a classification of 69 approaches dealing with the design, frequencies setting, timetabling of transit lines and their combinations. We provide a descriptive analysis of each work so as to highlight their main characteristics in the frame of a two-fold classification referencing both the problem tackled and the solution method used. Finally, we expose recent context evolutions and identify some trends for future research. This paper aims to contribute to unification of the field and constitutes a useful complement to the few existing reviews.

This work deals with an original problem with regard to the traditionally sequential planning process in public transit networks. This problem aims at modifying the network's timetables without rendering the vehicle and driver schedules obsolete. The objective is to improve the quality of service for passengers through number and quality of transfers. This approach goes in the opposite direction compared to the usual ap- proach which schedules resources once timetables are set. We propose a model and a solution method based on tabu search and a neighborhood specifically developed. Experiments are led on five instances related to a real transit network. Important gains are obtained on the considered case study, allowing for better mobility of users inside the network and on the intermodal level.

This work focuses on improving transit-service reliability by optimally reducing the transfer time required in the operations of transit networks. Service reliability of public-transit operations is receiving increased attention as agencies are faced with immediate problems of proving credible service while attempting to reduce operating cost. Unreliable service has also been cited as the major deterrent to existing and potential passengers. Due to the fact that most of the public transit attributes are stochastic: travel time, dwell time, demand, etc., the passenger is likely to experience unplanned waiting times and ride times. One of the main components of service reliability is the use of transfers. Transfers have the advantages of reducing operational costs and introducing more flexible and efficient route planning. However its main drawback is the inconvenience of traveling multi-legged trips. This work introduces synchronized (timed) time-tables to diminish the waiting time caused by transfers. Their use, however, suffers from uncertainty about the simultaneous arrival of two (or more) vehicles at an existing stop. In order to alleviate the uncertainty of simultaneous arrivals, operational tactics such as hold, skip stop and short-turn can be deployed considering the positive and negative effects, of each tactic, on the total travel time. A dynamic programming model was developed for minimizing the total travel time resulting with a set of preferred tactics to be deployed. This work describes the optimization model using simulation for validation of the results attained. The results confirm the benefits of the model with 10% reduction of total travel time and more than 200% increase of direct transfers (transfers in which both vehicles arrive simultaneously to the transfer point).

(cont.) showed that the benefits accrued from coordinating schedules on Route 53 were not significant mainly due to the headway compatibility requirement which reduces the number of transfers amenable for improvement. Greater benefits were encountered when the schedules on the connecting routes were allowed to change as well. For Route 63, schedule coordination is not worth attempting due to the combination of the short six-minute headway on that route and the high variability in vehicle arrival times. On the control side, the practice currently adopted at CTA is to hold a "ready" vehicle at a transfer stop if the connecting vehicle has already arrived and this is likely to be an effective as well as easy-to-implement control policy.

Transfers in public transport, especially in bus operations, are used to create a more efficient network by the reduction of operational costs and the allowance of more flexible route planning. However, because of the stochastic nature of traffic, scheduled transfers do not always occur; this situation increases the total passenger travel time and reduces the attractiveness of the public transport service. The use of selected operational tactics in public transport networks for increasing the actual occurrence of scheduled transfers was analyzed. A model was developed to determine the impact that instructing vehicles to either hold at or skip certain stops had on total passenger travel time and the number of simultaneous transfers. The model consisted of two components. First, a simulation of a public transport network examined the two tactics for maximizing the number of transfers. Second, an ILOG optimization model was used for optimal determination of the combination of the two tactics to achieve the maximum number of simultaneous transfers. A bus network was created as a case study, in Auckland, New Zealand, to verify the impact of the model's application. Results showed that applying online operational tactics dramatically improved the frequency of simultaneous transfers by more than 100%. The concept has great potential for increasing the efficiency and attractiveness of public transport networks that involve scheduled transfers.

Dynamic vehicle dispatching at the transfer station can improve the transit service quality by optimizing the transfer coordination of routes. In this paper, a dynamic vehicle dispatching model is proposed that aims to minimize the total waiting time of passengers at the transfer station and the downstream stops. A prediction model based on support vector machines (SVM) is also developed to forecast the arrival time of the next vehicles at the transfer station. To reduce the disconnected cases between the transfer routes, an SVM-based model is introduced to forecast the elastic time for the estimated arrival time at the transfer station. According to the estimated arrival time and elastic time, vehicles are dispatched in a dynamic way to reduce the total waiting time of passengers. The dynamic vehicle dispatching approach at the transfer station is examined with the data of three transfer routes in the city of Dalian, China. Results show that the approach proposed in this paper can reduce the total waiting time of passengers at the transfer station and the downstream stops. DOI: 10.1061/(ASCE)TE.19435436.0000311. (C) 2012 American Society of Civil Engineers.

