A two-stage policy for improving the efficiency of the traffic network by providing value-added ATIS service

. Based on the pay-per-use charge in mobile Apps, value-added advanced traveler information systems (VATIS) service can be provided in traffic networks. From the perspective of the traffic manager, we propose a two-stage policy for improving the efficiency of traffic networks by providing VATIS service. At the first stage, the traffic manager selects several ATIS service providers, then offers seed fund to each of them to encourage VATIS service provision. At the second stage, the traffic manager announces a given target of the total market penetration of VATIS service and encourages service providers to achieve it together. If they could complete the task, compensation will be paid. To evaluate the efficiency of this policy, four scenarios are formulated by four bi-level models, and the total travel time is set as the evaluation indicator. Numerical experiments show that, the suggested policy can reduce total travel time dramatically if the market penetration target has been appropriately selected.


Introduction
In previous years, people used to make their travel decisions with the aid of vehicle navigation systems, which are the predecessor of Advanced Traveler Information System (ATIS). At that time, ATIS service providers can sell navigators and charge for map updating services to gain profit. However, due to the severe competition in the ATIS market, nowadays almost all ATIS service providers (e.g., Goggle Map or Amap) offer the basic route guidance service for free. In this case, they begin to seek for profit by providing the value-added ATIS (VATIS) service based on the evidence that people are willing to pay to the save travel time [1][2][3][4][5]. As an actual example, Amap offers several kinds of valueadded services to travelers, such as taxi service, hotel reservation, and online coupons obtaining, which are bringing Amap a tidy profit. Consequently, ATIS service providers are dedicated to maximize their market scales in this new era. That can also contribute to enhancing the efficiency of the traffic networks [6]. But the expensive operating cost for collecting traffic information is the major limitation for ATIS service providers [7], especially when the information quality is required to be as accurate as possible. Thus, policies for supporting ATIS service providers, mainly by finance support, need to be issued.
In this study, we suggest a two-stage policy from the perspective of the traffic manager. At the first stage, the traffic manager selects several ATIS service providers, and offers seed funds to each of them. Considering that ATIS services of different service providers are coessential products, service providers will cooperate with each other after severe competition, then act as a community to maximize their profits. Then the policy should move to the second stage. The traffic manager announces a given target of the total market penetration of VATIS services and asks service providers to achieve it together. If they could complete the target, reasonable compensations will be paid to them.
If the traffic manager compensates service providers directly during the period of market competition and asks them to achieve fixed targets of the market penetration of VATIS services, it might be a tough work to decide which values of fixed targets should be set for each service providers, and how much compensates should be given. By dividing this policy into two stages, the policy can make full use of the market competition in the first stage, because the traffic manager can get a clear understanding of each service provider, so that both compensations and the fixed target of the total market penetration of VATIS services can be made more wisely and efficiently. Besides, compensations will be given to the community of service providers, this approach can avoid the trouble of setting sub-targets for every selected service provider.
We illustrate the evolution of traffic state of the traffic network where the two-stage policy implemented, by four cases, namely the basic case, the competition case, the cooperation case, and the restricted case. The basic case describes the initial state of the traffic network where only the basic ATIS service is provided, and it will be treated as the comparative standard of other three cases. The competition case and the cooperation case are used to depict market behaviour of VATIS service providers in the first stage. The restricted case presents the state of the traffic network in the second stage. Then, four models are proposed to formulate these cases, respectively. At last, the efficiency of the suggested policy is tested by the total travel time based on a traffic survey which is carried out in Hongkou district of Shanghai, China.
The study is structured as follows. In section 2, four models are developed for demonstrating the states of the traffic network after implemented the two-stage policy. Numerical analyses are given in Section 3 based on a traffic survey. Section 4 concludes this study.

Basic case: the initial state of the traffic network
Consider a traffic network ( , )  G N A which has N nodes and A links, its origin-destination (OD) matrices are given and fixed, and rs d (the set d ) denotes the total travel demand from origin r  R to destination s S . We assume that the basic ATIS service is provided for free, so there is no need to consider about their profit. Denote the basic ATIS service quality as 0  , then it can be used as the parameter of the Logit-based traffic assignment in the network. Therefore, the link flow pattern can be formulated by the following mathematical program:

Models for evaluating the efficiency of the two-stage policy
As we have mentioned in the introduction, the state of the traffic network after implemented the two-stage policy can be described by four cases: the basic case, the competition case, the cooperation case, and the restricted case. In this subsection, they are modeled in mathematical forms based on the bi-level models. In the lower-levels of these models, stochastic equilibrium theories will be applied to describe the equilibrium state of the traffic network. At the same time, the upper-levels of these models are formulated by profit functions of VATIS service providers. We will present the common lower-level model at first, and then give the upper-level models of three bi-level models one after another.

