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A BCMP Network Approach to Modeling and Controlling Autonomous Mobility-on-Demand Systems
Abstract
In this paper we present a queueing network approach to the problem of routing and rebalancing a fleet of self-driving vehicles providing on-demand mobility within a capacitated road network. We refer to such systems as autonomous mobility-on-demand systems, or AMoD. We first cast an AMoD system into a closed, multi-class BCMP queueing network model. Second, we present analysis tools that allow the characterization of performance metrics for a given routing policy, in terms, e.g., of vehicle availabilities, and first and second order moments of vehicle throughput. Third, we propose a scalable method for the synthesis of routing policies, with performance guarantees in the limit of large fleet sizes. Finally, we validate our theoretical results on a case study of New York City. Collectively, this paper provides a unifying framework for the analysis and control of AMoD systems, which subsumes earlier Jackson and network flow models, provides a quite large set of modeling options (e.g., the inclusion of road capacities and general travel time distributions), and allows the analysis of second and higher-order moments for the performance metrics.
... Locations in the network are modeled as queues, and system dynamics are described by the flow of vehicles and passengers between them [14], [15]. 1) Assumptions: First, these models represent passengers and vehicles as discrete entities. Customers are assumed to arrive according to an exogenous stochastic process (e.g., a Poisson process), reaching the origin station at a fixed rate and selecting their destination based on probabilities [16], [17]. ...
... To cast the AMoD problem within the queueing framework, specific assumptions about passenger arrivals, travel times, and passenger behavior are needed. Specifically, common assumptions include: demand following a time-invariant Poisson distribution, travel times between stations following an exponential distribution, and passengers immediately leaving the system if not matched with a vehicle [14]- [16]. Such assumptions simplify associated problems while preserving accuracy, as demonstrated in [18], where reasonable deviations were shown to have negligible impact on performance. ...
... It explicitly accounts for system randomness and ensures performance in expectation. The derived policies maintain system equilibrium, preventing queues and waiting times from growing indefinitely [14]- [16]. 3) Limitations: As discussed in Section II-A1, queueingtheoretic models rely on strong assumptions regarding passenger arrival rates and travel times. ...
Autonomous Mobility-on-Demand (AMoD) systems, powered by advances in robotics, control, and Machine Learning (ML), offer a promising paradigm for future urban transportation. AMoD offers fast and personalized travel services by leveraging centralized control of autonomous vehicle fleets to optimize operations and enhance service performance. However, the rapid growth of this field has outpaced the development of standardized practices for evaluating and reporting results, leading to significant challenges in reproducibility. As AMoD control algorithms become increasingly complex and data-driven, a lack of transparency in modeling assumptions, experimental setups, and algorithmic implementation hinders scientific progress and undermines confidence in the results. This paper presents a systematic study of reproducibility in AMoD research. We identify key components across the research pipeline, spanning system modeling, control problems, simulation design, algorithm specification, and evaluation, and analyze common sources of irreproducibility. We survey prevalent practices in the literature, highlight gaps, and propose a structured framework to assess and improve reproducibility. Specifically, concrete guidelines are offered, along with a "reproducibility checklist", to support future work in achieving replicable, comparable, and extensible results. While focused on AMoD, the principles and practices we advocate generalize to a broader class of cyber-physical systems that rely on networked autonomy and data-driven control. This work aims to lay the foundation for a more transparent and reproducible research culture in the design and deployment of intelligent mobility systems.
... Literature review: Control of AMoD systems has been addressed in multiple lines of work, including queueingtheoretical approaches [6], network flow approaches [7], [8], integer linear programming and model-predictive control approaches [9], [10], and simulation-based approaches [11], [12], [13]. However, throughout these works, AMoD systems are assumed to have no impact on the electric power network. ...
... The optimization problem in (6) can be solved with a number of variables on the order of O((|V R | + 1)|E| + M C + |V R |C). To see this, note that in Equation (5) ...
... Yet, from the mesoscopic perspective of this paper, network flow models are justifiable for three main reasons. First, on the foundational side, previous work by the authors [6] has shown that a stochastic queueing network model of an AMoD system, wherein the customer arrival process is Poisson and travel times between stations are stochastic, reduces to a (deterministic) network flow model in the (mesoscopic) limit of large fleet sizes. Notably, in such a limiting regime the network flows represent the expected values of the underlying stochastic quantities. ...
We study the interaction between a fleet of electric, self-driving vehicles servicing on-demand transportation requests (referred to as Autonomous Mobility-on-Demand, or AMoD, system) and the electric power network. We propose a model that captures the coupling between the two systems stemming from the vehicles' charging requirements and captures time-varying customer demand and power generation costs, road congestion, battery depreciation, and power transmission and distribution constraints. We then leverage the model to jointly optimize the operation of both systems. We devise an algorithmic procedure to losslessly reduce the problem size by bundling customer requests, allowing it to be efficiently solved by off-the-shelf linear programming solvers. Next, we show that the socially optimal solution to the joint problem can be enforced as a general equilibrium, and we provide a dual decomposition algorithm that allows self-interested agents to compute the market clearing prices without sharing private information. We assess the performance of the mode by studying a hypothetical AMoD system in Dallas-Fort Worth and its impact on the Texas power network. Lack of coordination between the AMoD system and the power network can cause a 4.4% increase in the price of electricity in Dallas-Fort Worth; conversely, coordination between the AMoD system and the power network could reduce electricity expenditure compared to the case where no cars are present (despite the increased demand for electricity) and yield savings of up $147M/year. Finally, we provide a receding-horizon implementation and assess its performance with agent-based simulations. Collectively, the results of this paper provide a first-of-a-kind characterization of the interaction between electric-powered AMoD systems and the power network, and shed additional light on the economic and societal value of AMoD.
... However, most existing vehicle allocation methods and charging scheduling approaches do not consider uncertainties by assuming the measurement and prediction models are perfect [1], [8], while model uncertainty affects the performance of decisions [9]. And it is difficult to accurately predict passengers' demand and EVs' charging patterns. ...
... To improve the performance of AMoD systems, multiple vehicle allocation and balancing approaches have been proposed. For instance, queuing network model [8], flow framework [13], model predictive control [1], [10], receding horizon control [14], and reinforcement learning method [15], [16] have been designed. However, most of them do not consider EV charging patterns nor uncertainties caused by EV charging behaviors. ...
... where J is the final objective defined in (13), }. We prove the following Lemma 1, there must exist a set of lower and upper bounds of the mobility supply-demand ratio in constraint (8) to guarantee that there is a feasible solution for the proposed DRO problem (12). ...
Electric vehicles (EVs) are being rapidly adopted due to their economic and societal benefits. Autonomous mobility-on-demand (AMoD) systems also embrace this trend. However, the long charging time and high recharging frequency of EVs pose challenges to efficiently managing EV AMoD systems. The complicated dynamic charging and mobility process of EV AMoD systems makes the demand and supply uncertainties significant when designing vehicle balancing algorithms. In this work, we design a data-driven distributionally robust optimization (DRO) approach to balance EVs for both the mobility service and the charging process. The optimization goal is to minimize the worst-case expected cost under both passenger mobility demand uncertainties and EV supply uncertainties. We then propose a novel distributional uncertainty sets construction algorithm that guarantees the produced parameters are contained in desired confidence regions with a given probability. To solve the proposed DRO AMoD EV balancing problem, we derive an equivalent computationally tractable convex optimization problem. Based on real-world EV data of a taxi system, we show that with our solution the average total balancing cost is reduced by 14.49%, and the average mobility fairness and charging fairness are improved by 15.78% and 34.51%, respectively, compared to solutions that do not consider uncertainties.
... However, most existing vehicle allocation methods and charging scheduling approaches do not consider uncertainties by assuming the measurement and prediction models are perfect [1], [8], while model uncertainty affects the performance of decisions [9]. And it is difficult to accurately predict passengers' demand and EVs' charging patterns. ...
... approaches have been proposed. For instance, queuing network model [8], flow framework [13], model predictive control [1], [10], receding horizon control [14], and reinforcement learning method [15], [16] have been designed. However, most of them do not consider EV charging patterns nor uncertainties caused by EV charging behaviours. ...
... We prove the following Lemma 1, there must exist a set of lower and upper bounds of the mobility supply-demand ratio in constraint (8) to guarantee that there is a feasible solution for the proposed DRO problem (12). Lemma 1. ...
Electric vehicles (EVs) are being rapidly adopted due to their economic and societal benefits. Autonomous mobility-on-demand (AMoD) systems also embrace this trend. However, the long charging time and high recharging frequency of EVs pose challenges to efficiently managing EV AMoD systems. The complicated dynamic charging and mobility process of EV AMoD systems makes the demand and supply uncertainties significant when designing vehicle balancing algorithms. In this work, we design a data-driven distributionally robust optimization (DRO) approach to balance EVs for both the mobility service and the charging process. The optimization goal is to minimize the worst-case expected cost under both passenger mobility demand uncertainties and EV supply uncertainties. We then propose a novel distributional uncertainty sets construction algorithm that guarantees the produced parameters are contained in desired confidence regions with a given probability. To solve the proposed DRO AMoD EV balancing problem, we derive an equivalent computationally tractable convex optimization problem. Based on real-world EV data of a taxi system, we show that with our solution the average total balancing cost is reduced by 14.49%, and the average mobility fairness and charging fairness are improved by 15.78% and 34.51%, respectively, compared to solutions that do not consider uncertainties.
