Study on Optimal Frequency Design Problem for Multimodal Network Using Probit-Based User Equilibrium Assignment

Abstract

In this paper, a probit-based multimodal transport assignment model is developed. Three transport modes (railway system, bus system, and automobiles) and their interactions are considered. The walking time to a bus stop or a station also plays an important role in multimodal networks. Thus, walking to a bus stop or to a railway station is included in the model. The factors affecting travelers’ route choices considered in this model include actual travel times, discomfort effects on transit systems, expected waiting times, fares, and constants specific to transport modes. A route in the model may be composed of different modes. The paper also deals with the optimal transit frequency design problem. The frequency design problem is formulated as an implicit program in which the objective function of total disutility in the multimodal network is minimized with respect to frequencies of transit lines. The flows on a multimodal network follow a probit-based stochastic user equilibrium assignment. A numerical example is presented.

On the allocation of new lines in a competitive transit network with uncertain demand and scale economies

“…A6 The effects of the scale economies of transit operations are explicitly considered in the definition of the transit operating cost and of the profit function of the operators. This relaxes the assumption that the transit operating cost is a linear function of the service frequency or fleet size made in many previous related studies, including those of Yang and Woo [3], Uchida et al [18], and Li et al [6].…”

“…A4 Transit passengers make their travel choice decisions based on a tradeoff between the service quality and travel disutility of different transit services. Travel disutility is measured by the weighted sum of the in-vehicle travel time, passenger waiting time at transit stops, in-vehicle crowding discomfort, and the transit fare [2,6,17,18].…”

“…Hence, passengers cannot decide beforehand which line to board between any pair of two consecutive transfer stops on their journeys. Here, it is assumed that passengers boarding or waiting at a transit link will be allocated to each line in the set of attractive lines associated with that link in proportion to the service frequencies of the lines [6,14,18].…”

“…Corollary 1 shows that the chance-constrained model (12)-(16) is actually equivalent to the robust (or mean-variance) model (18)- (21) with simple bound constraints. The sign of F À1 ð1ÀaÞ in objective function (18) reflects the risk attitude of the transit operators. Specifically, F À1 ð1ÀaÞ < 0 (or equivalently, a > 0:5) means that the transit operators are risk averse and F À1 ð1ÀaÞ ¼ 0 (or equivalently, a ¼ 0:5) means that they are risk neutral.…”

“…As previously stated, the risk attitude of the transit operators can be measured by the value of the parameter a in Equation (13) or Equation (18). To determine the effects of the risk attitude of the transit operators, the optimal solutions at a high level of potential demand variation (i.e., twice the base case) are compared for two values of a (i.e., 90 and 50%), as shown in Table III.…”