Within the morning and evening rush hour, the twoway road flows are always unbalanced in opposite directions. In order to make full advantage of the existing lanes, the twoway road lane has to be reallocated to play the best role in managing congestion. On the other hand, an effective tradable credit scheme can help to reduce the traffic demand and improve fairness for all travelers. So as to alleviate the commute congestion in urban transportation network, a discrete bilevel programming model is established in this paper. In the bilevel model, the government at the upper level reallocates lanes on the twoway road to minimize the total system cost. The traveler at the lower level chooses the optimal route on the basis of both travel time and credit charging for the lanes involved. A numerical experiment is conducted to examine the efficiency of the proposed method.
In many big cities, a large number of people commute from residential areas to their workplaces in the central business district (CBD) in the morning. It leads to the phenomenon that the lanes are congested in the direction from residential areas to CBD while the other lanes in the opposite direction are free. But in the evening, all of that will be reversed. In order to adjust the asymmetric amounts of traffic flow in the two directions of one road section, the lane reversal is employed as a traffic control technique. It is an effective way to make full use of existing road resource and can increase traffic supply.
Lane reversal has been used for many years in managing road congestion. In recent years, lane reversal has been introduced in Chinese big cities, such as Beijing, to relieve morning and evening commute congestion. In the last year, Chaoyang Road, a big thoroughfare on the city’s east side, has been tested as the first lane reversal in Beijing to allow traffic to travel in either direction depending on certain conditions. According to the practice, the lane reversal can help to alleviate traffic congestion to some extent.
The implement of lane reversal is a network design problem (NDP). A plenty of research works are focused on the effectiveness, feasibility, and safety of implementing lane reversal [
In addition to increasing supply, another efficient way to manage congestion is reducing traffic demand. It is widely acknowledged that congestion pricing is helpful in traffic demand management, but the equity debates confined its adoption all over the world. Without taking into account commuters’ income level, trip purposes, and valuation of time, congestion pricing scheme might increase individuals’ travel costs. Though it can improve the system performance, it often has to face public resistance.
According to the latest research on congestion control, tradable credit scheme is proved to be a fairer, more effective, and more practical congestion management scheme. It should be noticed that Yang and Wang first explored a tradable credit scheme in a general transportation network equilibrium context with homogeneous and heterogeneous travelers, respectively [
In this paper, a discrete bilevel programming model is constructed for managing rush hour congestion caused by underutilization of the existing road resource. The proposed model employs tradable credit scheme and lane reversal for increasing traffic supply and decreasing traffic demand, respectively. At the upper level, the government chooses optimal lanes to be reallocated to minimize the total system costs. Taking into account the generalized travel cost including travel time and linkspecific charges for using the links, the travelers at the lower level will choose the optimal route to minimize it.
This paper is organized as follows. In Section
Consider a twoway network
To all directed links in the road network,
For simplicity, consider a separable link travel cost function
Tradable credit scheme is characterized by its initial distribution and the charging scheme. To minimize complexity, the initial distribution schemes considered here will be OD specific for a given and fixed demand
Let
Let
It has been proved that not all
The following bilevel programming model is to minimize the sum of total system costs, while the travelers choose the optimal route for minimizing the generalized travel costs including both travel time and linkspecific credit charges for using the links. The model can be described by
The model is a mixed integer nonlinear programming program. The decision variable at upper level is integer while variable at lower level is real number. Chaos algorithm here is adopted to solve the proposed model [
Assume chaos variable is denote by random number
Chaos variable
Carrier can be produced by the following equation:
For given
Solve the model at the upper level and get
If the termination condition is met, output the optimal solution
In this paper, a basic twoway road network, as shown in Figure
Original structure of the test network before lane reversal.
The link cost function
Input data for the test network.



Link 




1 and 2  4.0  40  2  20 
3 and 4  6.0  40  2  20 
5 and 6  2.0  60  3  20 
7 and 8  5.0  40  2  20 
9 and 10  3.0  40  2  20 
The traffic flows under UE before lane reversal can be calculated and are shown in Table
Transportation condition before lane reversal and tradable credit scheme.
Link 
Link flow 
Link utilization rate 

1 and 2  52.5322 and 31.5193  1.3133 and 0.7880 
3 and 4  47.4678 and 28.4807  1.1867 and 0.7120 
5 and 6  15.7200 and 13.4320  0.2620 and 0.2239 
7 and 8  46.8122 and 28.0873  1.1703 and 0.7022 
9 and 10  53.1878 and 31.9127  1.3297 and 0.7978 


System cost 

Solve the models (
Results after lane reversal.
Lane reversal  SC  





 
0 and 0  1 and −1  0 and 0  1 and −1  0 and 0  1680 
It is shown in Table
Transportation condition after lane reversal.
Link 
Link flow 
Link utilization ratio 

1 and 2  48.9004 and 41.3251  1.2225 and 1.0331 
3 and 4  51.0996 and 18.6749  0.8517 and 0.9337 
5 and 6  00.0000 and 22.9740  0.0000 and 0.3829 
7 and 8  48.9004 and 18.3510  0.8150 and 0.9176 
9 and 10  51.0996 and 41.6490  1.2775 and 1.0412 


System cost 

The transportation condition after lane reversal is shown in Figure
The structure of the test network after lane reversal.
With the development of economics and city scales, the road becomes more and more congested in morning and evening rush hour. In order to achieve better effect in solving the congestion problem, traffic demand and increasing road supply are all considered at the same time in this paper. A bilevel programming model is proposed to deal with the twoway road unbalance usage problem. In order to make full advantage of the existing lanes, the twoway road lanes have to be reallocated to play the best role in managing congestion. An effective tradable credit scheme is also employed to help to alleviate the commute congestion with lane reversal in urban transportation network. The models and the algorithm are demonstrated with the basic twoway road network example.
In the future research, the heterogeneous users should be considered. Users with different job and income may have different value of time, so it will be helpful for transportation planning to simulate the real situation.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This study was jointly supported by the National Basic Research Program of China (2012CB725401) and the National Natural Science Foundation of China (71271205 and 71322102).