Passengers using public transport systems often experience waiting times when transferring between two scheduled services. In this paper we propose a planning approach that seeks to obtain a favourable trade-off between the two contrasting objectives passenger service and operating cost by modifying the timetable. The planning approach is referred to as the simultaneous vehicle scheduling and passenger service problem (SVSPSP). The SVSPSP is modelled as an integer programming problem and solved using a large neighborhood search metaheuristic. The proposed framework is tested on data inspired by the express-bus network in the Greater Copenhagen area. The results are encouraging and indicate a potential decrease of passenger transfer waiting times in the network of up to 20% with the vehicle scheduling costs remaining mostly unaffected

Transfer time is one of the most important service quality indicators for evaluating intermodal transit systems. In the advent of advanced public transportation systems, vehicle arrival times and transfer demand can be obtained in real time. Thus, the decision of dispatching vehicles at transfer stations can be optimized to reduce the transfer cost. A time-varying total-cost function, including connection delay and missed-connection costs incurred by transfer passengers and vehicle holding cost, is formulated as a function of holding times for vehicles that are ready to be dispatched at transfer stations. A procedure is developed to dynamically optimize the dispatching time for each ready vehicle by minimizing the time-varying objective function. A transit network consisting of four routes connecting at a transfer terminal is designed in this study to demonstrate the application of the dispatching model. The proposed method can be used to advance transit vehicle dispatching strategies and reduce the transfer time.

The static and dynamic transfer optimization problems are formulated and solved for various objective functions. In the static case these functions are related to different moments of the transfer waiting time (i.e. mean value, second-order moment, variance and probability of not exceeding some fixed threshold waiting time value). The analytical solutions with shifted truncated exponential randomness representation of the vehicles’ travel times, are presented and compared on an illustrative example for two cases: no holding and punctuality holding control realized at transfer point. This is followed by the formulation and solution of the problem of synchronizing different lines which partly use common route segments. In the dynamical case a measure of off-schedule deviations is used as the objective function and an optimal transfer synchronization problem is numerically illustrated by a real example. Finally, practically important conclusions and implementation possibilities are suggested.

Multi-objective decision-making is often used in line-cell conversion problem. It is the key issue of developing line-cell conversion successfully. In this article, a multi-objective optimisation model is proposed to investigate two line-cell conversion performances: the total throughput time and the total labour hours. It is proved that the model is a non-deterministic polynomial NP-hard problem and its Pareto-optimal front is non-convex. Owing to the properties of cell formation and cell loading in line-cell conversions, an approach of combining local search into non-dominated sorting genetic algorithm II is proposed to obtain better non-dominated solutions. Several numerical simulation experiments are performed to show the utility and performance of our approach.

This paper studies the scheduling problem in transit networks in order to decrease transfer waiting time. Transfer waiting time is calculated based on headway and departure time of intersecting routes and is divided into two parts. The first part can be reduced by changing departure times and was studied by the authors previously. The focus of the present research, however, is to minimize the second part of the transfer waiting time, dependent on the headways. The proposed optimization model in this paper includes both parts and is a nonlinear mathematical programming model. The model is decomposed to the departure time setting model (DSM) and the headway setting model (HSM). A solution method based on a genetic algorithm is also suggested to solve the model for large transit networks. Results of a case study show good performance of the model and the solution algorithm.

The line-cell (or line-seru) conversion is an innovation of assembly system applied widely in the electronics industry. Its essence is tearing out an assembly line and adopting a mini-assembly unit, called seru (or Japanese style assembly cell). In this paper, we develop a multi-objective optimization model to investigate two line-cell conversion performances: the total throughput time (TTPT) and the total labor hours (TLH). We analyze the bi-objective model to find out its mathematical characteristics such as solution space, combinatorial complexity and non-convex properties, and others. Owing to the difficulties of the model, a non-dominated sorting genetic algorithm that can solve large size problems in a reasonable time is developed. To verify the reliability of the algorithm, solutions are compared with those obtained from the enumeration method. We find that the proposed genetic algorithm is useful and can get reliable solutions in most cases.

