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A stochastic model for bus injection in an unscheduled public transport service
Abstract
Randomness affecting the operation of public transport systems generates significant increments in waiting times. A strategy to deal with this randomness is bus injection, in which buses are kept in specific points along the route ready to be dispatched when an event such as an extremely long headway occurs. In this work, a stochastic model based on the second moment of the headways distribution is developed to determine if one or more buses are worth reserving for injection in a public transport service. A single stop approach is initially used to determine an expression for the optimal headway threshold triggering the injection. Then, a model for the complete service is developed and used to determine when the empty bus should be injected within the headway once the decision to inject it has been taken. We show that the bus should be injected approximately when 57% of the headway has passed. Simulations with real data are used to test the proposed model, proving its accuracy in terms of measuring the impact on waiting times. The results show that reserving a bus to be injected can be better than operating the entire fleet continuously.
... While early research has predominantly focused on rail transit, recent studies have begun to explore demandresponsive public bus transit, leveraging data analytics to optimize scheduling and minimize passenger wait times [15,16,17,18,19,20,21,22]. The integration of General Transit Feed Specification (GTFS), Automatic Vehicle Location (AVL), and Automatic Passenger Counter (APC) technologies facilitates data collection for analysis in these advanced systems [23,24,25,26,27]. However, these technologies are only available in a fraction of public transportation systems and are often not utilized in real-time to adjust demand and supply dynamically. ...
... However, these technologies are only available in a fraction of public transportation systems and are often not utilized in real-time to adjust demand and supply dynamically. Consequently, static scheduling and load balancing remain prevalent, offering limited insight into realtime transit demand distribution [23,25]. ...
Access to adequate public transportation plays a critical role in inequity and socio-economic mobility, particularly in low-income communities. Low-income workers who rely heavily on public transportation face a spatial disparity between home and work, which leads to higher unemployment, longer job searches, and longer commute times. The overarching goal of this study is to get initial data that would result in creating a connected, coordinated, demand-responsive, and efficient public bus system that minimizes transit gaps for low-income, transit-dependent communities. To create equitable metropolitan public transportation, this paper evaluates existing CATS mobile applications that assist passengers in finding bus routes and arrival times. Our community survey methodology includes filling out questionnaires on Charlotte's current bus system on specific bus lines and determining user acceptance for a future novel smart technology. We have also collected data on the demand and transit gap for a real-world pilot study, Sprinter bus line, Bus line 7, Bus line 9, and Bus lines 97-99. These lines connect all of Charlotte City's main areas and are the most important bus lines in the system. On the studied routes, the primary survey results indicate that the current bus system has many flaws, the major one being the lack of proper timing to meet the needs of passengers. The most common problems are long commutes and long waiting times at stations. Moreover, the existing application provides inaccurate information, and on average, 80 percent of travelers and respondents are inclined to use new technology.
... A few early studies have examined demand-responsive public bus transit that uses data analytics to optimize scheduling and minimize passenger wait times ("A Multi-Agent Reinforcement Learning Approach for Bus Holding Control Strategies" n.d.; Moosavi, Ismail, and Yuen 2020;Chen et al. 2012;Yu, Yao, and Yang 2010;Sun et al. 2019;Koh et al. 2018;Gkiotsalitis and Kumar 2018;Nannapaneni and Dubey 2019;Morales, Muñoz, and Gazmuri 2020). A study by (Koh et al. 2018) examined Mobility-on-demand ride-sharing services in a densely populated area of Singapore. ...
Poor access to public transportation is a major contributor to inequity and socioeconomic mobility in lowincome communities. In low-income workers who rely heavily on public transportation, spatial disparities between home
and work result in higher unemployment, longer job search times, and longer commute times. This paper addresses
an extremely important long-term challenge to the accessibility of public transportation, particularly public bus transit,
for the underserved and low-income communities in West Charlotte. The ultimate goal is to create a demand-responsive
public transit system to efficiently meet dynamically changing daily transit demands and address ways of using existing
equipment to provide real-time information about passenger loads at bus stations, bus locations, and arrival times. This
paper aims to gather preliminary data that will enable us to develop an efficient, connected, coordinated, and demandresponsive public bus system that minimizes transit gaps in low-income, transit-dependent communities. As part of the
effort, this paper evaluates the current CATS mobile applications in order to help passengers find bus routes and times.