... Queueing network is used to represent the critical performance metrics such as the availability of vehicles at stations and customer waiting time [4,[47][48][49][50]. The road network is modeled as an abstract queueing network with infinite-server road queues when the road congestion is not considered. ...
... For the queueing modeling-based research, congestion is typically considered through capacity constraints on the queues [4,47]. [4] proposes a queue network model with finite-sever within a Jackson network model. ...
... [4] proposes a queue network model with finite-sever within a Jackson network model. In [47], the MoD system is cast within the framework of closed, multi-class BCMP queuing networks. The framework captures stochastic passenger arrivals, vehicle routing on a road network, and congestion effects. ...
Challenged by urbanization and increasing travel needs, existing transportation systems call for new mobility paradigms. In this article, we present the fleet management and charging scheduling of a shared mobility-on-demand system, whereby electric vehicle fleets are operated by a centralized platform to provide customers with mobility service. We provide a comprehensive review of system operation based on the operational objectives. The fleet scheduling strategies are categorized into four types: i) order dispatching, ii) order-dispatching and rebalancing, iii) order-dispatching, rebalancing and charging, and iv) extended. Specifically, we first identify mathematical modeling techniques implemented in the transportation network, then analyze and summarize the solution approaches including mathematical programming, reinforcement learning, and hybrid methods. The advantages and disadvantages of different models and solution approaches are compared. Finally, we present research outlook in various directions.
... The aforementioned papers Banerjee et al. (2016), Zhang and Pavone (2016), Iglesias et al. (2016) all share the same feature that the optimization problems of those papers equalize availabilities across all regions. This is either enforced via an explicit constraint Iglesias et al. (2016), (Zhang and Pavone 2016, Equation 10), or arises implicitly in the optimal solution of the approximating optimization problem in Banerjee et al. (2016). ...
... The aforementioned papers Banerjee et al. (2016), Zhang and Pavone (2016), Iglesias et al. (2016) all share the same feature that the optimization problems of those papers equalize availabilities across all regions. This is either enforced via an explicit constraint Iglesias et al. (2016), (Zhang and Pavone 2016, Equation 10), or arises implicitly in the optimal solution of the approximating optimization problem in Banerjee et al. (2016). The rationale behind enforcing the equal availability constraint is that in the infinite supply regime, at least one region achieves 100% availability. ...
This paper considers a closed queueing network model of ridesharing systems such as Didi Chuxing, Lyft, and Uber. We focus on empty-car routing, a mechanism by which we control car flow in the network to optimize system-wide utility functions, e.g. the availability of empty cars when a passenger arrives. We establish both process-level and steady-state convergence of the queueing network to a fluid limit in a large market regime where demand for rides and supply of cars tend to infinity, and use this limit to study a fluid-based optimization problem. We prove that the optimal network utility obtained from the fluid-based optimization is an upper bound on the utility in the finite car system for any routing policy, both static and dynamic, under which the closed queueing network has a stationary distribution. This upper bound is achieved asymptotically under the fluid-based optimal routing policy. Simulation results with real-world data released by Didi Chuxing demonstrate the benefit of using the fluid-based optimal routing policy compared to various other policies.
... [15] proposed a predictive method for the vehicle routing and assignment for an AMoD system with ridesharing. [16] formulated AMoD systems as a closed, multi-class Baskett-Chandy-Muntz-Palacios (BCMP) queuing network model to characterize the passenger arrival process, traffic, the state-of-charge of electric vehicles, and the availability of vehicles at the stations and derive the routing and charging policies. [17] used agent-based simulations to evaluate the performance of AV-traveler assignment strategies. ...
... In the logit model, the scaling parameter µ relates to the variance (denoted as σ 2 ) of Gumbel distributed random disturbance through µ = π √ 6σ [53]. Since the randomness is multiplied by different parameters in the generalized costs of distinct income classes, i.e, (14)- (16), the value of µ may differ for distinct income classes. However, for sake of simplicity, we assume an equal scaling parameter η and µ for distinct income classes, which is consistent with existing works [40], [54]. ...
This paper assesses the equity impacts of for-hire autonomous vehicles (AVs) and investigates regulatory policies that promote spatial and social equity in future autonomous mobility ecosystems. To this end, we consider a multimodal transportation network, where a ride-hailing platform operates a fleet of AVs to offer mobility-on-demand services in competition with a public transit agency that offers transit services on a transportation network. A game-theoretic model is developed to characterize the intimate interactions between the ride-hailing platform, the transit agency, and multiclass passengers with distinct income levels. An algorithm is proposed to compute the Nash equilibrium of the game and conduct an ex-post evaluation of the performance of the obtained solution. Based on the proposed framework, we evaluate the spatial and social equity in transport accessibility using the Theil index, and find that although the proliferation of for-hire AVs in the ride-hailing network improves overall accessibility, the benefits are not fairly distributed among distinct locations or population groups, implying that the deployment of AVs will enlarge the existing spatial and social inequity gaps in the transportation network if no regulatory intervention is in place. To address this concern, we investigate two regulatory policies that can improve transport equity: (a) a minimum service-level requirement on ride-hailing services, which improves the spatial equity in the transport network; (b) a subsidy on transit services by taxing ride-hailing services, which promotes the use of public transit and improves the spatial and social equity of the transport network. We show that the minimum service-level requirement entails a trade-off: as a higher minimum service level is imposed, the spatial inequity reduces, but the social inequity will be exacerbated. On the other hand ...
... The rule-based heuristics usually lead to sub-optimal solutions [7], [8]. Optimizationbased approaches usually propose an optimization problem based on the system dynamic model [9], [10], [11]. The performance of these methods is therefore heavily affected by modeling knowledge. ...
... However, with limited EAV supply, achieving high supply-demand ratios in all regions is impossible. Keeping the supplydemand ratio of each region at a similar level allows passengers in the city to receive fair service [9], [19]. Similarly, given the limited amounts of charging stations and spots, to improve charging service quality and charging efficiency with limited infrastructure, balancing the charging utilization rate of all regions across the entire city is usually one objective for EV charging [12], [15]. ...
Electric autonomous vehicles (EAVs) are getting attention in future autonomous mobility-on-demand (AMoD) systems due to their economic and societal benefits. However, EAVs' unique charging patterns (long charging time, high charging frequency, unpredictable charging behaviors, etc.) make it challenging to accurately predict the EAVs supply in E-AMoD systems. Furthermore, the mobility demand's prediction uncertainty makes it an urgent and challenging task to design an integrated vehicle balancing solution under supply and demand uncertainties. Despite the success of reinforcement learning-based E-AMoD balancing algorithms, state uncertainties under the EV supply or mobility demand remain unexplored. In this work, we design a multi-agent reinforcement learning (MARL)-based framework for EAVs balancing in E-AMoD systems, with adversarial agents to model both the EAVs supply and mobility demand uncertainties that may undermine the vehicle balancing solutions. We then propose a robust E-AMoD Balancing MARL (REBAMA) algorithm to train a robust EAVs balancing policy to balance both the supply-demand ratio and charging utilization rate across the whole city. Experiments show that our proposed robust method performs better compared with a non-robust MARL method that does not consider state uncertainties; it improves the reward, charging utilization fairness, and supply-demand fairness by 19.28%, 28.18%, and 3.97%, respectively. Compared with a robust optimization-based method, the proposed MARL algorithm can improve the reward, charging utilization fairness, and supply-demand fairness by 8.21%, 8.29%, and 9.42%, respectively.
... The fleet management modeling problem for ride-hailing system has been investigated by two main lines of work. The first line of work addresses the fleet management problem via mathematical programming-based approaches, such as network flow [9]- [12] and queueing theoretical models [3], [13]- [15]. Duan et al. [16] introduce a utility function to optimize the order dispatch for ride-hailing systems that jointly considers both passengers' and drivers' interests. ...
... Due to the definition of cumulative distribution function and distortion function, the first term of (12) equals 0. Thus, we can rewrite it as (13). (13) Notably, (13) is the expectation of weighted distortion for cumulative reward by g(τ ). ...
