A short-term management strategy for improving transit network efficiency

American Journal of Applied Sciences, Feb, 2009 by Amir Samimi, hedayat Z. Aashtiani, Abolfazl (Kouros) Mohammadian

INTRODUCTION

Public transit system, a basic part of the transportation network in urban areas, benefit society by providing mobility to people in shared vehicles. Although transit-oriented development may not always be the best way, it is one of the best solutions for transportation problems in large cities and is being focused on frequently, especially in the metropolitan areas. Public transit systems have attracted the attention of both public and private sectors for a while and have drawn lots of investments.

A significant component of a public transit system is the bus network, which has had considerable research but still needs more advanced and comprehensive methods of design, operation and maintenance. Improving the current condition of bus networks might be performed in several ways such as increasing or improving the service. Since two essential parts of the design process of an urban bus network are determining the bus routes and setting the vehicle frequencies, both bus routes and the associated frequencies might be examined to improve current operating conditions. Ideally, both fleet assignment and route selection should be modeled simultaneously. Some optimization methods have been practiced for uncongested networks (1), however for overcrowded networks the pure optimization problems would be unmanageable and require more simplification. A common simplifying assumption is to separate the problems and approximate the optimal solution by means of heuristic algorithms. In addition to the complexity of the bus network design that presses the researchers to split it up into the fleet assignment and route selection problems, the short term nature of the fleet assignment problem requires it to be solved independent of the route selection problem. Unlike fleet assignment, route selection should be considered a long term problem. In other words, system operators should not change the bus routes very often, even if it benefits total system revenue in the short term. In general, forcing users to change their travel patterns makes them unhappy about the system and has a negative impact on their satisfaction, which leads to a decline in their long term use. On the other hand, fleet assignment could be used in short time spans as a strategy that is both economical and imperceptible to the users to avoid such inefficiencies in the system. Therefore, a reliable fleet assignment algorithm could be a helpful short term management tool for the transit network operators. The main objective of this paper is to propose a simple approach to effectively manage the fleet in a bus network.

Transit Assignment: In most of the bus network studies, a transit assignment procedure has been utilized in order to have a good representation of passengers' decision making process in a transit system. Any transit trip may be broken into four different movement types: walking, boarding, riding and alighting movements. Transit assignment predicts the behavior of all the passengers in choosing the movements, given the origin-destination (OD) demand matrix and network specifications. In order to minimize the waiting time, each traveler considers a set of attractive lines at each boarding node and the first bus that belongs to this set with at least one vacant place would be taken. Part of the complexity of the transit assignment problem arises from the stochastic nature of a passenger's waiting time, which is relative to the boarding movement. This problem has been investigated by many researchers, including Spiess and Florian (2), DeCea and Fernandez (3) and Babazadeh and Aashtiani . In a seminal study, Spiess and Florian formulated the transit assignment problem in a linear optimization framework. The optimization problem was called Optimal Strategy and a 2-step solving algorithm was proposed for that. The algorithm finds the optimal strategy at the first step and then assigns the demand to that strategy.

DeCea and Fernandez (3) introduced a transit assignment algorithm for congested bus networks by controlling the capacity of transit lines and stations. In this model, the passengers who are not able to take their desired bus, reroute their trip to less crowded lines in order for the model to capture the capacity restrain. Recently, Babazadeh and Aashtiani (4) formulated the transit assignment problem in a series of complementary equations and replicated the congestion effect in the transit network perfectly. Because of the size and also nonlinearity of the complementary model, it was almost impossible to find the equilibrium solution for an extensive network. A practical solving algorithm was suggested to lessen the problem size and make it solvable for the real conditions. The algorithm consists of a bi-level decomposition pattern and a recursive route generation procedure. Nonlinearity of the model was resolved by linearizing the links' travel times. This model is able to control the transit line capacity by imposing enough penalty to the congested lines. The penalty function, shown in Equation 1, is added to all the links and is capable of keeping the flow of the link under maximum capacity by any desired accuracy.