Our community survey methodology includes a questionnaire about the current bus system of the city of Charlotte with
regard to a specific bus line and finding out potential user acceptance for future new smart technology. Using real-world
transportation data, the Sprinter bus line connecting Charlotte's downtown with the Charlotte Douglas International
Airport is selected for a pilot study. According to the primary survey results, the current bus system along the studied
route has many flaws, the most important being the lack of timely service. It has been identified that long waiting times
at stations and long commutes are the most common problems. In addition, the existing mobile application doesn't
provide accurate information, and 90 percent of those surveyed are inclined to use new technology and mobile
applications.
... 23 A more recent procedure was proposed 12 for estimating the N-order polynomial approximation of a PDF based on statistical moments. The method has been used for various applications such as fast adaptive filtering, 24 bus injection for public transport, 25 modeling solar irradiance 26 and formulating a reduced order model to characterize nonequilibrium population distribution of molecules in a gas mixture. 27 The main characteristic of the procedure 12 is that it uses a standard monomial form, such as a power series, to approximate the distribution. ...
BACKGROUND
Determination of a probability density function (PDF) is an area of active research in engineering sciences as it can improve process systems. A previously developed polynomial method‐of‐moments‐based PDF estimation model has been applied in the research to produce accurate approximations to both standard and more complex PDF. A model with a different polynomial basis than a monomial is still to be developed and evaluated. This is the work that is undertaken in this study.
RESULTS
A set of standard PDF (Normal, Weibull, Log Normal and Bimodal) and more complex distributions (solutions to the Smoluchowski coagulation equation and Population Balance equation) were approximated by the method‐of‐moments using Chebyshev, Hermite and Lagrange polynomial‐based density functions. Results show that Lagrange polynomial‐based models improve the fit compared to monomial based‐modeling in terms of RMSE and Kolmogorov–Smirnov test statistic estimates. The Kolmogorov–Smirnov test‐statistics decreased by 19% and the RMSE values were improved by around 85% compared to the standard monomial basis when using Lagrange polynomial basis.
CONCLUSION
This study indicates that the procedure using Lagrange polynomials with method‐of‐moments is a more reliable reconstruction procedure that calculates the approximate distribution using lesser number of moments, which is desirable. © 2024 The Authors. Journal of Chemical Technology and Biotechnology published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry (SCI).
... A more recent procedure was proposed by Munkhammar et al. 5 for estimating the -order polynomial approximation of a PDF based on statistical moments. The method has been used for various applications such as fast adaptive filtering 18 , bus injection for public transport 19 , modeling solar irradiance 20 and formulating a reduced order model to characterize non-equilibrium population distribution of molecules in a gas mixture 21 . The main characteristic of the procedure 5 is that it uses a standard monomial form, such as a power series, to approximate the distribution. ...
Moment-based determination of a probability density function (PDF) is widely used in chemical and process engineering applications as they provide an efficient approach to analyze and solve complex systems. In this study, three different approaches are implemented for estimating probability distributions from their moments. These procedures are based on the reconstruction of a distribution knowing only a limited number of moments using Chebyshev polynomials, Hermite polynomials and Lagrange polynomials. To show the applicability of these approaches, various test cases with reduced set of moments are solved with a set of standard distribution families (Normal, Weibull, Log Normal and Bimodal) and with complex distributions (Smoluchowski coagulation equation and population balance equation). The results are compared with their analytical solutions using both small and big variance distributions. The Kolmogorov-Smirnov (K-S) matrix and the RMSE values of the interpolation procedure using Lagrange polynomials predict a better estimation for all the test cases compared to the other approaches including the standard monomial approach (with higher number of moments) implemented in this study. The K-S test values decreased by 19% compared to the standard monomial procedure and 11% compared to both Chebyshev and Hermite polynomial approaches. Similarly, the RMSE values improved by 85% compared to the standard monomial procedure and 62% compared to both Chebyshev and Hermite polynomial approaches. This indicates that the procedure using Lagrange polynomials is a more reliable reconstruction procedure that calculates the approximate distribution using lesser number of moments N which is desirable.
... The algorithm generates work shifts for Integra SA's drivers. Morales et al [24] developed a stochastic model to examine the impact of introducing a bus at a single station on waiting times. ...