With the development of mobility on-demand and transportation electrification technologies, electric vehicle (EV)-based ride-hailing fleets are playing an increasingly important role in the urban ground transportation system. Due to the stochastic nature of order request arrival and electricity price, there exists decision-making risks for ride-hailing EVs operated in order grabbing mode. It is important to investigate their risk-aware operation and model their impact on fleet charging demand and trajectory. In this paper, we propose a distributional reinforcement learning framework to model the risk-aware operation of ride-hailing EVs in order grabbing mode. First, we develop a risk quantification scheme based on the dual theory of choices under risk. Then, we combine Implicit Quantile Network, distorted quantile sampling, and distributional temporal difference learning methods to capture the intrinsic uncertainties and depict the risk-aware EV operation decisions. The proposed framework can provide a more accurate spatial-temporal portrayal of the charging demand and fleet management results. The real-world data from Haikou city is used to illustrate and verify the effectiveness of the proposed scheme.
... 3) Emerging Mobility Systems: The advent of disruptive technologies such as autonomous driving, connectivity, and power-train electrification has enabled the development of new mobility paradigms, such as autonomous mobility-on-demand (AMoD) systems, where self-driving vehicles provide ondemand transportation services [48]. Several approaches have been proposed to study and optimize the operation of AMoD systems, including agent-based simulation [49], queueingtheoretical models [50], and network flow-based models [51]. ...
This paper introduces a mobility equity metric (MEM) for evaluating fairness and accessibility in multi-modal intelligent transportation systems. The MEM simultaneously accounts for service accessibility and transportation costs across different modes of transportation and social demographics. We provide a data-driven validation of the proposed MEM to characterize the impact of various parameters in the metric across cities in the U.S. We subsequently develop a routing framework that aims to optimize MEM within a transportation network containing both public transit and private vehicles. Within this framework, a system planner provides routing suggestions to vehicles across all modes of transportation to maximize MEM. We evaluate our approach through numerical simulations, analyzing the impact of travel demands and compliance of private vehicles. This work provides insights into designing transportation systems that are not only efficient but also equitable, ensuring fair access to essential services across diverse populations.
... In this context, network ŕow models have been extensively used to capture their operation from a mesoscopic planning perspective [15]. Compared to agent-based [17,18] and queueingtheoretical counterpart [19,20], network ŕow models enjoy better computational and scalability properties, whilst still capturing the behavior of queuing models at steadystate [21,22], which is in line with our operational planning perspective. In particular, they have been used to optimize the operation of AMoD ŕeets accounting for congestion effects [23,24], also in the presence of private cars [25], and for their interaction with the power grid [26] and public transit [27,28], in ride-pooling settings [29,30] also with fully electric vehicles [31]. ...
Most applied research exploring justice in the domain of transport has focused on the equity evaluation of existing systems. At the same time, most research on transport planning has been implementing conventional utilitarian paradigms, e.g., minimizing the average travel time of the population, without accounting for fairness. This paper aims to bridge this gap and adds to this literature in two ways: by exploring to what extent the application of different justice principles can enhance the fairness of the transport system; and by focusing on realizing such principles in the operation of transport systems rather than merely assessing a given system design. We use an intermodal Autonomous Mobility-on-Demand (AMoD) system as our case study, where a fleet of centrally controlled self-driving cars provides on-demand mobility synergistically with public transit and active modes (biking and walking). We explore how its operation can improve the situation of users that do not own a car. We first formally define a set of justice metrics that differ in terms of distributive principle and the good of concern. The metrics include: minimization of average travel time for the car-less population (i.e., a population-specific application of utilitarianism); avoidance of unacceptably long travel times for the car-less population in line with a sufficientarian approach; and delivery of reasonable travel times to a sufficient set of destinations. We showcase our framework in a real-world case-study in the city of Eindhoven, the Netherlands. Our results show that, compared to conventional utilitarian minimum-travel-time planning, it is possible to significantly improve the situation of the car-less users without affecting conventional performance metrics such as average travel time. Whilst the differences between the proposed sufficientarian deployment models are rather modest, they highlight intrinsic crucial trade-offs that require further consideration and analysis. Overall, these results underscore the importance of taking a transdisciplinary approach addressing planning problems from conceptualization to modeling and optimization in transport and mobility.
... In the field of rebalancing SAVs, researchers primarily rely on queue optimization methods [5] [6] along with various other optimization techniques. For instance, [7] used a network simplex algorithm to decide the rebalancing of idle vehicles, [8] proposes a linear programming (LP) model to determine the number of vehicles rebalanced to each region, and [9] develops a Mixed Integer LP (MILP) model along with a novel clustering-based rebalancing strategy. ...
This paper presents a two-layered rebalancing model tailored for Shared Automated Electric Vehicle (SAEV) systems. The first layer aims to narrow the gap between supply and demand in different zones, while the second layer focuses on minimizing rebalancing costs. The model offers seamless integration with various dispatching models. We evaluate the model's efficacy through agent-based simulations using Yellow Taxi data from Midtown Manhattan. Results show that implementing this model can reduce customers' average waiting time by approximately 10% compared to scenarios without rebalancing. Moreover, our study reveals that higher accuracy in demand prediction models leads to improved rebalancing performance.
... 3) Emerging Mobility Systems: The advent of disruptive technologies such as autonomous driving, connectivity, and power-train electrification has enabled the development of new mobility paradigms, such as autonomous mobility-on-demand (AMoD) systems, where self-driving vehicles provide ondemand transportation services [48]. Several approaches have been proposed to study and optimize the operation of AMoD systems, including agent-based simulation [49], queueingtheoretical models [50], and network flow-based models [51]. ...
This paper introduces a mobility equity metric (MEM) for evaluating fairness and accessibility in multi-modal intelligent transportation systems. The MEM simultaneously accounts for service accessibility and transportation costs across different modes of transportation and social demographics. We provide a data-driven validation of the proposed MEM to characterize the impact of various parameters in the metric across cities in the U.S. We subsequently develop a routing framework that aims to optimize MEM within a transportation network containing both public transit and private vehicles. Within this framework, a system planner provides routing suggestions to vehicles across all modes of transportation to maximize MEM. We evaluate our approach through numerical simulations, analyzing the impact of travel demands and compliance of private vehicles. This work provides insights into designing transportation systems that are not only efficient but also equitable, ensuring fair access to essential services across diverse populations.
... This assumption is reasonable if the travel requests vary slowly w.r.t. the average time of serving each request. This is the case especially in highly populated metropolitan areas [16]. Second, our framework does not take into account the stochastic nature of the exogenous congestion that determines the travel time in each road arc. ...
... This assumption is reasonable if the travel requests vary slowly w.r.t. the average time of serving each request. This is the case especially in highly populated metropolitan areas [21], [22]. Second, our framework does not take into account the stochastic nature of the exogenous congestion which determines that travel time in each road arc. ...
This paper presents a framework to incorporate ride-pooling from a mesoscopic point of view, within time-invariant network flow models of Mobility-on-Demand systems. The resulting problem structure remains identical to a standard network flow model, a linear problem, which can be solved in polynomial time. In order to compute the ride-pooling assignment, which is the matching between two or more users so that they can be pooled together, we devise a polynomial-time knapsack-like algorithm that is optimal w.r.t. the minimum vehicle travel time with users on-board. Finally, we conduct two case studies of Sioux Falls and Manhattan, where we validate our models against state-of-the-art results, and we quantitatively highlight the effects that maximum waiting time and maximum delay thresholds have on the vehicle hours traveled, overall pooled rides and actual delay experienced. Last, we show that allowing for four people ride-pooling can significantly boost the performance of the system.
... A Mobility on Demand service places even higher demands on optimisation, as online optimisation is required to adjust vehicle routes in near real time. Various approaches exist for this, including queuing theory (Iglesias et al., 2019), simulation-based approaches (Tilg et al., 2020) and multi-commodity flow problems (Stenberg et al., 2021). In this context, we plan to research optimisation methods that enable an online solution for ondemand mobility and also take into account rebookings and cancellations while maintaining the profitability of the overall system. ...
Public transportation is often poorly developed, especially in rural areas, which leads to an increased dependence on personal vehicles. Moreover, since transportation is one of the main drivers of climate change, our research project aims to explore cost-effective methods for sustainable last-mile logistics in rural areas and support decision-makers utilizing a dashboard. For this purpose, an open marketplace platform is planned that intelligently networks suppliers and service providers in a region and bundles orders and deliveries. The aim is also to motivate customers and users to behave in a more environmentally friendly way by suggesting appropriate offers through the way they are presented on the marketplace. This is achieved by integrating Digital Twin (DT) technologies, cognitive agent-based social simulation, transport management systems and recommendation systems. To ensure the project aligns with public needs and acceptance of proposed approaches, we conduct census-representative surveys alongside the development and experimentation phases. In this paper, the overall structure of the research project and the submodels underpinning our solution are introduced. It also includes a visual mockup of a rural region’s DT and introduces several use cases.
... The authors consider the cost of empty vehicle movements when developing the MILP optimisation problem. Iglesias et al. [49] presented a case study using BCMP CQNs to model an autonomous on-demand mobility system in Manhattan and determine the optimal fleet size. The network was used to encapsulate the stochastic behaviour of the mobility system. ...
