Hindawi Journal of Advanced Transportation Volume 2017, Article ID 2960728, 9 pages https://doi.org/10.1155/2017/2960728 Research Article Real-Time Integrated Limited-Stop and Short-Turning Bus Control with Stochastic Travel Time Hu Zhang, Shuzhi Zhao, Yang Cao, Huasheng Liu, and Shidong Liang College of Transportation, Jilin University, Changchun 130022, China Correspondence should be addressed to Yang Cao; [email protected] Received 12 March 2017; Revised 20 May 2017; Accepted 6 June 2017; Published 12 July 2017 Academic Editor: Seungjae Lee Copyright © 2017 Hu Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. In a traditional transit system, passenger arrival time and bus running time are typically random and uncoordinated. This randomness gives the appearance of unbalanced passenger demand and unreliable transit services. Therefore, this paper proposes a real-time control method for bus routes. In our method, buses skip some stations and turn back at appropriate stations, in order to balance passenger demand along the bus route and improve the overall transit service. Our real-time control method considers the typical changes in passenger demand and the stochastic travel time of buses. In this paper, the number of controlled vehicles at any given time is determined, and the bus holding time at the turn-back station is adopted. When implemented correctly, the optimal scheme indicates which stations should be skipped, where it is suitable for buses to turn back, and how long the holding time should be at turn-back stations, which in turn will minimize the total cost of a transit system. This paper formulates such an integrated strategy, presents the solution method of the formulation, and proves the validity of the real-time control method. 1. Introduction (APC). These technologies can effectively assure that vehicle movements and passenger flows can be fairly and accurately In virtually any transit system, passenger demand is unbal- predicted over a short time interval. With regard to real- ancedalongthebusroute.Also,thetimeittakesthebusto time control strategies, many studies have been conducted travel the designated route cannot be consistent in practice, on bus holding strategies. Turnquist and Blume [1] found that because of road traffic situations and driver operating habits, holding strategies could be used to increase service regularity. which combined to make the change of travel time stochastic. Abkowitz and Lepofsky [2] proposed holding buses at appro- Various levels of passenger demand at different stations and priate stopping points and then dispatching them when a stochastic travel time can decrease the transit service quality minimum headway time could be achieved, thus minimizing when buses run along their same routes with the same the total passenger waiting time. Considering safety head- operation techniques employed all day, every day. Without ways, Eberlein et al. [3] set a rolling horizon and presented additional strategies, public resources cannot be fully utilized. a formulation to minimize the total waiting time. Their re- In addition, the variety of factors mentioned above and the search results indicated that holding could reduce dwelling stochastic changes brought about will create a “bus bunching” time and interstation stopping time. Fu and Yang [4] argued, effect and increase passenger waiting time. Thus, a real-time however, that large headway variations would increase the control strategy should be implemented among the transit waiting time. As such, they proposed holding buses at a single system routes as a means to avoid confusion surrounding bus station, in order to minimize headway variations. Delgado operations and to improve the level of service. et al. [5] proposed an integrated holding and boarding limits Lately, ITS technologies have been widely applied to tran- strategy. This strategy does not allow passengers to board sit system operations. These technologies include automatic buses once the strategic limit has been reached, even when vehicle location (AVL) or automatic vehicle identification the bus in question has sufficient capacity to take additional (AVI) systems, as well as automatic passenger counters passengers. 2 Journal of Advanced Transportation N N/2 + 1 Meanwhile, operational strategies (whereby buses do not ······ need to serve all stations along the route) are controlled Terminal through a real-time method. Various operational strategies Terminal have been proposed, including short-turning, deadheading, ······ 12 N/2 and limited-stop services [6–8]. To increase the speed of a subway service, Suh et al. [9] formulated a stop-skipping Figure 1: The transit route. strategy on a rail system. This formula used an OD matrix, the distances between stations, and departure intervals. Fu et al. [10] proposed a real-time control strategy that would N N/2 + 1 ······ provide a limited-stop line every second trip, thus mini- mizing total waiting time costs. In addition, a rolling time horizon approach was used to define the stops which could be skipped. Sun and Hickman [11] also presented a stop- skipping strategy. However, their strategy merely restricted theboardingofpassengersattheskippedstationswherepas- sengers were still allowed to alight. Sidi et al. [12] considered a disruption strategy. Sidi et al. proposed a multiobjective optimization approach to determine which stations should be ······ skipped, as well as the departure time of the controlled buses. 