The amount of time users have to wait influences their mode of transportation choice. Commuters don't like to wait in the bus station, especially when the weather is terrible and for the purpose of keeping appointments. Scheduling buses to the various bus terminals will meet the commuter's needs. The aim of the study is to reduce the waiting time of commuters at bus station and to assign buses to each route. A mathematical model called linear programming (LP) was developed to schedule buses to improve the smooth process of the Bus Rapid Transit (BRT) system. The linear programming model was applied to the Lagos Metropolitan Area Transport Authority (LAMATA) data in Lagos State. The proposed method generated three (3) shifts from 6-11am in the morning, 11-4pm in the midday and 4-9pm in the evening subject to two (2) shifts of fifteen (15) hours to reduce the number of hours buses operate per day and also allocated buses for each route for weekdays with five (5) hours per each shift instead of seven (7) hours buses operated per shift. A properly implemented strategy would significantly decrease passengers' long waits at bus stops, reduce the breakdown of buses, man-hours lost, and allows commuters to meet their various schedule for works, meetings, and other assignments.
... holding, stop-skipping and dead heading (Ibarra-Rojas et al. (2015)). Several new methods have been proposed in recent years, e.g., bus substitution (Petit et al. (2018) and Petit et al. (2019)) and bus injection (Morales et al. (2020)). Among these control methods, holding is the most commonly and widely used. ...
In this paper, we focus on controlling multiline buses operated in networks with curbside bus stops. In such networks, both bus bunching and bus queueing, which often result in passenger inconvenience as well as bus waiting delays, are frequently observed during bus operations. To address the adverse influences of these two phenomena, we propose a mixed integer programming (MIP) model to provide guidance on real-time bus cruising speeds based on the real-time state of the whole system. The proposed model can avoid bus bunching by coordinating bus cruising speeds and alleviate bus queueing congestion by restricting the number of bus arrivals at each stop. Specifically, to address bus bunching, the model has a quadratic objective function that minimizes the total expected passenger waiting time; while for bus queueing, the model has big-M and time-indexed constraints that restrict the number of bus arrivals in each time interval of length g based on the waiting capacity Q s of each stop s. Simulation experiments are conducted with different sizes of virtual networks, and the corresponding results show that the proposed model can lead to both a shorter average passenger waiting time and less bus congestion at stops. The improvement with respect to bus waiting delay is more significant: the percentage decrease can reach 46.9%. Moreover, the results of the average computing time show that the control model can be solved before a bus finishes service in most cases, which means decisions can be fed back to drivers in a timely manner; therefore, the proposed model can meet the requirements of real-time control. A sensitivity analysis with respect to parameters Q s and g is also performed. These two parameters are shown to only affect control performance with respect to bus waiting delays at stops, and shorter bus waiting delays can be achieved with relatively small Q s and large g. Further experiments are conducted within a real network, and the experimental results show that our method is suitable for implementation in practice.
... Li et al. [36] took the bus travel time as a fuzzy variable, constructed a bi-objective optimization model to minimize the total vehicle travel time and the total passenger waiting time in the bus network, and designed a genetic algorithm with variable chromosome length to solve the model. To cope with the impact of randomness, Morales et al. [37] proposed a bus injection bus operation strategy, namely the bus scheduling strategy for the situation of extremely long headway. e authors established a random model based on the second moment of interval distribution to determine whether the bus is worth injecting and developed a complete service model to determine when the bus should be injected. ...
The design of the timetable is essential to improve the service quality of the public transport system. A lot of random factors in the actual operation environment will affect the implementation of the synchronous timetable, and adjusting timetables to improve synchronization will break the order of normal service and increase the cost of operation. A multi-objective bus timetable optimization problem is characterized by considering the randomness of vehicle travel time and passenger transfer demand. A multi-objective optimization model is proposed, aiming at minimizing the total waiting time of passengers in the whole bus network and the inconsistency between the timetable after synchronous optimization and the original timetable. Through large sample analysis, it is found that the random variables in the model obey normal distribution, so the stochastic programming problem is transformed into the traditional deterministic programming problem by the chance-constrained programming method. A model solving method based on the augmented epsilon-constraint algorithm is designed. Examples show that when the random variables are considered, the proposed algorithm can obtain multiple high-quality Pareto optimal solutions in a short time, which can provide more practical benefits for decisionmakers. Ignoring the random influence will reduce the effectiveness of the schedule optimization scheme. Finally, sensitivity analysis of random variables and constraint confidence in the model is made.