The time control point strategy is often adopted by bus operators in China and Singapore to provide more reliable transit service. It is thus important to design a schedule, in which bus drivers should devote their efforts to catch up a scheduled arrival time at a predetermined time control point on a bus route because passengers can definitely benefit from a reliable bus route schedule. This paper first proposes a novel reliable bus route schedule design problem by taking into account the bus travel time uncertainty and the bus drivers’ schedule recovery efforts. It proceeds to develop a robust optimization model for the proposed problem, which aims to minimize the sum of the expected value of the random schedule deviation and its variability multiplied by a weighting value. A Monte Carlo simulation based solution method is subsequently designed to solve the robust optimization model. Finally, a numerical example based on a real bus route in Suzhou city of China is carried out to demonstrate the strength of the robust optimization model. We find that the optimal scheduled travel time (or slack time) depends on bus drivers’ schedule recovery behavior and on decision makers’ scheduling philosophies.

This paper describes a procedure for solving the bus network design problem and its application in a large urban area (the city of Rome), characterized by: (a) a complex road network topology; (b) a multimodal public transport system (rapid rail transit system, buses and tramways lines); (c) a many-to-many transit demand. The solving procedure consists of a set of heuristics, which includes a first routine for the route generation based on the flow concentration process and a parallel genetic algorithm for finding a sub-optimal set of routes with the associated frequencies. The final goal of the research is to develop an operative tool to support the mobility agency of Rome for the bus network design phase.

Timetable generation is a subproblem of bus network strategic planning, in which the departure time of each trip is determined. We study the bus network of Monterrey, Mexico, which is similar to those of other cities in Latin America. It is a large bus network where passenger transfers must be favored, almost evenly spaced departures are sought, and bus bunching of different lines must be avoided. We formulate the timetabling problem of this network with the objective of maximizing the number of synchronizations to facilitate passenger transfers and avoid bus bunching along the network. We define these synchronizations as the arrivals of two trips with a separation time within a time window to make a flexible formulation. This flexibility is a critical aspect for the bus network, since travel times vary because of reasons such as driver speed, traffic congestion, and accidents. By proving that our problem is NP-hard we answer a 10-year-old open question about the NP-hardness of similar problems present in literature. Next, we analyze the structural properties of the feasible solution space of our model. This analysis leads to a preprocessing stage that eliminates numerous decision variables and constraints. Moreover, this preprocessing defines feasible synchronization and arrival time windows that are used in a new metaheuristic algorithm. Empirical experimentation shows that our proposed algorithm obtains high-quality solutions for real-size instances in less than one minute.

This work defines Transit Schedule Design (TSD) as an optimization problem to construct the transit schedule with the decision variables of the location of timing points and the amount of slack time associated with each timing point. Two heuristic procedures, Ant Colony and Genetic Algorithms, are developed for constructing optimal schedules for a fixed bus route. The paper presents a comparison of the fundamental features of the two algorithms. They are then calibrated based on data generated from micro-simulation of a bus route in Melbourne, Australia, to give rise to (near) optimal schedule designs. The algorithms are compared in terms of their accuracy and efficiency in providing the minimum cost solution. Although both procedures prove the ability to find the optimal solution, the Ant Colony procedure demonstrates a higher efficiency by evaluating less schedule designs to arrive at a ‘good’ solution. Potential benefits of the developed algorithms in bus route planning are also discussed.

This chapter reviews a survey on the operations research literature applied to the domain of public transit, with a focus on recent contributions. It highlights a fruitful cooperation between the public transit agencies and the operations research community. Indeed, public transit has provided interesting and challenging problems to operations research, while operations research has been successful at solving efficiently several important public transit problems—for example, network design, timetabling, vehicle scheduling, and crew scheduling. New problems—the integration of vehicle and crew scheduling, bus parking and dispatching, as well as a wide variety of real-time control problems—that presents new challenges to the operations research community have also been studied recently. Research on these problems has already suggested innovative models and solution methodologies, which might be applicable in practice in a near future. The main goal of most transit agencies is to offer to the population a service of good quality that allows passengers to travel easily at a low fare. The agencies, thus, have a social mission that aims at reducing pollution and traffic congestion as well as increasing the mobility of the population.

