Reliability Based Disaggregate Stochastic Process Models with Strict Capacity Constraints in Congested Transit Networks

Reliability is considered the most important attribute of transit service by passengers. There are congested transit environments wherein even if a transit service is perfectly on schedule it is termed unreliable from a passenger’s perspective when they are unable to board the first service of their choice set. The phenomenon ‘failure to board’ arises in congested transit networks having strict physical capacity constraints wherein the transit service cannot take in passengers beyond its capacity. This results in some of the passengers being left waiting for the next service at the transit stops.
The existing transit assignment models; be it hyperpath based effective frequency models, Bureau of Public Roads (BPR) based route section models or aggregate stochastic process models with strict capacity constraints, all assume that the passengers have perfect knowledge of the network seldom discussing the sources of such information. In the current thesis this assumption is renounced and a reliability based disaggregate stochastic process model with strict capacity constraints (R-DSPM) using route section approach is proposed such that each passenger in the absence of information updates his/her route choice based on their individual experience. Though the aggregate stochastic process model implements the strict capacity constraint for each transit service generated; the model along with the assumption of perfect knowledge of the network assumes that the passengers are risk neutral. The proposed R-DSPM implements a strict capacity constraint for each transit service generated thereby accounting for failure to board situation in congested network. The proposed model differs from the existing aggregate stochastic process model in its assumption of risk averse passengers. Risk aversion in R-DSPM considers variance associated with:- interarrival times of transit service at the transit stop; the waiting time of passengers due to the ‘failure to board’ condition; the in-vehicle travel times of routes comprising of route sections containing more than one attractive line section and the variable demand generated for each day’s travel. The risk aversion of each passenger is accounted for in R-DSPM through the linear combination of mean total travel time and total travel variance (mean-variance) and a linear combination of mean total travel time and expected lateness (mean-lateness). A generic day to day framework is developed with markovian properties such that it enables the integration of both mean-variance and mean-lateness costs with ease and results in a unique stationary distribution of costs and flows for each route.
The proposed R-DSPM thus accounts for: strict capacity constraints of transit vehicle, passengers learning process, risk aversion of passengers, differences in passenger perceptions, day to day variability in demand and supply of transit network. The micro simulation framework shows through implementation on example networks that while accounting for passenger’s risk aversion the R-DSPM is able to arrive at a unique stationary distribution irrespective of its initial conditions. The sensitivity of the proposed R-DSPM with strict capacity constraint under different parameter assumptions has been carried out .
A calibration of the parameters involved in the route section based BPR styled cost function and the hyperpath based effective frequency cost function using the proposed R-DSPM indicates that different congestion function parameters are required for different sections of a transit network. It is also shown through implementation on an example network that the proposed R-DSPM framework enables the passengers to learn about the reliability of routes and strategies. At higher dispersion values R-DSPM assign risk averse passengers such that the standard deviation of flows and experienced total travel time on various routes and strategies are lesser than that obtained by accounting for risk aversion using the aggregate stochastic process models.
The impact of accounting for risk aversion on various policy measures that could be carried out by the operators to improve the waiting time reliability of passengers is also assessed using the proposed R-DSPM with strict capacity constraints. It is shown that for certain parameter assumptions and for certain policy measures the assumption of risk aversion in transit assignment could result in an entirely different reliability profile from that of an assignment process assuming risk neutral passengers. The implementation of the proposed R-DSPM with strict capacity constraints on a real network has been carried out on a section of London underground and several possible policy measures have been evaluated. The evaluation of policies has further emphasised the need to consider the risk aversion in passengers especially to account for the number of passengers preferring to make a transfer (in absence of transfer penalty) at the transfer stops to minimise their risk aversion costs.