... Wu et al. [6] studied the coordination of multiple bus schedules within transfer stations. Morales et al. [7] established an injection stochastic model based on the second moment of headway distribution to determine when a bus should be injected within the headway. Liu et al. [8] established a dual-objective integer-programming model that considers the common interests of passengers and bus operators. ...
It is of great significance to ensure public transportation management capabilities by improving urban public transport services. One method is to solve the problems related to the quality of data submitted for public funding as well as the accuracy and transparency of the supervision and review processes; moreover, improving public-transportation-service systems is a viable method to solve such problems. With technological advancements and the application of new technologies such as automatic driving and multiple payment, it has gradually become difficult for user-data verification systems, based on the original single bus payment method, to cater to these new technologies. Diversified payment and complex management methods have highlighted the need for new verification methods. Firstly, in this paper, we constructed the Origin–Destination (OD) model of bus-passenger flows by using real-time transmission of passenger-multiple-payment data, on-board-video passenger flow detection data and vehicle real-time positioning data. On this basis, the bus waybill data of other intelligent bus systems and the wait data of bus stations were integrated, so as to establish the travel chain theory by matching passenger flow and the temporal and spatial distribution model. Then, an OD analysis of public-transport passenger flows could be carried out, with a detailed analysis of vehicle, station and line-passenger flow, and the travel characteristics of public transport passenger flow could be excavated. Then, according to the means-end chain theory, the spatiotemporal distribution of the passenger flow data was obtained to carry out an OD analysis of the passenger flow, so as to perform a refinement analysis of the vehicle, station, and passenger flow. Thereby, the characteristics of the passenger flow were explored. Subsequently, payment-authenticity-verification models were established for the data-validity assessment, video-data analysis, passenger-flow estimation, and early warnings in order to determine the authenticity of the payment data. Lastly, based on the multi-sensor passenger flow data fusion and the data authenticity verification models, combined with the application of new technologies such as the use of autonomous buses, the test was promoted. That is, by taking intelligent bus scheduling as the scenario, the research method was tested and verified with real-time passenger flow data according to historical data. The results showed that the method accurately predicted the passenger flow, and had a positive role in improving the efficiency of payment-data-authenticity verification. The application of the method can enhance the management and service quality of public transportation.
... Integrated headway control considering bus corridors served by multiple lines are presented by Seman et al. (2019). Strategies regarding bus dispatching and injection have also been explored, Morales et al. (2019) presented a stochastic model to correct headway by injecting new buses, while Gkiotsalitis and van Berkum (2020) presented an exact model for bus dispatch time considering a rolling horizon. ...
The problem of operating exclusive bus corridors that have segments with bidirectional lanes is treated. On these lanes, only one direction of movement is allowed when a bus is present. Such construct requires less road space, which is a scarce resource in dense urban areas, and thus may be the only feasible alternative for the installation of exclusive bus corridors. The system model includes limits on bus passenger capacity. The control method for real-time operation integrates bus headway corrections and bus priority through signalized intersections, while enforcing mutual exclusion of opposing buses on the bidirectional lanes. Effectively, the control avoids bus bunching over the entire corridor and coordinates the passage of opposing buses on bidirectional lanes. The objective is to minimize the total waiting time of passengers, both onboard and at stops. Simulation results indicate the applicability of the integrated holding and priority bidir-ectional lane control method.
This dissertation presents a new contribution to the field of incident management in public transport (PT) systems. In addition to the results of a PT user survey concerning the perception of incidents, this work introduces a novel model to redirect passengers and reallocate capacities during incidents. The results of the case studies conducted demonstrate the great potential of this model to reduce passenger delays during incidents and thus to improve the reliability of PT systems.