Background: This study addresses optimising fleet size in a system with a heterogeneous truck fleet, aiming to minimise transportation costs in interfacility material transfer operations. Methods: The material transfer process is modelled using a closed queueing network (CQN) that considers heterogeneous nodes and customised service times tailored to the unique characteristics of various truck types and their transported materials. The optimisation problem is formulated as a mixed-integer nonlinear programming (MINLP), falling into the NP-Hard, making exact solution computation challenging. A numerical approximation method, a modified sequential quadratic programming (SQP) method coupled with a mean value analysis (MVA) algorithm, is employed to overcome this challenge. Validation is conducted using a discrete event simulation (DES) model. Results: The proposed analytical model tested within a steel manufacturing plant’s material transfer process. The results showed that the analytical model achieved comparable optimisation of the heterogeneous truck fleet size with significantly reduced response times compared to the simulation method. Furthermore, evaluating performance metrics, encompassing response time, utilisation rate, and cycle time, revealed minimal discrepancies between the analytical and the simulation results, approximately ±8%, ±8%, and ±7%, respectively. Conclusions: These findings affirm the presented analytical approach’s robustness in optimising interfacility material transfer operations with heterogeneous truck fleets, demonstrating real-world applications.
... Different distributions could be used to model this parameter in a BSS (Cheng et al., 2021;Iglesias et al., 2019;Negahban, 2019). Nonetheless, the Poisson distribution is the most popular one (Liu & Pelechrinis, 2021). ...
Bike-Sharing Systems (BSSs) have exploded in popularity worldwide because of their beneficial impacts on traffic, pollution levels, and public health, which has resulted in moving toward a green city. The rebalancing problem, as one of the most important operational problems of such systems, deals with planning bike distribution at different stations. Regarding conducted studies, simulation models are the most common tool for analyzing BSSs and decision-making. This popularity is based on simulation’s capabilities in modeling complexities of systems and uncertainty. Despite their advantages, lack of quickness is a significant drawback of simulation-based methods, making them inefficient for real-time decision-making processes, especially in large-scale and complex systems. In this regard, this paper introduces a Supervised Learning-Based Simulation (SLBS) method as an alternative to the conventional simulation-based methods dealing with rebalancing problems. SLBS is a huge step toward developing a real-time Decision Support System (DSS) for BSSs. For developing SLBS, firstly, we have developed a simulation model based on real-world assumptions of station-based BSSs and big data analysis of CitiBike, a well-known BSS located in New York City. The simulation model is able to calculate the number of unsatisfied demands (either number of failed pick-ups (FPs) or failed drop-offs (FDs)) as a result of different rebalancing plans. Then, the developed simulation model was used to generate quality and quantity training datasets to train Machine Learning (ML) algorithms involved in SLBS. While these ML models are trained once, SLBS will be capable of predicting the number of unsatisfied demands without running highly time-intensive simulations replications. The results obtained from a wide range of conducted experiments indicate that SLBS, up to 300 times faster than simulation models, can provide predictions with over 90% of R2 Score.
... Rebalancing methods based on queuing theory have also been proposed. For example, Iglesias et al. (2019) proposed a closed multi-class Baskett, Chandy, Muntz and Palacios (BCMP) queuing network aiming to minimize the number of rebalancing vehicles and the fleet size. formulated a LP to minimize the number of rebalancing vehicles in the system using a closed Jackson Network. ...
Shared mobility on demand (MoD) services are receiving increased attention as many high volume ride-hailing companies are offering shared services (e.g. UberPool, LyftLine) at an increasing rate. Also, the advent of autonomous vehicles (AVs) promises further operational opportunities to benefit from these developments as AVs enable a centrally operated and fully connected fleet. There are two fundamental tasks for a shared MoD service: ride-matching and vehicle rebalancing. Traditionally, these two functions are performed sequentially and independently. In this paper, we propose and formulate an integrated ride-matching problem which aims to integrate ride-matching and rebalancing into a single formulation. The integrated problem benefits from interactions between these two tasks. We also propose a methodology to solve the integrated shared ride-matching problem by using supply level information based on a grid representation of the city network. We demonstrate the effectiveness of the proposed methodology through a comparative case study using a benchmark sequential approach and an open source data set. Our results show that the integrated model is able to serve at least the same amount of passengers with significant gains in terms of level of service and sustainability metrics.
... Ö zkan and Ward (2020) study revenue-maximizing, state-independent dispatch control by solving a minimum cost flow problem in the fluid limit. Iglesias et al. (2016) consider centralized matching and repositioning decisions in the context of a closed network model. Braverman et al. (2019) model the system as a closed queueing network of all vehicles and propose optimal routing decisions based on the corresponding fluid model. ...
Balancing the Abandonment and Cancellation of a Ride-Matching Market.
In “On-Demand Ride-Matching in a Spatial Model with Abandonment and Cancellation,” Wang, Zhang, and Zhang propose a spatial model to approximate pickup times based on the number of waiting passengers and idle drivers. They analyze the dynamics of passengers and drivers in a queueing model in which the platform can control the matching process by setting a threshold on the expected pickup time. Applying fluid approximations, we obtain accurate performance evaluations and an elegant optimality condition based on which they propose a policy that adapts to time-varying demand.
... Shared autonomous vehicles and car-sharing services reposition empty cars to make them available for customers to drive. Examples of repositioning applied to shared autonomous vehicles include Iglesias et al. (2019), Zhang and Pavone (2016), and Smith et al. (2013). On shared taxis and other on-demand transport modes, Alonso-Mora et al. (2017), Wallar et al. (2018), Simonetto et al. (2019), and Liu and Samaranayake (2020) repositioned empty vehicles to the location of recently unsatisfied customers. ...
Dynamic network-level models directly addressing ride-sourcing services can support the development of efficient strategies for both congestion alleviation and promotion of more sustainable mobility. Recent developments presented models focusing on ride-hailing (solo rides), but no work addressed ridesplitting (shared rides) in dynamic contexts. Here, we sought to develop a dynamic aggregated traffic network model capable of representing ride-sourcing services and background traffic in a macroscopic multi-region urban network. We combined the Macroscopic Fundamental Diagram (MFD) with detailed state-space and transition descriptions of background traffic and ride-sourcing vehicles in their activities to formulate mass conservation equations. Accumulation-based MFD models might experience additional errors due to the variation profile of trip lengths, e.g., when vehicles cruise for passengers. We integrate the so-called M-model that utilizes the total remaining distance to capture dynamics of regional and inter-regional flows and accumulations for different vehicle (private or ride-sourcing) states. This aggregated model is capable to reproduce the dynamics of complex systems without using resource-expensive simulations. We also show that the model can accurately forecast the vehicles' conditions in near-future predictions. Later, a comparison with benchmark models showed lower errors in the proposed model in all states. Finally, we evaluated the model's robustness to noises in its inputs, and forecast errors remained below 15% even where inputs were 20% off the actual values for ride-sourcing vehicles. The development of such a model prepares the path for developing real-time feedback-based management policies such as priority-based perimeter control or repositioning strategies for idle ride-sourcing vehicles and developing regulations over ride-sourcing in congested areas.
... queuing-theoretical models (Zhang and Pavone, 2016;Banerjee et al., 2015;Iglesias et al., 2019), to simulationbased ones (Levin et al., 2017;Maciejewski et al., 2017;Hörl et al., 2019). Multi-commodity network flow models, Spieser et al., 2014;Iglesias et al., 2018;Salazar et al., 2020) are suited for efficient optimization and allow for the implementation of a variety of complex constraints. ...
The advent of vehicle autonomy, connectivity and electric powertrains is expected to enable the deployment of Autonomous Mobility-on-Demand systems. Crucially, the routing and charging activities of these fleets are impacted by the design of the individual vehicles and the surrounding charging infrastructure which, in turn, should be designed to account for the intended fleet operation. This paper presents a modeling and optimization framework where we optimize the activities of the fleet jointly with the placement of the charging infrastructure. We adopt a mesoscopic planning perspective and devise a time-invariant model of the fleet activities in terms of routes and charging patterns, explicitly capturing the state of charge of the vehicles by resampling the road network as a digraph with iso-energy arcs. Then, we cast the problem as a mixed-integer linear program that guarantees global optimality and can be solved in less than 10 min. Finally, we showcase two case studies with real-world taxi data in Manhattan, NYC: The first one captures the optimal trade-off between charging infrastructure prevalence and the empty-mileage driven by the fleet. We observe that jointly optimizing the infrastructure siting significantly outperforms heuristic placement policies, and that increasing the number of stations is beneficial only up to a certain point. The second case focuses on vehicle design and shows that deploying vehicles equipped with a smaller battery results in the lowest energy consumption: Although necessitating more trips to the charging stations, such fleets require about 12% less energy than the vehicles with a larger battery capacity.
