Control Strategies for an Idealized Public Transportation System
TL;DR: In this paper, the problem of determining the optimal strategy (dispatch or hold) for a system of m vehicles is formulated as a dynamic programming problem and analyzed in detail for m = 1 and m = 2.
Abstract: Vehicles load passengers at a single service point and, after traversing some route, return for another trip. The travel times of successive trips are independent identically distributed random variables with a known distribution function. After a vehicle returns to the service point, one has the option of holding it, or dispatching it immediately. Passengers arrive at a uniform rate and the objective is to minimize the average wait per passenger. The problem of determining the optimal strategy (dispatch or hold) for a system of m vehicles is formulated as a dynamic programming problem. It is analyzed in detail for m = 1 and m = 2. For m = 1, the optimal strategy will hold a vehicle if it returns within less than about half the mean trip time. For m = 2, and for a small coefficient of variation of trip time C(T), the optimal strategy will control the vehicles so as to retain nearly equally spaced dispatch times, within a range of time proportional to C4/3(T).
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TL;DR: In this paper, the authors propose an adaptive control scheme to mitigate the problem of short headway on busy lines by dynamically determining bus holding times at a route's control points based on real-time headway information.
Abstract: Bus schedules cannot be easily maintained on busy lines with short headways: experience shows that buses offering this type of service usually arrive irregularly at their stops, often in bunches. Although transit agencies build slack into their schedules to alleviate this problem - if necessary holding buses at control points to stay on schedule - their attempts often fail because practical amounts of slack cannot prevent large localized disruptions from spreading system-wide. This paper systematically analyzes an adaptive control scheme to mitigate this problem. The proposed scheme dynamically determines bus holding times at a route's control points based on real-time headway information. The method requires less slack than the conventional, schedule-based approach to produce headways within a given tolerance. This allows buses to travel faster than with the conventional approach, reducing in-vehicle passenger delay and increasing bus productivity.
383 citations
TL;DR: In this article, a genetic algorithm is developed to solve the multi-station problem through a special binary coding method that indicates a train departure or cancellation at every possible time point, and a local improvement algorithm is presented to find optimal timetables for individual station cases.
Abstract: This article focuses on optimizing a passenger train timetable in a heavily congested urban rail corridor. When peak-hour demand temporally exceeds the maximum loading capacity of a train, passengers may not be able to board the next arrival train, and they may be forced to wait in queues for the following trains. A binary integer programming model incorporated with passenger loading and departure events is constructed to provide a theoretic description for the problem under consideration. Based on time-dependent, origin-to-destination trip records from an automatic fare collection system, a nonlinear optimization model is developed to solve the problem on practically sized corridors, subject to the available train-unit fleet. The latest arrival time of boarded passengers is introduced to analytically calculate effective passenger loading time periods and the resulting time-dependent waiting times under dynamic demand conditions. A by-product of the model is the passenger assignment with strict capacity constraints under oversaturated conditions. Using cumulative input–output diagrams, we present a local improvement algorithm to find optimal timetables for individual station cases. A genetic algorithm is developed to solve the multi-station problem through a special binary coding method that indicates a train departure or cancellation at every possible time point. The effectiveness of the proposed model and algorithm are evaluated using a real-world data set.
369 citations
TL;DR: This paper formulates the holding problem as a deterministic quadratic program in a rolling horizon scheme, and develops an efficient solution algorithm to solve it, and tests the algorithm and the impact of the resulting holding policies.
Abstract: Holding is one of the most commonly used real-time control strategies in transit operations. Given a transit network and its operations plan, the holding problem is to decide at a given time at a control station, which vehicle is to be held and for how long, such that the total passenger cost along the route is minimized over a time period. Previous research on the holding problem has always assumed no real-time information available. Such an assumption not only poses great difficulties in solving the problem, but also limits practical applications in a real-time, dynamic operations environment. In this paper we formulate the holding problem as a deterministic quadratic program in a rolling horizon scheme, and develop an efficient solution algorithm to solve it. Using headway data collected by an automated system, we tested the algorithm and evaluated the impact of the resulting holding policies. Important and interesting properties of the holding solution, obtained from both theoretical and computational analyses, are presented.
277 citations
TL;DR: This paper proposes an adaptive control scheme that adjusts a bus cruising speed in real-time based on both, its front and rear spacings much as if successive bus pairs were connected by springs, and is shown to yield regular headways with faster bus travel than existing control methods.
Abstract: Schedule-based or headway-based control schemes to reduce bus bunching are not resilient because they cannot prevent buses from losing ground to the buses they follow when disruptions increase the gaps separating them beyond a critical value. This critical gap problem can be avoided, however, if buses at the leading end of such gaps are given information to cooperate with the ones behind by slowing down. This paper builds on this idea. It proposes an adaptive control scheme that adjusts a bus cruising speed in real-time based on both its front and rear spacings, much as if successive bus pairs were connected by springs. The scheme is shown to yield regular headways with faster bus travel than existing control methods. Its simple and decentralized logic automatically compensates for traffic disruptions and inaccurate bus driver actions. Its hardware and data requirements are minimal.
265 citations
Cites background from "Control Strategies for an Idealized..."
...1There is also a literature dealing with small systems and strategies that do not fully use available real-time information; e.g., Osuna and Newell (1972), Barnett (1974), Newell (1974), Ignall and Kolesar (1974), Hickman (2001) and Zhao et al. (2006)....
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TL;DR: In this article, a family of dynamic holding strategies that use bus arrival deviations from a virtual schedule at the control points is proposed, which can both closely adhere to a published schedule and maintain regular headways without too much slack.
Abstract: As is well known, bus systems are naturally unstable. Without control, buses on a single line tend to bunch, reducing their punctuality in meeting a schedule. Although conventional schedule-based strategies that hold buses at control points can alleviate this problem these methods require too much slack, which slows buses. This delays on-board passengers and increases operating costs. It is shown that dynamic holding strategies based on headways alone cannot help buses adhere to a schedule. Therefore, a family of dynamic holding strategies that use bus arrival deviations from a virtual schedule at the control points is proposed. The virtual schedule is introduced whether the system is run with a published schedule or not. It is shown that with this approach, buses can both closely adhere to a published schedule and maintain regular headways without too much slack. A one-parameter version of the method can be optimized in closed form. This simple method is shown to be near-optimal. To put it in practice, the only data needed in real time are the arrival times of the current bus and the preceding bus at the control point relative to the virtual schedule. The simple method was found to require about 40% less slack than the conventional schedule-based method. When used only to regulate headways it outperforms headway-based methods.
240 citations
Cites background from "Control Strategies for an Idealized..."
...Among the literature that analytically addresses the bus bunching problem with holding methods, most of the studies (Osuna and Newell, 1972; Newell, 1974; Barnett, 1974; Hickman, 2001; Eberlein et al., 2001; Zhao et al., 2006) try to minimize passenger time (either waiting time at the station only…...
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...The problem can be also alleviated with holding strategies that do not leave passengers stranded; see e.g. the pioneering works in Osuna and Newell (1972), Newell (1974), and Barnett (1974)....
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...Among the literature that analytically addresses the bus bunching problem with holding methods, most of the studies (Osuna and Newell, 1972; Newell, 1974; Barnett, 1974; Hickman, 2001; Eberlein et al., 2001; Zhao et al., 2006) try to minimize passenger time (either waiting time at the station only or both waiting at the station and riding time on board)....
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