The dissertation is publicly accessible via this link:
https://mediatum.ub.tum.de/?id=1707338
Several developed vehicle spaces and time headway distribution models in traffic flow theory have been widely used in the literature, reflecting the primary uncertainty in drivers’ car-following movements and explaining the traffic flow stochastic features. Moreover, effective vehicle-to-vehicle (V2V) communication is a key to decentralizing traffic information systems. Accurate vehicle headway distribution estimation will ensure reliable communication and benefit passengers’ safety and comfort. Consider several proposals for headway distribution in the literature; this paper studies the effect of space-headway distribution on information propagation delay in assessing the reliability of the V2V communication networks. We utilize the properties of reliability measurement for headway data by introducing the quasi-maximum likelihood estimator (QMLE) to measure the effects that different headway models have on estimating the parameters of headway distribution in a V2V communication network. The statistical analysis is then applied to the real Next-Generation Simulation (NGSIM) data. It validates the proposed methodology and formulations by measuring the effects of model selection on headway data and information propagation delay on the reliability of the V2V network. The results show that the effect of headway distribution when the vehicle’s transmission range is smaller than the road segmentation is not negligible, especially when cars are very distant. Based on our results, we recommend new metrics based on Kullback–Leibler divergence for model selection of headway data, thereby enhancing the reliability of the V2V network.
When bus priority control is implemented, if there is a bus station between upstream detector and downstream signalized intersection, it will lead to the unpredictability of bus dwell time caused by the stochastic number of passengers waiting at the station. This uncertainty means that the bus’s arrival time at the intersection cannot be predicted quite accurately. Therefore, the signal priority control strategy made in advance may fail, which brings about a negative impact on the operation for both buses and cars at the intersection. To solve this problem, this paper proposes a two-stage transit signal priority (TTSP) control method. The first stage is robust optimal signal control (ROC) and aims to minimize bus delay expectation and variance. Bus delay expectation and variance calculation models considering the uncertainty of bus dwell time and the uncertainty of buses in line ahead in an exclusive bus lane are proposed based on mathematical statistics theory to formulate the stochastic process of bus operation. However, extreme situations cannot be avoided by the first-stage control completely. To make up for the deficiency of ROC, this paper adds the second-level real-time priority control, which is enabled in the case of the first-stage control failure to ensure the priority of public transit. The simulation test results show that the proposed TTSP method preforms better in reducing bus delay expectation, from 9.2 s to 3.2 s, reaching 65.2%. In addition, bus delay standard deviation decreases from 8.3 s to 3.9 s by 53.1%, improving the reliability of bus operation.
Bus priority has been proposed for many years to improve traffic congestion, energy conservation, and emissions reduction. Transit signal priority is a main measure of executing bus priority. Moreover, because the time that buses arrive at an intersection should be predicted quite precisely to make a signal control scheme in advance, bus lane is an important segment in transit priority at signalized intersections to avoid disturbances from other vehicles on the road. However, in practice, the bus route of demand responsive transport is widespread, which is not inappropriate to set bus lane for each bus route because of low frequency. Therefore, in this paper, a robust optimization control method is proposed to solve the bus priority problem at signalized intersections without exclusive bus lanes and improve reliability of demand responsive transport priority at signalized intersections. First, the bus delay probability density function is formulated to describe the interaction mechanism about the bus and other vehicles at the signalized intersection. Then, the accurate bus delay expectation and variance calculation mathematical models are formulated based on the bus delay probability density function. Furthermore, a robust optimal signal control method is proposed followed by the discussions of boundary conditions. Finally, simulation test and case study were conducted to illustrate the performance of the robust optimization control method proposed in this paper. The results show that the proposed control method could significantly improve bus delay compared to considering the bus operation process as stable.
In a BRT system, for an efficient planning and management of fleets and drivers, precision of operations is required at the intervals provided. However, sometimes actions are taken that change the order of buses on the circuit, such as overtaking. Despite their impact on operations, these changes are not fully addressed by main headway control algorithms found in the literature and, when considered, they are dealt with enumerating processes to decide on the reordering of buses. To mitigate this issue, this paper presents a generalized formulation for auto-sequencing buses in headway control strategies. The proposed methodology allows the modeling of overtaking, injection, and removal of buses, without resorting to enumerating methods for bus ordering. The obtained results demonstrate that the proposed formulation can handle the events of change of order in a BRT circuit while, at the same time, controlling the headway between the buses and reducing the waiting time for passengers. Thus, the generalized auto-sequencing method is a framework that can be used to augment other control strategies already present in the literature.