... Monitoring the real-time state of charge (SOC) of SAEVs and implementing related techniques to appoint some vehicles to a specific charging station/pile or parking space is referred to as parking and recharging assignment (Iglesias et al., 2018). According to Chen and Kockelman (2016), while charging cars are not allowed to undock and service a new trip request, Bauer et al. (2018) think that still-charging vehicles are. ...
The Autonomous Mobility-on-Demand system is an emerging green and sustainable transportation system providing on-demand mobility services for urban residents. To achieve the best recharging, delivering, and repositioning task assignment decision-making process for shared autonomous electric vehicles, this paper formulates the fleet dynamic operating process into a multi-agent multi-task dynamic dispatching problem based on Markov Decision Process. Specifically, the decision-making process at each time step is divided into 3 sub-processes, among which recharging and delivery task assignment processes are transformed into a maximum weight matching problem of bipartite graph respectively, and the repositioning task assignment process is quantified as a maximum flow problem. Kuhn-Munkres Algorithm and Edmond-Karp Algorithm are adopted to solve the above two mathematical problems to achieve the optimal task allocation policy. To further improve the dispatching performance, a new instant reward function balancing order income with trip satisfaction is designed, and a state-value function estimated by Back Propagation-Deep Neural Network is defined as a matching degree between each shared autonomous electric vehicle and each delivery task. The numerical results show that: (i) a reward function focusing on income and satisfaction can increase total revenue by 33.2%, (ii) the introduction of task allocation repositioning increases total revenue by 50.0%, (iii) a re-estimated state value function leads to a 2.8% increase in total revenue, (iv) the combination of charging and task repositioning can reduce user waiting time and significantly improve user satisfaction with the trip.
... However, the charging station supply is a random variable that the prediction error can not be ignored [5], [12], [15], and we define the uncertainty set as c ∼ F * c , F * c ∈ F c . Function (5) is not concave over uncertainty parameter c k , for computationally tractability, we consider minimizing the following utilization quality function J E ...
As electric vehicle (EV) technologies become mature, EV has been rapidly adopted in modern transportation systems, and is expected to provide future autonomous mobility-on-demand (AMoD) service with economic and societal benefits. However, EVs require frequent recharges due to their limited and unpredictable cruising ranges, and they have to be managed efficiently given the dynamic charging process. It is urgent and challenging to investigate a computationally efficient algorithm that provide EV AMoD system performance guarantees under model uncertainties, instead of using heuristic demand or charging models. To accomplish this goal, this work designs a data-driven distributionally robust optimization approach for vehicle supply-demand ratio and charging station utilization balancing, while minimizing the worst-case expected cost considering both passenger mobility demand uncertainties and EV supply uncertainties. We then derive an equivalent computationally tractable form for solving the distributionally robust problem in a computationally efficient way under ellipsoid uncertainty sets constructed from data. Based on E-taxi system data of Shenzhen city, we show that the average total balancing cost is reduced by 14.49%, the average unfairness of supply-demand ratio and utilization is reduced by 15.78% and 34.51% respectively with the distributionally robust vehicle balancing method, compared with solutions which do not consider model uncertainties.
Autonomous ride-hailing platforms, such as Waymo and Cruise, are quickly expanding their services, but their interactions with the existing ride-hailing companies, such as Uber and Lyft, are rarely discussed. To fill this gap, this paper focuses on the competition between an emerging autonomous ride-hailing platform and a traditional ride-hailing platform by characterizing the equilibrium of their competition and the impact of technology transfer. In particular, we consider an autonomous ride-hailing platform that owns the AV technology and offers ride-hailing services to passengers through a fleet of AVs. In the meanwhile, it competes with a traditional ride-hailing platform that primarily relies on a fleet of human-driver vehicles (HDVs) but may rent a sub-fleet of AVs from the autonomous ride-hailing platform to complement the human-driver fleet (referred to as AV technology transfer). A game-theoretic model is formulated to characterize the competition between the autonomous ride-hailing platform and the traditional ride-hailing platform over a transportation network, encapsulating the passengers’ mode choices, the drivers’ job options, the network traffic flows and the strategic decisions of the platforms. An algorithm is proposed to compute the approximate Nash equilibrium of the game and conduct an ex-post evaluation on the performance of the obtained solutions. The proposed framework and solution algorithm are validated through a realistic case study for Manhattan. Based on numerical simulations, we find that technology transfer of AVs between the two platforms can lead to a win-win situation where both two platforms get a higher profit, but this comes at the cost of reduced surpluses for human drivers and passengers. In the simulation, a critical trade-off is revealed for the autonomous ride-hailing platform: it strategically forfeits some of its market share in ride-hailing services to encourage the traditional ride-hailing platform to rent more AVs, thereby increasing its rental revenue and consequently, the overall profit. Furthermore, we also find it intriguing that as AV technology improves and operational costs decrease, the traditional ride-hailing platform cannot enjoy any benefit in its profit although it has the option of leasing AVs from the autonomous ride-hailing platform at lower operational costs. Instead, it is compelled to rent a larger fleet of AVs from the autonomous ride-hailing platform at a higher rental price, consequently suffering a reduced profit. Conversely, the autonomous ride-hailing platform significantly benefits from the reduced AV operational cost by capturing a larger market share in the ride-hailing market and earning higher revenue from the AV technology transfer.
In order to achieve the stability and safety of the autonomous vehicle while reducing the control cost, a driving strategy for uncertain autonomous vehicle is presented. There are many uncertainties in the autonomous vehicle driving, and the boundary of the uncertainty maybe unknown. To solve this problem, a gated leakage type adaptive robust control based on the tracking deviation is developed. The salient feature of the control lies in the novel leakage mechanism designs. The leakage mechanism is designed to provide gated value for the leakage to prevent excessive control effort. The control system ensures the performance of the autonomous vehicle in terms of lateral and yaw displacement, which in turn prevents the vehicle from sideslip even in uncertainty. Compared with the constant leakage type adaptive robust control and Linear Quadratic Regulator (LQR) control, the effectiveness and superiority of the proposed control method are verified
Online ride-hailing platforms have developed into an integral part of the transportation infrastructure in many countries. The primary task of a ride-hailing platform is to match trip requests to drivers in real time. Although both passengers and drivers prefer a prompt pickup to initiate the trips, it is often difficult to find a nearby driver for every passenger. If the driver is far from the pickup point, the passenger may cancel the trip while the driver is heading toward the pickup point. For the platform to be profitable, the trip cancellation rate must be maintained at a low level. We propose a computationally efficient data-driven approach to ride matching, in which a pickup time target is imposed on each trip request and an optimization problem is formulated to maximize the joint probability of all the pickup times meeting the targets. By adjusting pickup time targets individually, this approach may assign more high-value trip requests to nearby drivers, thus boosting the platform’s revenue while maintaining a low cancellation rate. In numerical experiments, the proposed approach outperforms several ride-matching policies used in practice.
History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete.
Funding: This work of D. Rong and X. Sun was supported in part by the National Natural Science Foundation of China [Grant 71971165], the National Key Research and Development Program of China [Grant 2021YFB3301801], the MOE Project of Humanities and Social Science of China [Grant 19YJE630002], and the Soft Science Research Program of Shannxi [Grant 2018KRZ005]. The work of S. He was supported in part by the Singapore Ministry of Education Social Science Research Council [Grant MOE2022-SSRTG-029].
Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2021.0210 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0210 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .
Autonomous vehicles are rapidly evolving and will soon enable large-scale mobility-on-demand (MoD) systems applications. Managing the fleets of available vehicles, commonly known as “rebalancing”, is crucial to ensure that vehicles are distributed properly to meet customer demands. This paper presents an optimal control approach to optimize vehicle scheduling and rebalancing in an autonomous mobility-on-demand (AMoD) system. We use graph theory to model a city partitioned into virtual zones. Zones represent small areas of the city where vehicles can stop and pick up/drop off customers, whereas links denote corridors of the city along which autonomous vehicles can move. They are considered vertices and edges in the graph. Vehicles employed in the AMoD scheme are autonomous, and rebalancing can be executed by dispatching available empty vehicles to areas undersupplied. Rebalancing is performed on the graph’s vertices, i.e., between city areas. We propose a linear, discrete-time model of an AMoD system using a transformed network. After acquiring the model, the desired number of rebalancing vehicles for the AMoD model is derived through an optimization problem. Moreover, the well-posedness of the model is illustrated. To leverage the proposed model, we implemented the model predictive control (MPC) framework to find the optimal rebalancing and scheduling policy. We show the MPC’s effectiveness and how the MPC framework can be implemented in real-time for a real-world case study. The numerical results show that the MPC with a linear cost function and linear reference, which it tracks, is effective, outperforming other MPC-based and state-of-the-art algorithms across all evaluation criteria.