Transfer optimization attempts to minimize the overall inconvenience to passengers who must transfer between lines in a transit network. Bus trips are scheduled to depart from their terminal so as to minimize some objective function measuring that inconvenience. In this paper, the transit network is assumed to be given, and the scheduled headway is treated as fixed on each line. We denote by t(i) the departure time of the first bus on line i. {t(i)} are termed "offset times," and constitute the decision variables of our model. To take into account stochastic travel times of buses, our treatment of transfer optimization employs a simulation procedure in combination with an optimization model That model turns out to be a relaxation of the Quadratic Assignment Problem. It can incorporate a wide range of objective functions (measures of overall passenger disutility) and a variety of policies for holding buses at a transfer point. In the case where buses are not held at all, we show, for a number of different objective functions and transit networks, the negative consequences of optimizing transfers with a deterministic bus-travel-times assumption, if these travel times are in fact random variables. Suggestions are then made for future research.

The timed transfer concept, which seeks to schedule vehicles from various routes to arrive at some transfer stations simultaneously (or nearly so), can significantly improve service quality in transit networks. It has been implemented in some cities but with insufficient efforts to optimize coordination among connecting routes. Our problem is to optimize the headways and slack times jointly for timed transfers to minimize the total costs of operating a multiple-hub transit network. In this paper, a heuristic algorithm is used to optimize the headways and slack times for all coordinated routes. Here, headways are integer multiples of a base cycle to ensure that vehicles on different routes can operate in phase and arrive nearly simultaneously at transfer stations. The results show that as demand decreases, optimized headways increase and the net benefits of coordinated operation also increase. For routes with significantly different demand or route length, coordination with integer-ratio headways is preferable to a single common headway. The sensitivity of the transit service characteristics to various demand and cost parameters is discussed. The results also show that the optimized slack times for routes vary with such variables as headways, vehicle arrival-time variance, transfer volumes, and passenger time values. For routes with high standard deviations of arrivals, it is not worth attempting schedule coordination. Journal of Urban Planning and Development

Scheduling of urban transit network can be formulated as an optimization problem of minimizing the overall transfer time (TT) of transferring passengers and initial waiting time (IWT) of the passengers waiting to board a bus/train at their point of origin. In this paper, a mathematical programming (MP) formulation of the scheduling problem at one transfer station is presented. The MP problem is large and nonlinear in terms of the decision variables, thereby making it difficult to classical programming techniques to solve the problem. The authors apply genetic algorithms (GAs)--search and optimization methods based on natural genetics and selection--to solve the scheduling problem. The main advantage of using GAs is that the problem can be reformulated in a manner that is computationally more efficient than the original problem. Further, the coding aspect of GAs inherently takes care of most of the constraints associated with the scheduling problem. Results from a number of test problems demonstrate that the GAs are able to find optimal schedules with a reasonable computational resource. The paper concludes by presenting a number of extensions to the present problem and discusses plausible solution techniques using GAs. The success of GAs in this paper suggests their efficacy as a solution tool for similar optimization problems arising in transportation systems.

Optimal fleet size distribution and scheduling with transfer consideration for a transit system is a difficult optimization problem. A traditional formulation of the problem leads to a large non‐linear mixed integer programming problem. Past experience has shown that traditional optimization methods are unable to give optimal solutions to even simpler versions of the problem (like the optimal scheduling problem with known fleet size distribution). In this paper, a simple binary coded genetic algorithm (GA) based approach to the optimization problem is presented. The use of GA allows a more efficient formulation of the problem and the GA based approach gives optimal/near‐optimal results with limited computation effort.

This paper presents a systemwide approach based on a genetic algorithm for the optimization of bus transit system transfer times. The algorithm attempts to find the best feasible solution for the transfer time optimization problem by shifting existing timetables. It makes use of existing scheduled timetables and ridership data at all transfer locations and takes into consideration the randomness of bus arrivals. The complexity of the problem is mainly due to the use of a large set of binary and discrete variables. The combinatorial nature of the problem results in a significant computational burden, and thus it is difficult to solve with classical methods. Scheduling data from Broward County Transit, Florida, were used to calculate total transfer times for the existing and proposed systems. Results showed that the algorithm produced significant transfer time savings.