In recent decades, the main focus in public transport operations has been increasing its speed. Increasing speed not only allows for faster trips, but also a higher frequency with the same fleet size, thus reducing waiting times and crowdedness inside the vehicles. This interest in speed has ignored a second key dimension in level of service: reliability. In this article, we provide a review of a full range of impacts of an unreliable public transport service. We show how regularising headway could improve level of service beyond the gains of simply increasing the operational speed. Regular headways positively affect comfort, reliability, travel and wait time, operational costs, and even some urban impacts of bus services. Thus, the focus for public transport agencies and operators should bend into reliability’s direction. This is fundamental for making public transport an attractive travel alternative, and therefore must become a core goal for urban sustainability.
We suggest a procedure for estimating Nth degree polynomial approximations to unknown (or known) probability density functions (PDFs) based on N statistical moments from each distribution. The procedure is based on the method of moments and is setup algorithmically to aid applicability and to ensure rigor in use. In order to show applicability, polynomial PDF approximations are obtained for the distribution families Normal, Log-Normal, Weibull as well as for a bimodal Weibull distribution and a data set of anonymized household electricity use. The results are compared with results for traditional PDF series expansion methods of Gram–Charlier type. It is concluded that this procedure is a comparatively simple procedure that could be used when traditional distribution families are not applicable or when polynomial expansions of probability distributions might be considered useful approximations. In particular this approach is practical for calculating convolutions of distributions, since such operations become integrals of polynomial expressions. Finally, in order to show an advanced applicability of the method, it is shown to be useful for approximating solutions to the Smoluchowski equation.
One of the greatest problems facing transit agencies that operate high-frequency routes is maintaining stable headways and avoiding bus bunching. In this work, a real-time holding mechanism is proposed to dispatch buses on a loop-shaped route using real-time information. Holds are applied at one or several control points to minimize passenger waiting time while maintaining the highest possible frequency, i.e. using no buffer time. The bus dispatching problem is formulated as a stochastic decision process. The optimality equations are derived and the optimal holding policy is found by backward induction. A control method that requires much less information and that closely approximates the optimal dispatching policy is found. A simulation assuming stochastic operating conditions and unstable headway dynamics is performed to assess the expected average waiting time of passengers at stations. The proposed control strategy is found to provide lower passenger waiting time and better resiliency than methods used in practice and recommended in the literature.
This paper presents a microscopic model for the study of operations at public transport stops, mainly bus stops and light rail transit stations, from the perspective of the traffic analysis. Firstly, a description of a public transport stop as a traffic mechanism is offered. Then the issue of stop capacity is reviewed, providing typical values of transit system capacities. The most wide-spread analytical model of stop capacity – the Highway Capacity Manual formula – and its components is discussed. Next, a microscopic simulation model as a tool for computing stop capacities and related impacts is described. Results of the calibration and validation of the model are also presented. Two applications are developed to illustrate the model capabilities. The first example deals with a light rail transit station and articulated trams; the second one consists of different classes of buses stopping at a bus stop. It can be concluded from these applications that the proposed model may provide more detailed information about stop operations than other existing approaches.
Bus headways are typically susceptible to external disturbances (e.g., due to traffic congestion, clustered passenger arrivals, and special passenger needs), which create gaps in the system that grow eventually into bunching. Although many control strategies, such as static and dynamic holding strategies, have been implemented to mitigate the effects of unreliable bus schedules, most of them would impose longer dwell times on the passengers. In this paper, we investigate the potential of an alternative bus substitution strategy that is currently implemented by some transit agencies in an ad-hoc manner. In this strategy, the agency deploys a fleet of standby buses to take over service from any early or late buses so as to contain deviations from schedule, and the intention is to impose minimum penalties on the onboard passengers. We develop a discrete-time infinite-horizon approximate dynamic programming approach to find the optimal policy to minimize the overall agency and passenger costs. It is shown through numerical examples that schedule deviations can be controlled by regularly inserting standby buses as substitutions. In some implementation scenarios, the proposed strategy holds the potential to achieve comparable performance with some of the most advanced strategies, and to outperform the conventional slack-based schedule control scheme. In light of the emerging opportunities associated with autonomous driving, the performance of the proposed strategy can become even stronger due to the reduction in costs for keeping the fleet of standby buses.