This paper studies spatiotemporal pricing and fleet management for autonomous mobility-on-demand (AMoD) systems while taking elastic demand into account. We consider a platform that offers ride-hailing services using a fleet of autonomous vehicles and makes pricing, rebalancing, and fleet sizing decisions in response to demand fluctuations. A network flow model is developed to characterize the evolution of system states over space and time, which captures the vehicle-passenger matching process and demand elasticity with respect to price and waiting time. The platform’s objective of maximizing profit is formulated as a constrained optimal control problem, which is highly nonconvex due to the nonlinear demand model and complex supply-demand interdependence. To address this challenge, an integrated decomposition and dynamic programming approach is proposed, where we first relax the problem through a change of variable, then separate the relaxed problem into a few small-scale subproblems via dual decomposition, and finally solve each subproblem using dynamic programming. Despite the nonconvexity, our approach establishes a theoretical upper bound to evaluate the solution optimality. The proposed model and methodology are validated in numerical studies for Manhattan. We find that compared to the benchmark case, the proposed upper bound is significantly tighter. We also find that compared to pricing alone, joint pricing and fleet rebalancing can only offer a minor profit improvement when demand can be accurately predicted. However, during unanticipated demand surges, joint pricing and rebalancing can lead to substantially improved profits, and the impacts of demand shocks, despite being more widespread, can dissipate faster.
The rebalancing of idle vehicles is critical to mitigating the supply–demand imbalance in on-demand ride services. Motivated by a ride service platform, this paper investigates a short-term vehicle rebalancing problem under demand uncertainty in the presence of contextual data. We deploy a novel data-driven robust optimization approach that takes a direct path from “Data” to “Decision” instead of the predict-then-optimize paradigm and leverages the prediction problem structure to seamlessly integrate demand predictions with optimization models. We further develop a risk-based uncertainty set to evaluate how well uncertain demand is estimated from contextual data by prediction models, and discuss the classes of prediction models that are highly compatible with robust optimization models. Based on the convex analysis and duality theory, we reformulate the original models into equivalent Mixed Integer Second Order Cone Programmings (MISOCPs) that are solvable via state-of-the-art commercial solvers. To solve large-scale instances, we utilize the affine decision rule technique to derive polynomial-sized reformulations. Extensive experiments are conducted on the instances based on a real-world on-demand ride service in Chengdu. The computational experiments demonstrate the promising performance of our rebalancing strategies and solution approaches.
This paper studies the joint charging scheduling and rebalancing of employees and electric vehicles in one-way car sharing systems (OCS). Consider an OCS consisting of a fleet of vehicles and a team of employees responsible for charging low-battery level vehicles and rebalancing the idle vehicles in the system. The employees need also to rebalance themselves by service vehicles or by sharing a car with some customers. Firstly, a joint optimization method to ensure vehicle and employee balance is proposed, where the variation of the number of vehicles, customers and employees is described by fluid models, while the charging process of electric vehicles at charging stations is modeled by an M/M/S queue. Then, the well-posedness and equilibrium of the fluid model are proven, and the minimum fleet size and employee size for the system to reach equilibrium is given. Next, a rebalancing method is presented to minimize the number of empty vehicles and rebalancing employees traveling in the network. Numerical experiment and case study show that the proposed method can significantly improve the quality of service and reduce the number of rebalancing employees.
Fleet sizing is an important problem in the planning procedure of one-way car-sharing systems. This article investigates the fleet-sizing problem for reservation-based car-sharing systems allowing cruise parking. The system with traffic congestion is modeled as a mixed queuing network with its servers mapping the remaining road capacity. The optimal fleet size with maximum operating profit is derived, taking into account asymptotic performance metrics like reservation, vehicle availability and utilization, and occupancy of parking spaces of each of the stations. The solution is obtained based on an exact mean value analysis (MVA) algorithm and an approximate Schweitzer–Bard MVA (SB-MVA) algorithm. Numerical experiments demonstrate that the proposed method with cruise parking can meet the travel demands with greatly reduced operating cost. Another interesting finding is that a larger reservation time window implies lower parking capacity and smaller fleet size, whereas, as the time window exceeds a threshold, reducing the fleet size may damage the quality of service.
Ride-sourcing drivers, as individual service suppliers, can freely adopt their own relocation strategies, including waiting, cruising freely, or following the platform recommendations. These decisions substantially impact the balance between supply and demand, and consequently affect system performance. We conducted a stated choice experiment to study the searching behaviour of ride-sourcing drivers and examine novel policies. A unique dataset of 576 ride-sourcing drivers working in the US was collected and a choice modelling approach was used to estimate the effects of multiple existing and hypothetical attributes. The results suggest that ride-sourcing drivers’ relocation strategies vary considerably between different drivers groups. Surge pricing significantly stimulates drivers to head toward the designated areas. However, the distance between the driver’s location and surge or high-demand areas demotivates them from following the platform repositioning recommendations. We discuss the implications of our findings for various platform policies on real-time information sharing and platform repositioning guidance.
Shared micromobility systems are rapidly pervading urban environments. Usually, they are either dockless, in line with free-floating paradigms whereby vehicles can be left and picked up anywhere within the region of operation, or have docking stations with predefined parking slots. In this paper, we present an optimization-based framework to analyze and compare the advantages and disadvantages of these two different types of micromobility systems. We also include the possibility of rebalancing the system by the operator. First, we leverage graph theory to build a linear time-invariant network flow model of the two systems and use it to frame the time-optimal routing problem. Specifically, we formulate a linear program (LP) for the dockless system and a mixed-integer linear program (MILP) for the docked one whereby we jointly optimize the siting of the docking stations. Given their structure, both problems can be solved with off-the-shelf algorithms and global optimality guarantees. Second, we showcase our framework with a case study of Manhattan, NYC, whereby we quantitatively compare the performance achievable by the two micromobility paradigms. Our simulations suggest that increasing the number of stations of docked micromobility systems may decrease the average travel time up to a minimum aligned with the travel time achievable by dockless systems. Thereby, adding more stations does not significantly improve the system’s performance. Moreover, due to the slightly asymmetric travel demands, a mild rebalance of the system is enough to boost its performance.
In this paper, we propose a closed queueing network model for performance analysis of electric vehicle sharing systems with a certain number of chargers in each neighborhood. Depending on the demand distribution, we devise algorithms to compute the optimal fleet size and number of chargers required to maximize profit while maintaining a certain quality of service. We show that the profit is concave with respect to the fleet size and the number of chargers at each charging point. If more chargers are installed within the city, we show that it can not only reduce the fleet size, but it also improves the availability of vehicles at all the points within a city. We further show through simulation that two slow chargers may outperform one fast charger when the variance of charging time becomes relatively large in comparison to the mean charging time.
The emergence of automated vehicles holds great promise for the future of transportation. Although commercial sales of fully self-driving vehicles will not commence for several more years, once these sales are possible a new transportation mode for personal travel promises to arrive. This new mode is the shared autonomous (or fully automated) vehicle (SAV), combining features of short-term, on-demand rentals with self-driving capabilities: in essence, a driverless taxi. This investigation examined the potential implications of the SAY at a low level of market penetration (1.3% of regional trips) by simulating a fleet of SAVs serving travelers in the 12-mi by 24-mi regional core of Austin, Texas. The simulation used a sample of trips from the region's planning model to generate demand across traffic analysis zones and a 32,272-link network. Trips called on the vehicles in 5-min departure time windows, with link-level travel times varying by hour of day based on MATSIM's dynamic traffic assignment simulation software. Results showed that each SAY could replace about nine conventional vehicles within the 24-mi by 12-mi area while still maintaining a reasonable level of service (as proxied by user wait times, which averaged just 1 min). Additionally, approximately 8% more vehicle miles traveled (VMT) may be generated because of SAV's ability to journey unoccupied to the next traveler or relocate to a more favorable position in anticipation of its next period demand.
TRB Transportation Research Circular E-C153: Dynamic Traffic Assignment: A Primer is designed to help explain the basic concepts and definitions of dynamic traffic assignment (DTA) models and addresses the application, selection, planning, and execution of a DTA model.The report also describes the general DTA modeling procedure and modeling issues that may concern a model user.
Electric vehicle-sharing systems have been introduced to a number of cities as a means of increasing mobility, reducing congestion, and pollution. Electric vehicle-sharing systems can offer one or two-way services. One-way systems provide more flexibility to users since they can be dropped-off at any station. However, their modeling involves a number of complexities arising from the need to relocate vehicles accumulated at certain stations. The planning of one-way electric vehicle-sharing systems involves a host of strongly interacting decisions regarding the number, size and location of stations, as well as the fleet size.
In this paper we develop and solve a multi-objective MILP model for planning one-way vehicle-sharing systems taking into account vehicle relocation and electric vehicle charging requirements. For real world problems the size of the problem becomes intractable due to the extremely large number of relocation variables. In order to cope with this problem we introduce an aggregate model using the concept of the virtual hub. This transformation allows the solution of the problem with a branch-and-bound approach.
