In this seminar we discuss two applications of real time optimization in bus transit scheduling. We specifically focus on operations of high frequency buses serving curbside bus stops. During bus daily operations, there are two kinds of phenomena that can affect the level of bus service in a major way, namely the queueing of buses at bus stops and the bunching of buses during their transit times between stops. Bus queues are common at curbside stops and may cause significant delays; bus bunching of buses of the same bus line is frequently observed and can impair the reliability of bus service.
Overtaking is a standard maneuver used by buses at curbside stops. When overtaking is allowed, the analysis of the bus queues becomes more difficult, since such maneuvers violate the first-in-first-out rule and affect the capacity of the bus stop as well as the average waiting delay. It is important to understand the effects that overtaking maneuvers have on bus operations at stops. In general, there are two kinds of overtaking maneuvers, namely overtaking-in and overtaking-out. We consider four different bus overtaking rules at curbside stops, and analyze four related queuing models with finite tandem berths. Furthermore, a more general queueing model with overtaking maneuvers occurring at random is presented. Through simulation, the accuracy of the models and the effects of the coefficient of variation of the dwell times on the waiting delays are examined. Theoretical analyses as well as simulation results show the positive effects overtaking has on the capacities of bus stops and on the expected average delays at curbside stops when dwell times are varied. A comparison of different overtaking maneuvers reveals performance differences among the various rules, and shows why buses should rather be encouraged to overtake when departing a stop than when entering it.
With regard to bus bunching, a new optimization-based control method is proposed to alleviate corresponding adverse effects. Since the conventional holding method may not be suitable for implementation at curbside stops, we choose to control bus cruising speeds between stops. A holding model M0 and a model M1, which decide the travel times between stops, are considered. In order to make control decisions easy to understand as well as to implement, an improved speed-control model M2 is further proposed. All the models allow for control decisions in real time based on the state of the entire system. The three models are programmed in a rolling horizon scheme within a simulation system. Simulation experiments are conducted to examine these models in different scenarios associated with different levels of traffic randomness. Two merits of the speed-control method are unveiled based on experimental results. In addition, the improved model M2 is more attractive than the other two models, especially when traffic randomness is high. The practical applications of the proposed speed-control models are discussed.