On high-frequency routes, buses tend to bunch together, creating gaps in service and causing undue passenger waiting time. There are many approaches to solving the bus bunching problem in the literature but there lacks empirical analysis on practical implementation. In this study, a real-time holding method from the literature was implemented on three high-frequency transit routes, the Atlanta Streetcar and the Georgia Tech Red Route in Atlanta, GA, and the VIA Route 100 in San Antonio, TX. The performance of the method was evaluated in terms of headway stability, holding time, and mean passenger waiting time. The method was found to improve headway stability compared to the schedule, but required longer holds in some cases. Overall, the holding method reduced the waiting time of passengers at stops in all three case studies. The challenges associated with location data quality, prediction accuracy, the human element and the surrounding environment are discussed and strategies to address them are recommended.
A highly developed and flexible simulation model of an urban bus route in peak hour traffic is described. The simulation program is presented, with particular emphasis on the facilities for interactive control of the simulation run and for presentation of overall and detailed statistics from the simulation. An independent statistical program system, based on the mathematical models underlying the simulation model, has been used to provide input parameters for the simulation. This program is applied to the analysis of a bus route in central Stockholm; in this connection the mathematical models are discussed.
The efficiency of a transport system depends on several elements, such as available technology, governmental policies, the planning process, and control strategies. Indeed, the interaction between these elements is quite complex, leading to intractable decision making problems. The planning process and real-time control strategies have been widely studied in recent years, and there are several practical implementations with promising results. In this paper, we review the literature on Transit Network Planning problems and real-time control strategies suitable to bus transport systems. Our goal is to present a comprehensive review, emphasizing recent studies as well as works not addressed in previous reviews.
Bus bunching affects transit operations by increasing passenger waiting times and its variability. This work proposes a new mathematical programming model to control vehicles operating on a transit corridor minimizing total delays. The model can handle a heterogeneous fleet of vehicles with different capacities without using binary variables, which make solution times compatible with real-time requirements. Two control policies are studied within a rolling horizon framework: (i) vehicle holding (HRT), which can be applied at any stop and (ii) holding combined with boarding limits (HBLRT), in which the number of boarding passengers at any stop can be limited in order to increase operational speed. Both strategies are evaluated in a simulation environment under different operational conditions. The results show that HBLRT and HRT outperform other benchmark control strategies in all scenarios, with savings of excess waiting time of up to 77% and very low variability in performance. HBLRT shows significant benefits in relation to HRT only under short headway operation and high passenger demand. Moreover, our results suggest implementing boarding limits only when the next arriving vehicle is nearby. Interestingly, in these cases HBLRT not only reduces an extra 6.3% the expected waiting time in comparison with HRT, but also outperforms other control schemes in terms of comfort and reliability to both passengers and operators. To passengers HBLRT provide a more balanced load factor across vehicles yielding a more comfortable experience. To operators the use of boarding limits speed up vehicles reducing the average cycle time and its variability, which is key for a smooth operation at terminals.
A real-time mathematical programming model of buses operating on a transit corridor that incorporates vehicle-capacity constraints is proposed. The objective for the model is to minimize the total times experienced by all passengers in the system, from the moment they arrive at a stop to the moment they reach their destination. Two control policies are considered: (a) vehicle holding, which is applicable at any stop, and (b) boarding limits that constrain the number of passengers entering a vehicle even when the vehicle is at less than physical capacity, to increase operating speed. The objective function is quadratic, but not convex with linear constraints. This problem is solved by using MINOS in a reasonable amount of computation time. A case study in a high-demand scenario shows that the proposed control achieves reductions in the objective function of more than 22% and 12% compared with no control and only holding strategies, respectively.
A public transport telematics system was launched in Helsinki, Finland, in 1999. The system provides several public transport telematics functions such as real-time passenger information, bus and tram priorities at traffic signals, and schedule monitoring. The impacts, socioeconomic benefits, and technical performance of the telematics applications were investigated. The methods included before-and-after field studies, an interview and survey, a simulation, and socioeconomic evaluation. The results indicate that delays at signals were reduced by more than 40%. The regularity and punctuality of the service were considerably improved. On both lines, the number of passengers increased from the level before the system was implemented. The studies indicated reductions of 1% to 5% in fuel consumption and exhaust emissions. The information systems were regarded very positively, and the systems were considered useful. In particular, the information displays on stops were considered necessary and were used often. Most effects were more substantial on the bus line than on the tramline because of the longer intervals between buses and the fact that the tramline already had signal priorities before the system was introduced. The benefit-cost ratio of the system was calculated to be 3.3. For the transport operator, the return on capital increased by 6% on the bus line and decreased by 1% on the tramline.