The proposed approach generates the efficient frontier and allows decision makers to examine the trade-off between operator’s and users’ benefits. The capabilities of the proposed approach are demonstrated on a large scale real world problem with available data from Nice, France. Extensive sensitivity analysis was performed by varying demand, station accessibility distance and subsidy levels. The results provide useful insights regarding the efficient planning of one-way electric vehicle-sharing systems and allow decision makers to quantify the trade-off between operator’s and users’ benefits.
In this paper we develop methods for maximizing the throughput of a mobility-on-demand urban transportation system. We consider a finite group of shared vehicles, located at a set of stations. Users arrive at the stations, pickup vehicles, and drive (or are driven) to their destination station where they drop-off the vehicle. When some origins and destinations are more popular than others, the system will inevitably become out of balance: vehicles will build up at some stations, and become depleted at others. We propose a robotic solution to this rebalancing problem that involves empty robotic vehicles autonomously driving between stations. Specifically, we utilize a fluid model for the customers and vehicles in the system. Then, we develop a rebalancing policy that lets every station reach an equilibrium in which there are excess vehicles and no waiting customers and that minimizes the number of robotic vehicles performing rebalancing trips. We show that the optimal rebalancing policy can be found as the solution to a linear program. We use this solution to develop a real-time rebalancing policy which can operate in highly variable environments. Finally, we verify policy performance in a simulated mobility-on-demand environment and in hardware experiments.
Micro-simulations for transport planning are becoming increasingly important in traffic simulation, traffic analysis, and traffic forecasting. In the last decades the shift from using typically aggregated data to more detailed, individual based, complex data (e.g. GPS tracking) and the continuously growing computer performance on fixed price level leads to the possibility of using microscopic models for large scale planning regions. This chapter presents such a micro-simulation. The work is part of the research project MATSim (Multi Agent Transport Simulation, http://matsim.org). In the chapter here the focus lies on design and implementation issues as well as on computational performance of different parts of the system. Based on a study of Swiss daily traffic - ca. 2.3 million individuals using motorized individual transport producing about 7.1 million trips, assigned to a Swiss network model with about 60'000 links, simulated and optimized completely time-dynamic for a complete workday - it is shown that the system is able to generate those traffic patterns in about 36 hours computation time.
We study optimal static routing problems in open multiclass networks with state-independent arrival and service rates. Our
goal is to study the uniqueness of optimal routing under different scenarios. We consider first the overall optimal policy,
that is the routing policy whereby the overall mean cost of a job is minimized. We then consider an individually optimal policy
whereby jobs are routed so that each job may feel that its own expected cost is minimized if it knows the mean cost for each
path. This is related to the Wardrop equilibrium concept in a multiclass framework. We finally study the case of class optimization,
in which each of several classes of jobs tries to minimize the averaged cost per job within that class; this is related to
the Nash equilibrium concept. For all three settings, we show that the routing decisions at optimum need not be unique, but
that the utilizations in some large class of links are uniquely determined.
The minimum-cost multicommodity flow problem involves simultaneously shipping multiple commodities through a single network so that the total flow obeys arc capacity constraints and has minimum cost. Multicommodity flow problems can be expressed as linear programs, and most theoretical and practical algorithms use linear-programming algorithms specialized for the problems’ structures. Combinatorial approximation algorithms yield flows with costs slightly larger than the minimum cost and use capacities slightly larger than the given capacities. Theoretically, the running times of these algorithms are much less than that of linear-programming-based algorithms. We combine and modify the theoretical ideas in these approximation algorithms to yield a fast, practical implementation solving the minimum cost multicommodity flow problem. Experimentally, the algorithm solved our problem instances (to 1% accuracy) two to three orders of magnitude faster than the linear-programming package CPLEX and the linear-programming based multi-commodity flow program PPRN.
The joint equilibrium distribution of queue sizes in a network of queues containing N service centers and R classes of customers is derived. The equilibrium state probabilities have the general form P(S) equals Cd(S) f//1(x//1)f//2(x//2). . . f//N(x//N), where S is the state of the system, x//i is the configuration of customers at the ith service center, d(S) is a function of the state of the model, f//i is a function that depends on the type of the ith service center, and C is a normalizing constant. It is assumed that the equilibrium probabilities exist and are unique. Four types of service centers to model central processors, data channels, terminals, and routing delays are considered.
In this paper, we establish criteria for the optimality of routing and flow control solutions. More precisely, we investigate the convexity of the network delay function in closed queueing networks and show it exists in single chain networks. Then we derive the derivative of the network delay function with respect to relative throughput and show it can be easily obtained from the MVA algorithm. Finally, we propose a closed-network version of the FD algorithm to find the exact optimal routing solution in single chain closed queueing networks. Numerical results are presented to demonstrate the correctness and efficiency of the optimization algorithm.
There are natural synergies between shared autonomous vehicle (AV) fleets and electric vehicle (EV) technology, since fleets of AVs resolve the practical limitations of today’s non-autonomous EVs, including traveler range anxiety, access to charging infrastructure, and charging time management. Fleet-managed AVs relieve such concerns, managing range and charging activities based on real-time trip demand and established charging-station locations, as demonstrated in this paper. This work explores the management of a fleet of shared autonomous electric vehicles (SAEVs) in a regional, discrete-time, agent-based model. The simulation examines the operation of SAEVs under various vehicle range and charging infrastructure scenarios in a gridded city modeled roughly after the densities of Austin, Texas.
We study optimal pricing strategies for ride-sharing platforms, using a queueing-theoretic economic model. Analysis of pricing in such settings is complex: On one hand these platforms are two-sided - this requires economic models that capture the incentives of both drivers and passengers. On the other hand, these platforms support very high temporal-resolution for data collection and pricing - this requires stochastic models that capture the dynamics of drivers and passengers in the system.
We focus our attention on the value of dynamic pricing: where prices can react to instantaneous imbalances between available supply and incoming demand. We find two main results: We first show that profit under any dynamic pricing strategy cannot exceed profit under the optimal static pricing policy (i.e., one which is agnostic of stochastic fluctuations in the system load). This result belies the prevalence of dynamic pricing in practice. Our second result explains the apparent paradox: we show that dynamic pricing is much more robust to fluctuations in system parameters compared to static pricing. Moreover, these results hold even if the monopolist maximizes welfare or throughput. Thus dynamic pricing does not necessarily yield higher performance than static pricing - however, it lets platforms realize the benefits of optimal static pricing, even with imperfect knowledge of system parameters.
In this paper we present a model predictive control (MPC) approach to
optimize vehicle scheduling and routing in an autonomous mobility-on-demand
(AMoD) system. In AMoD systems, robotic, self-driving vehicles transport
customers within an urban environment and are coordinated to optimize service
throughout the entire network. Specifically, we first propose a novel
discrete-time model of an AMoD system and we show that this formulation allows
the easy integration of a number of real-world constraints, e.g., electric
vehicle charging constraints. Second, leveraging our model, we design a model
predictive control algorithm for the optimal coordination of an AMoD system and
prove its stability in the sense of Lyapunov. At each optimization step, the
vehicle scheduling and routing problem is solved as a mixed integer linear
program (MILP) where the decision variables are binary variables representing
whether a vehicle will 1) wait at a station, 2) service a customer, or 3)
rebalance to another station. Finally, by using real-world data, we show that
the MPC algorithm can be run in real-time for moderately-sized systems and that
the algorithm outperforms previous control strategies for AMoD systems.
A solution to the imbalance of vehicles in one-way carsharing systems is vehicle relocation which involves staff members to redistribute the vehicles between stations. Vehicle relocation, however, can lead to an imbalance of staff members between stations. Thus, staff members, themselves, need to be relocated between stations to perform the vehicle relocations. This study addresses the joint optimization of vehicle relocation and staff rebalancing using two integrated multi-traveling salesman formulations. Results show that fleet size is more sensitive to demand than staff size, staff size is inversely related to vehicle cost, and that vehicle relocation time increases with vehicle cost.
The objective of this work is to provide analytical guidelines and financial justification for the design of shared-vehicle mobility-on-demand systems. Specifically, we consider the fundamental issue of determining the appropriate number of vehicles to field in the fleet, and estimate the financial benefits of several models of car sharing. As a case study, we consider replacing all modes of personal transportation in a city such as Singapore with a fleet of shared automated vehicles, able to drive themselves, e.g., to move to a customer’s location. Using actual transportation data, our analysis suggests a shared-vehicle mobility solution can meet the personal mobility needs of the entire population with a fleet whose size is approximately 1/3 of the total number of passenger vehicles currently in operation.
The objective of this work is to provide analytical guidelines and financial justification for the design of shared-vehicle mobility-on-demand systems. Specifically, we consider the fundamental issue of determining the appropriate number of vehicles to field in the fleet, and estimate the financial benefits of several models of car sharing. As a case study, we consider replacing all modes of ion in a city such as Singapore with a fleet of shared automated vehicles, able to drive themselves, e.g., to move to a customer’s location. Using actual transportation data, our analysis suggests a shared-vehicle mobility solution can meet the personal mobility needs of the entire population with a fleet whose size is approximately 1/3 of the total number of passenger vehicles currently in operation.