12 N/2 Cortes´ et al. [13] and Saez´ et al. [14] proposed an integrated stop-skipping and holding strategy, which was intended High demand Low demand to minimize waiting time costs and the passengers’ in- Figure 2: The integrated limited-stop and short-turning strategy. vehicle time. In these strategies, GAs were used to solve the formulation. Yu et al. [15] presented a partway deadheading strategy to improve transit service. This method determines the controlled vehicles by a reliability assessment of fur- 2. Problem Setting ther transit services. Munoz˜ et al. [16] compared several of the mechanisms which had already been proposed in 2.1. Stop-Skipping Strategy Description. This paper considers various studies and then estimated the validity of those stud- a transit route with stops, as shown in Figure 1. Buses ies. are dispatched from terminals 1 ()and/2 + 1 (/2), Obviously, some of these previous studies indicate that according to a given schedule. In one direction, buses operate real-time control strategies can increase service regularity from Station 1 to Station /2. In the other directions, station and reduce the overall cost of a transit system. This paper /2 + 1 and station are the starting and ending terminals, proposes and reveals a real-time integrated limited-stop and respectively. We assume the largest passenger demand is close short-turn strategy. Our limited-stop strategy allows buses to station 1 (). to skip some stations, in order to better serve high-demand The integrated limited-stop and short-turning strategy areas and times and thus can balance the demand distribution is different from the regular transit service, as shown in along the bus route. The short-turn strategy is a useful means Figure 2. Buses use the integrated limited-stop and short- bywhichtoreducebusrunningtime.Inthisstrategy,buses turning strategy service high-demand stations and skip the turn back to service the return direction of their route, thus low demand stations. Meanwhile, some buses may turn back creating a shorter cycle. What is more, in order to reflect the before they reach the low demand station, if the stations near realityofthetransitsystem,theimpactofstochastictravel terminals /2+1 (/2) in both directions have low demand. time is considered. In this paper, the holding time at the turn- Stop-skipping and turn-back services are therefore able to back station is determined, and the numbers of vehicles to be supply more buses for high-demand stations. controlled at any given time are calibrated. The results of our An integrated limited-stop and short-turning strategy test indicate that our real-time integrated strategy can reduce can allow buses to serve stations with higher demand. the total operating cost. In addition, implementing the hold- Considering that passenger demand cannot always be high ing strategy at turn-back stations can have a significantly pos- before the turn-back station, the buses using the integrated itive effect on the overall result. Following this introduction, strategy will firstly operate a limited-stop service, in order Section 2 describes our integrated strategy and establishes to reduce the riding time of in-vehicle passengers. Secondly, formulations to express the arrival time, departure time, and under the short-turning strategy, buses will turn back to holding time of buses. Section 3 establishes the objective skip those stations with low demand when driving in both function to minimize the total transit system cost. Section 4 directions. This in turn will, to a great extent, reduce bus travel presents our solution methods to solve the objective function. time. Since passenger transfers must be considered, a fleet of Section 5 determines the number of controlled vehicles and buses which operate an all-stop service will be utilized in our tests the real-time integrated strategy, comparing our results integrated strategy. The decisions regarding which stations to other strategies. Finally, Section 6 presents our conclu- can be skipped and whether or not a turn-back action should sions. be used will be controlled in real-time. Journal of Advanced Transportation 3 N−j㰀 +1 A real-time control problem is dynamic in nature. We ······ consider that there is a group of controlled vehicle trips at any given time. There are −1vehicles to be controlled with the integrated strategy. Meanwhile, the th vehicle is also controlled and just operates with normal service. Those tℎ +tR controlled buses are denoted as , +1,...,+−1.Thus,the i,j㰀 j㰀 ,N−j㰀 +1 buses −1and +will service all stations.