The problem of determining the optimal strategy (dispatch or hold) for a system of m vehicles is formulated as a dynamic programming problem. It is analyzed in detail for m equals 1 and m equals 2. For m equals 1, the optimal strategy will hold a vehicle if it returns within less than about half the mean trip time. For m equals 2, and for a small coefficient of variation of trip time C(T), the optimal strategy will control the vehicles so as to retain nearly equally spaced dispatch times,% within a range of time proportional to C//4///3(T).
In practice punctuality of transit service has been a chronic operational problem mainly due to the random environment and very high complexity of the public transport processes. This challenging problem affects both travellers (reliability of service) as well as operators (productivity and efficiency of resources utilization). The potential of new information and communication technologies and existing hardware possibilities offer great opportunities for the development of effective and flexible management and control tools for public transport. In this paper the simulation decision-support tool for dynamic optimal dispatching control purposes have been developed, with the use of the SIMULINK package with Toolboxes. The following optimal dispatching control problems have been solved: punctuality control (which compensates deviations from schedule), regularity control (which compensates deviations from regular headway) and synchronizing control with linear (LQ, dead-beat) feedback and control and system state constraints; LQG stochastic control with real-time estimation of the model parameters; and bus route zone control for synchronising passenger transfers or the operation of different lines on common segments of the route. The results presented are illustrated by 15 numerical examples.
Bus schedules cannot be easily maintained on busy lines with short headways: experience shows that buses offering this type of service usually arrive irregularly at their stops, often in bunches. Although transit agencies build slack into their schedules to alleviate this problem – if necessary holding buses at control points to stay on schedule – their attempts often fail because practical amounts of slack cannot prevent large localized disruptions from spreading system-wide. This paper systematically analyzes an adaptive control scheme to mitigate this problem. The proposed scheme dynamically determines bus holding times at a route’s control points based on real-time headway information. The method requires less slack than the conventional, schedule-based approach to produce headways within a given tolerance. This allows buses to travel faster than with the conventional approach, reducing in-vehicle passenger delay and increasing bus productivity.
Schedule-based or headway-based control schemes to reduce bus bunching are not resilient because they cannot prevent buses from losing ground to the buses they follow when disruptions increase the gaps separating them beyond a critical value. (Following buses are then overwhelmed with passengers and cannot process their work quick enough to catch up.) This critical gap problem can be avoided, however, if buses at the leading end of such gaps are given information to cooperate with the ones behind by slowing down.This paper builds on this idea. It proposes an adaptive control scheme that adjusts a bus cruising speed in real-time based on both, its front and rear spacings much as if successive bus pairs were connected by springs. The scheme is shown to yield regular headways with faster bus travel than existing control methods. Its simple and decentralized logic automatically compensates for traffic disruptions and inaccurate bus driver actions. Its hardware and data requirements are minimal.
This paper describes an analytic model that determines the optimal vehicle holding time at a control stop along a transit route. This model is based on a stochastic transit service model presented by Andersson and Scalia-Tomba (1981) and enhanced by Marguier (1985). The use of a stochastic service model allows greater realism in the analytic modeling. Making use of these results, the paper presents an analytic model that may be used to determine the optimal holding time for a vehicle at a control stop. As it is formulated, the single vehicle holding problem is a convex quadratic program in a single variable, and is easily solved using gradient or line search techniques. The analytic holding model overcomes two noted problems in the literature: it includes stochastic service attributes of vehicle running times and passenger boarding and alighting processes, and the model may be used for real-time control purposes. The use and potential benefits of the model are illustrated in a simple example. This model may be useful in developing a computerized decision support system to enhance the effectiveness of transit operational decision-making.
Brrt: adding an r for reliability. Restructuring Public Transport Through Bus Rapid Transit: An International and Interdisciplinary Perspective
- F Delgado
- J C Munoz
- R Giesen
Transit Capacity and Quality of Service Manual
- T R Board
- N A Of Sciences Engineering
Bus service design under demand diversion and dynamic roadway congestion based on aggregated network models
- M Yildirimoglu
- A Petit
- N Geroliminis
- Y Ouyang