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In most of transportation literature, users are assumed to be perfectly rational in minimizing their own travel costs or perceived travel costs. However, users may not be perfectly rational in implementing their choices in reality. There exists a kind of boundedly rational users, that is, oblivious users. These oblivious users make their route choices by simple criteria, for example, selecting the shortest (or the most direct) route only based on physical distance or simply following routes recommended by a GPS system. This paper investigates how the existence of oblivious users affects the equilibrium bus line choice behavior in a public transit system. And we propose a method to design a more realistic system.

The purpose of this paper is duple to advance our understanding on the boundedly rational behavior of public transit users when choosing bus lines in a transit network and to design a more realistic public transit system when considering the boundedly rational users.

In the literature, user equilibrium models play an important role in the traffic assignment problems. By assuming that all road users behave in a completely rational way and seeking to minimize their own disutility, Wardrop [

The third equilibrium type is boundedly rational user equilibrium (BRUE). As a relaxation of perfect rationality and optimality, the notion of bounded rationality was proposed by Simon [

Recently, Karakostas et al. [

The above studies are only subject to private car systems. In this paper, we will proceed to our study in a public transit system. In the microeconomic analysis of urban public transportation, two types of resources have to be taken into account: those provided by operators, such as vehicles, fuel, terminals, or labor, and those provided by users, namely, their time, usually divided into waiting, access for, and in-vehicle times. In addition, Kraus [

There is a kind of users, called oblivious users, who make their bus lane choices without caring about the delay and in-carriage congestion experienced. Their decisions rely on simple criteria, for example, finding the most direct line from the transit map. Recently, Raveau et al. [

The remainder of this paper is organized as follows. In Section

In order to explore the analytical results, we proceed to the study in a simple transit network as shown in Figure

A transit network with two lines.

In Figure

Under this setting, two bus lines, Line A and Line B, are designed to serve the demand

We assume that the percentage of oblivious users among all commuters is

The total cost

The body congestion cost is formulated by

For a constant arrival rate of passengers and regular bus headways, the average waiting time

Because the commuters who choose Line B have to transfer at node

The in-vehicle time includes the bus running time, the time waiting for other commuters’ boarding at origin, and the time waiting for other commuters’ alighting at destination. For different bus lines, the in-vehicle time is different.

For Line A, the in-vehicle time is

For Line B, there is a transfer at node

An equilibrium state is reached when all commuters are satisfied with their bus line choice. In other words,

For facilitating the presentation of the essential idea, we assume that the passenger/capacity ratio of each line is larger than 1 and

Clearly, the above bus line split solution is affected by the bus cycle running time, bus frequency, capacity, and fare. Next, we derive some results in three special cases.

Equation (

Equation (

Equation (

When oblivious users are considered, that is,

If

Substituting (

Obviously, in (

Consider a corner of the initial state that all oblivious users choose Line A and all rest rational users choose Line B.

If

If

In this proposition, the parameter

In this section, we only consider the situation that

For Lines A and B, suppose that the parameters

For Line A, the VRC can be written as a function of frequency only as follows:

Equation (

Making it equal to zero and noting that the second derivative is positive, we get the optimal frequency of Line A:

In this paper, we studied the equilibrium bus line choice behavior with oblivious users and investigated how the equilibrium state is affected by these users. We further optimized each line’s bus frequency of the transit system. Oblivious users are those who stubbornly adhere to some options, regardless of actual conditions. Obviously, such users or passengers indeed exist in reality. Hence, we have to consider them when formulating the option choice model. Our on-going work is to calibrate the model parameters and extend the proposed approach to explore the types of behavior in more complex transit networks.

The authors declare that there is no conflict of interests regarding the publication of this paper.

The work described in this paper was supported by a Grant from the National Basic Research Program of China (2012CB725401).