The mixed stochastic equilibrium state of the traffic network
Suppose that there has M VATIS service providers in the traffic network, and the set of VATIS service providers is denoted by . Let 0 m  be the initial class of travelers who only use the basic ATIS service for free, and mM  be the class of travelers who use the service of VATIS service provider m and pay for the service. Therefore, the whole set of travelers in the traffic network can be expressed as where m is the index of both VATIS service providers and the classes of travelers. Under assumptions of homogeneous travelers, principles of stochastic user equilibrium (SUE) [8], the mixed stochastic equilibrium model can be formulated as below: subject to ,, , ,, ,,   (14)-(15) is formulated in the similar way to Yang [9] has did,  and  are parameters in it.

Competition case in the first stage
At the first stage of the suggested two-stage policy, VATIS service providers will compete by altering their service strategies, including alter service prices and service qualities of themselves to maximize their profits. Denote m  as the profit of the m th VATIS provider, its pricing strategy as In equation (17), the first term is the total revenue of the m th VATIS service provider, the second term is the total operation cost of the m th VATIS service provider, im  is the cost coefficient of the cost related to the information quality and { : . We construct the operation cost function in the exponential form under the consideration of arguments of related literatures on ATIS service pricing [10][11][12].
It should be noted that the service quality and the service price are two sets of decision variables in the upper-level model of Model-2. If we simplify the competition case into a process of sequential decision making, the competition among VATIS service providers would turn out to be a Nash game [13]. The reaction method in game theory can be applied in analyzing the optimal solution of Model-2. Obtain the first order partial derivatives of m  with respect to m  and rs m  , and let them equal to 0, we can obtain the optimal decision of the m th VATIS service provider: The optimal solution should meet , , Solving Model-2, we have its optimal solution:

Cooperation case in the first stage
In most cases, service providers can gain more profit by cooperation, so in the first stage, VATIS service providers will choose cooperation after the drastic market competition.

Restricted case in the second stage
Cooperation among VATIS service providers may lead to the increasing of the total travel time and other loses of social welfare issues while they pursuing higher profit. The second stage of this policy is aimed at dealing with this problem by restricted measures. The specific approach is, the traffic manager promises to compensate

Find the suitable fixed market penetration target of VATIS service
To find the most suitable fixed market penetration target of VATIS services in the traffic network, an analysis on the fixed market penetration target of VATIS services has been conducted. In summary, we find that there has a stable value of the fixed market penetration fixed Q , in our experiments, it equals 0.80, where the biggest effectiveness of reducing the total travel time of the network can be attained. At the same time, a total compensation   (in our experiments,  should be larger than 10811 yuan) also needs to be guaranteed, with the aim of motivating VATIS service providers to do their best in improving the efficiency of the traffic network.

Conclusion
In this study, a two-stage policy aiming at improving the efficiency of the traffic network is proposed based on the feasibility of charging value-added ATIS services. Models of describing each case in this policy are formulated and the evaluation indicators are pointed out. Numerical results show that the suggested policy can decrease the total travel time substantially.
The proposed two-stage policy can be very helpful to the traffic manager in regulating the behavior of ATIS service providers, especially when they are competing for ATIS market shares. However, this study also has limitations. It only has discussed about competition and cooperation among ATIS service providers by considering pricing strategy and the information quality they provided. Other potential factors, such as the influence of word-of-mouth, preferences of travelers, also need to be discussed in the future study.
Further extensions of this study can be investigated as below. Constitutes of the profit function of VATIS service providers would be an important issue in analyzing the effectiveness of this policy. Investigating its constituent part can enhance the veracity and rationality of the suggested policies. Besides, the evaluation criteria of target completion in the second stage of the suggested policy are interesting extension, hierarchic criteria might be the proper way of the evaluation of the suggested policy. Moreover, the suitable total compensation paid by the traffic manager needs to be further discussed.