Integrated timed-transfer (ITT) systems are starting up in Switzerland, Austria, and many regions of Germany. They distinguish themselves from regular timed-transfer systems, in which vehicles arrive at and depart from a station at approximately the same time to minimize waiting time-for passengers, by intergrating the timed-transfer systems of individual metropolitan areas into one complete public transportation system for a region. Very little has been written about ITT in the English language literature, and the purpose here is to close the information gap. The advantages and disadvantages of an ITT system are illustrated by discussing a concrete example. Technical and economic aspects of ITT are discussed. Terms such as "symmetry time" and "optimal minimum headway" are defined. Early results of ITT systems in demonstrated with the example of the San Jose-Oakland-Sacramento corridor. The public transporation system in this area is currently disjointed, and the introduction of ITT would increase the usability of Public transit.

Suburban trains and public buses can play,a better,role in public transportation if they are coordinated. Coordination of these two services will reduce the journeys made by intermediate public transport services and private vehicles from railway stations, which have become major traffic generators. Thus, congestion, delays, and environmental pollution due to these services can be reduced to a great extent. In this study, the Andheri and Vileparle suburban railway stations in Mumbai, India are taken as study locations, and schedule coordination between suburban trains and public buses [Bombay Electric and Suburban Transport (BEST) buses] at these suburban railway stations is attempted. The coordinated schedules of BEST buses have been determined on already developed feeder routes for these two stations using the schedule optimization model (SOM). The objective function of the SOM is the minimization of transfer time between two services and vehicle operating costs of BEST buses. The objective function and constraints make the problem nonlinear and nonconvex with a large number of variables, making it difficult to solve by classical approaches. Therefore, the genetic algorithm, a robust optimization technique, is used for optimization. So far there have been few studies pertaining to the integration of public transport modes, and these studies were limited to analytical modeling. Analytical models do not meet real-life objectives under realistic constraints. In the absence of studies related to realistic modeling, it can be claimed that this study is a specific contribution toward operational integration of public transport modes.

Genetic algorithms have become increasingly popular as a means of solving hard combinatorial optimization problems of the type familiar in operations research. This feature article will consider what genetic algorithms have achieved in this area, discuss some of the factors that influence their success or failure, and offer a guide for operations researchers who want to get the best out of them.

In complex networks schedule synchronization has a major importance when constructing timetables. Restrictions in this field are based on the structure and the complexity of the existing network, different headways, and the origin-destination pairs of the demand structure. With respect to service quality one main objective coming to mind consists of minimizing the sum of all waiting times of all passengers at transfer nodes in a transit system. Furthermore, modifications of such an objective function incorporating the maximum waiting time may have to be observed as well as interrelationships between service level and operating cost.
Due to the problems’ complexity a number of heuristic solution procedures has been developed for schedule synchronization. In a moderate number of case studies for some public transport networks of German cities we applied a regret heuristic together with some improvement strategies, i.e., simulated annealing and tabu search. Within the latter strategy modifications of a dynamic tabu list management including a look ahead method have been tested. Numerical results are reported and the obtained timetables based on our heuristic approach clearly underline its advantage over previously applied planning tools.

In urban areas where transit demand is widely spread, passengers may be served by an intermodal transit system, consisting of a rail transit line (or a bus rapid transit route) and a number of feeder routes connecting at different transfer stations. In such a system, passengers may need one or more transfers to complete their journey. Therefore, scheduling vehicles operating in the system with special attention to reduce transfer time can contribute significantly to service quality improvements. Schedule synchronization may significantly reduce transfer delays at transfer stations where various routes interconnect. Since vehicle arrivals are stochastic, slack time allowances in vehicle schedules may be desirable to reduce the probability of missed connections. An objective total cost function, including supplier and user costs, is formulated for optimizing the coordination of a general intermodal transit network. A four-stage procedure is developed for determining the optimal coordination status among routes at every transfer station. Considering stochastic feeder vehicle arrivals at transfer stations, the slack times of coordinated routes are optimized, by balancing the savings from transfer delays and additional cost from slack delays and operating costs. The model thus developed is used to optimize the coordination of an intermodal transit network, while the impact of a range of factors on coordination (e.g., demand, standard deviation of vehicle arrival times, etc) is examined.

This paper describes a simulation model of schedule design for a fixed transit route adopting the holding control strategy. The model is capable of determining the locations of time points and the amount of slack time allocated to each time point by minimizing the total cost associated with the schedule. The optimization is carried out through a process, which combines a heuristic search, enumeration, and population ranking and selection techniques. Examples showing applications and potential savings of the proposed model are given. It is shown that the model can serve as a practical tool for designing reliable, economical as well as operational transit schedules.