UC Berkeley

Travel time variability is a perennial problem for both bus transit operators and passengers. On the operations side, travel time variability is caused by variations in traffic effects and station dwell times. These variations lead to a longer cycle time for transit vehicles which increases operating costs. Passengers experience longer out-of-vehicle waiting times when buses are late or headways are unstable. Lateness and instability are also likely to increase the expectation and variance of transfer times, which may be the largest source of travel time variability for transferring passengers. Making matters worse, other works have found that out-of-vehicle waiting time is the part of transit trips that passengers find most onerous. To address the problem of travel time reliability, this work proposes a system of conditional signal priority (CSP) which aims to keep buses on schedule and help them to recover from delays. The use of CSP opens the door for a complementary strategy of transfer coordination, which can further reduce out-of-vehicle waiting time and make transit more reliable for passengers.

Previous papers have considered conditional signal priority, but only in the context of a case study for a particular corridor. No general evaluation has been done, and the potential for reducing travel time variability has been noted but not quantified. The literature on transfer coordination is more developed, but no previous papers have considered multiple connecting buses, uncertain information, or the use of CSP to recover holding delay. Transfer coordination strategies have also been developed for aviation and passenger rail, but these methods are not well suited to buses. Buses have an ability to act independently in a way that these other modes do not.

The strategy of conditional signal priority is based on the rule that buses can request priority at signals only when they meet a certain condition. In the simplest form of the strategy, this condition is that the bus is late. Given this rule, the main control guide is the bus schedule. On a long homogeneous corridor schedules can be defined by their commercial speed (or, inversely, average pace). The schedule pace is treated as a control parameter, with possible values ranging from the pace with priority at all signals (referred to as transit signal priority (TSP)) to the pace with no signal priority (referred to as no control). The strategy is distributed, so each bus is an independent decision maker which decides whether or not to request priority as it is approaching an intersection. Several assumptions make it possible to consider one bus and one signal at a time. First, the pairing effect is ignored. Second, conflicting requests are possible but are resolved with simple rules and are therefore modeled as random events. Third, there is assumed to be one station per block. The arrival time within each cycle is therefore assumed to be random because of the variability introduced by the intermediate station (which could be skipped or have a random dwell time) and traffic effects. When a request is made, signals respond with green extensions or early greens when possible to accommodate buses, as in most TSP implementations. Buses are assumed to have a queue jump or reserved bus lane at intersections so that they can depart as soon as the signal turns green. This assumption obviates the need to consider queues of other vehicles. Variations of CSP are proposed which use signals to delay buses, select control actions based on the predicted outcome instead of the current state, and introduce a threshold that modifies the condition for requesting priority. It is argued that the schedule deviation of a bus controlled by CSP can be represented by a Brownian motion with two-valued drift representing the cases when schedule deviation is above or below the condition for requesting priority, respectively. The Brownian motion representation leads to formulas for the expected value and variance of schedule deviation in steady state conditions. Similarly, Brownian motion can predict the expectation and variance of distance to recovery after a delay.

Simulations of a single CSP-controlled bus over a long corridor show that a steady state is reached where the Brownian motion formulas accurately predict performance. It is acknowledged that not all bus routes are long enough to reach steady state or to fully recover from a long delay. Nevertheless, a comparison with no control and TSP shows that CSP has better schedule adherence regardless of route length. Simulations of the variants show that using signals to delay buses would be highly disruptive to signal timing and therefore to other vehicles, that selecting control actions based on predicted outcome could avoid overcorrection, and that nonzero threshold values are useful when schedule pace cannot be optimized to balance the two values of drift.

Next, a strategy of transfer coordination is introduced which is made possible by the communications technology and delay recovery mechanism that CSP-controlled buses possess. The transfer coordination strategy is distributed. Each bus looks for the optimal holding time based on available information when it arrives at a transfer point. The optimal holding time is obtained by constructing a cumulative arrival curve for transferring passengers and comparing it to the holding cost, including downstream effects. A case study constructed from observations at a transfer point in Oakland, California shows that this method could reduce transfer delay (the out-of-vehicle waiting time of transferring, through, and downstream passengers) by 30% or more. Simulations show that the strategy never leaves passengers worse off, even with uncertain information.

This work addresses the problem of travel time variability in bus transit systems and its consequences for passengers, namely an increase in out-of-vehicle waiting time due to late buses and missed transfers. The core of this work is a strategy of conditional signal priority, which is shown to guide buses to a steady state and to provide a mechanism for delay recovery. The delay recovery mechanism, in particular, allows for complementary strategies. To this end, an optimal control strategy for transfer coordination is developed. This strategy advances the state of practice by considering multiple connecting buses, uncertain information, and downstream effects.

Finally, both control strategies have been described in a general way that can be extended to all bus routes that meet the technological requirements. They are designed to run in the background and take action only when needed. Routes where priority is not available at all signals or where the use of priority is constrained by other control strategies are acceptable provided that the bus schedule is adjusted to reflect these restrictions. Similarly, the transfer coordination method can be applied at all transfer points.

This form of conditional signal priority which considers one bus at a time can be generalized to headway-based service. However, there are likely to be additional benefits from considering forward and backward headway when pairing is of concern and a variant of CSP with this feature will be developed in future work.