In this paper we present and analyze a queueing-theoretical model for
autonomous mobility-on-demand (MOD) systems where robotic, self-driving
vehicles transport customers within an urban environment and rebalance
themselves to ensure acceptable quality of service throughout the entire
network. We cast an autonomous MOD system within a closed Jackson network model
with passenger loss. It is shown that an optimal rebalancing algorithm
minimizing the number of (autonomously) rebalancing vehicles and keeping
vehicles availabilities balanced throughout the network can be found by solving
a linear program. The theoretical insights are used to design a robust,
real-time rebalancing algorithm, which is applied to a case study of New York
City. The case study shows that the current taxi demand in Manhattan can be met
with about 8,000 robotic vehicles (roughly 60% of the size of the current taxi
fleet). Finally, we extend our queueing-theoretical setup to include congestion
effects, and we study the impact of autonomously rebalancing vehicles on
overall congestion. Collectively, this paper provides a rigorous approach to
the problem of system-wide coordination of autonomously driving vehicles, and
provides one of the first characterizations of the sustainability benefits of
robotic transportation networks.
Carsharing programs that operate as short-term vehicle rentals (often for one-way trips before ending the rental) like Car2Go and ZipCar have quickly expanded, with the number of US users doubling every 1–2 years over the past decade. Such programs seek to shift personal transportation choices from an owned asset to a service used on demand. The advent of autonomous or fully self-driving vehicles will address many current carsharing barriers, including users’ travel to access available vehicles.This work describes the design of an agent-based model for shared autonomous vehicle (SAV) operations, the results of many case-study applications using this model, and the estimated environmental benefits of such settings, versus conventional vehicle ownership and use. The model operates by generating trips throughout a grid-based urban area, with each trip assigned an origin, destination and departure time, to mimic realistic travel profiles. A preliminary model run estimates the SAV fleet size required to reasonably service all trips, also using a variety of vehicle relocation strategies that seek to minimize future traveler wait times. Next, the model is run over one-hundred days, with driverless vehicles ferrying travelers from one destination to the next. During each 5-min interval, some unused SAVs relocate, attempting to shorten wait times for next-period travelers.Case studies vary trip generation rates, trip distribution patterns, network congestion levels, service area size, vehicle relocation strategies, and fleet size. Preliminary results indicate that each SAV can replace around eleven conventional vehicles, but adds up to 10% more travel distance than comparable non-SAV trips, resulting in overall beneficial emissions impacts, once fleet-efficiency changes and embodied versus in-use emissions are assessed.
This paper deals with a new problem that is a generalization of the many to many pickup and delivery problem and which is motivated by operating self-service bike sharing systems. There is only one commodity, initially distributed among the vertices of a graph, and a capacitated single vehicle aims to redistribute the commodity in order to reach a target distribution. Each vertex can be visited several times and also can be used as a buffer in which the commodity is stored for a later visit. This problem is NP-hard, since it contains several NP-hard problems as special cases (the TSP being maybe the most obvious one). Even finding a tractable exact formulation remains problematic.This paper presents efficient algorithms for solving instances of reasonable size, and contains several theoretical results related to these algorithms. A branch-and-cut algorithm is proposed for solving a relaxation of the problem. An upper bound of the optimal solution of the problem is obtained by a tabu search, which is based on some theoretical properties of the solution, once fixed the sequence of the visited vertices. The possibility of using the information provided by the relaxation receives a special attention, both from a theoretical and a practical point of view. It is proven that to build a feasible solution of the problem by using the one obtained by the relaxation is an NP-hard problem. Nevertheless, a tabu search initialized with the optimal solution of the relaxation often shows that it is the optimal one.The algorithms have been tested on a set of instances coming from the literature, proving their effectiveness.
This paper presents theory and algorithms, heuristic as well as
convergent, for one of the core problems in the transportation
planning process - the problem of traffic assignment. Given a transportation
network, and certain assumptions on the route choice
behaviour of the tripmakers, the problem of traffic assignment is
to assign traffic onto the network, so as to fulfill the demands for
transportation and to minimize some merit function, based on the
behavioural assumption made.
Discussions on behavioural principles can be traced to the 1920's.
Mathematical modeling and
algorithmic approaches evolved (by the growing
interest of the problem), as a result of the highway construction
in the U.S.\ in the 1950's. The equivalence between the proposed
principles of trip assignment and nonlinear optimization models was
established in the mid-1950's. Because the mathematical models were not
known to
the practitioners, rather inferior heuristic schemes were developed
during the 1950's and 1960's. In the
end of the 1960's the first convergent methods for the problem of
traffic assignment was presented, and in the mid-70's most practitioners
seems to have accepted the convergent methods as better instruments
for their transportation analysis, due to the large amount of
comparative studies
presented and program packages developed during this period.
In order to incorporate more general flow-travel time relationships,
for instance for multimodal traffic, more general models have been
developed since the 1970's. These models lead to equivalent
formulations of the
assignment principles as finite-dimensional
variational inequalities, nonlinear
complementarity problems or fixed point problems. Algorithms proposed
for the more general problems stem from the algorithms employed to
nonlinear equations and variational inequalities.
We present the mathematical
programs to be solved to obtain the network flows, corresponding to the
two most important principles of
route choices, and outline some relations between them.
The development of nonconvergent heuristic schemes are then presented.
These methods fail to
recognize both the behavioural assumptions, and to take into
account the congestion effects evolving with increasing flow.
We then present
the important developments in the construction of convergent algorithms
for traffic assignment, and outline some relationships. Method classes
include linearization methods, cyclic decomposition methods and
algorithms based on duality.
We present the development of mathematical models evolving from the
definition of the more general travel costs, and give a presentation
of the development
of the methods used to solve them. Finally, we give a comprehensive
bibliography on the research performed on theory and algorithms for the
traffic assignment problem.
Closed product-form queueing networks are considered. Recursive schemata are proposed for the higher moments of the number of customers in the queues, called “moment analysis”. As with mean value analysis (MVA), in general no state probabilities are needed. Approximation techniques for these schemata similar to those existing for MVA are introduced.
Optimal static routing problems in open BCMP queueing networks with state-independent arrival and service rates are studied. They include static routing problems in communication networks and optimal static load balancing problems in distributed computer systems. We consider an overall optimal policy that is the routing policy whereby the overall mean response (or sojourn) time of a job is minimized. We obtain the routing decisions of the overall optimal policy and show that they may not be unique, but that the utilization of each service center is uniquely determined by the overall optimal policy. We also consider an individually optimal policy whereby jobs are routed so that each job may feel that its own expected response time is minimized if it knows the mean delay time for each path.
In this paper, we address the problem of determining the optimal fleet size for a vehicle rental company and derive analytical results for its relationship to vehicle availability at each rental station in the company’s network of locations. This work is motivated by the recent surge in interest for bicycle and electric car sharing systems, one example being the French program Vélib (2010). We first formulate a closed queueing network model of the system, obtained by viewing the system from the vehicle’s perspective. Using this framework, we are able to derive the asymptotic behavior of vehicle availability at an arbitrary rental station with respect to fleet size. These results allow us to analyze imbalances in the system and propose some basic principles for the design of system balancing methods. We then develop a profit-maximizing optimization problem for determining optimal fleet size. The large-scale nature of real-world systems results in computational difficulties in obtaining this exact solution, and so we provide an approximate formulation that is easier to solve and which becomes exact as the fleet size becomes large. To illustrate our findings and validate our solution methods, we provide numerical results on some sample networks.
Stochastic Modeling and Decentralized Control Policies for Large-Scale Vehicle Sharing Systems via Closed Queueing Networks
- D K George
George, D.K.: Stochastic Modeling and Decentralized Control Policies for Large-Scale Vehicle Sharing Systems via Closed Queueing Networks. Ph.D. thesis, The
Ohio State University (2012)
- Public Bureau
- Roads
Bureau of Public Roads: Traffic Assignment Manual. Tech. rep., U.S. Department
of Commerce, Urban Planning Division, Washington, D.C (1964) (1964)
Kockelman: A general framework for modeling shared autonomous vehicles
- Michael W Levin
- Tianxin Li
- Stephen D Boyles
- M Kara
Michael W. Levin, Tianxin Li, Stephen D. Boyles, Kara M. Kockelman: A general
framework for modeling shared autonomous vehicles. In: 95th Annual Meeting of
the Transportation Research Board (2016)
A general framework for modeling shared autonomous vehicles
- M W Levin
- T Li
- Boyles
- Sd
- K M Kockelman
Many Americans are just a plug away from owning an electric car
- E Evarts
Could self-driving cars spell the end of ownership
- D Neil
Dan Neil: Could Self-Driving Cars Spell the End of Ownership? wsj.com (2015)
Pricing in ride-sharing platforms: A queueing-theoretic approach