Split allocation model of intersection group oriented to network carrying capacity limit

. In view of the network carrying capacity limit under over-saturated condition, a split allocation model of intersection group was developed, which takes total network delay, total output and total queue length as a comprehensive evaluation index. Based on the analysis of the influence of traffic flow turning, road section capacity, signal cycle length and split on traffic control, under the condition of network carrying capacity limit, the global optimization of intersection group splits was realized, taking the network traffic operation state as the basic judgment criterion and the corresponding constraint conditions were constructed. The numerical example analysis and simulation results show that the proposed model can ensure the traffic signal control effect under the premise of different demand states and control objectives, so that the effective prevention and quick dredging of traffic congestion can be realized under the condition of the network carrying capacity limit.

allocation of phase split at each signalized intersection of the network is the key to signal control of traffic network.

Basic assumptions
The over-saturated state is a subcategory in the blocking state [7], the performance is that the queue extends to the upstream intersection and has a negative impact on the upstream intersection. Generally speaking, the ultra-long queue spreads to the upstream intersection, which is impossible to dissipate in a single cycle of the intersection, and even causes the deadlock of the intersection. Based on the above research conclusions, the basic assumptions of the model are proposed as follows: (1) The effective green time of any approach of over-saturated intersection group can be used effectively, and there is no phenomenon of empty green time. ) (k C is the kth signal cycle length.

1)Incoming and outgoing traffic at the approach
According to the basic assumptions of the model (1), the intersection in the control area is in an over-saturated state at this time, vehicles at each approach is driven out at a saturation flow rate in the release state. Therefore, the average incoming and outgoing traffic of each approach at the upstream and downstream intersections in the control area shall meet the following relationship:

2)Stranded traffic at the approach
As can be seen from the analysis, the stranded traffic at the end of a certain cycle of the signalized intersection is equal to the sum of the stranded traffic in the previous cycle and the difference of incoming and outgoing traffic in the current cycle, the lower limit of the stranded traffic is 0. Thus, the relationship of the stranded traffic at the approach can be obtained as follows:

3)Road section capacity constraints
In order to maintain the dynamic balance of incoming and outgoing traffic between any node in the network for a certain period of time, the capacity constraint relationship of lane in the network is as follows: where veh l is the average space headway of the queuing traffic; j  is the corresponding road section capacity reduction factor on the importance of the road section; j l D is the distance between corresponding intersections.

4)Cycle constraints
In order to ensure the overall control effect of over-saturated intersection group and take into account the control benefit of each network node, according to the actual operation condition of intersection, the signal cycle length shall meet a certain range of values, that is: In this formula, are the upper and lower limits of the kth signal cycle length of node p, respectively.

5)Split constraints
In order to ensure the safety of vehicles and pedestrians at intersections, it is necessary to set the minimum green time for each intersection, that is the split of each approach of the intersection should be greater than or equal to its minimum split, and the sum of the split of each phase of the intersection should meet certain upper limit value requirements, and the constraint relationship is as follows: In this formula, * J is the set of key traffic lane groups of node p; is the loss of split of node p; are the upper and lower limits of the kth split of node p, respectively.

Criteria for judging the state of network traffic
Under the condition of the network carrying capacity limit, the traffic operation states of each node and road section in the network are mainly divided into three types: dynamic diffusion state, dynamic equilibrium state and dynamic dissipation state, the traffic flow contained in the network is also related to these three states. When the network state changes from the dynamic diffusion state to the dynamic dissipation state, the total input of the network traffic flow is less than the total output, the total network queuing traffic is decreased gradually.
The total network input traffic: The total network output traffic: The total network queue length:

1)Criteria for judging the dynamicdiffusion state:
are the initial state of the network.

2)Criteria for judging the dynamic equilibrium
state: are the initial state of the network.

3)Criteria for judging thedynamic dissipation state:
are the initial state of the network.

Objective function
To ensure that the split allocation of intersections in the network is reasonable, and maximize the efficiency of the In this formula,  is the weight coefficient for the total network delay ( 1 0    );  is the weight coefficient of the total network queue length ( 1 0    );  is the weight coefficient of the total network output ).

Case study
To illustrate the applicability of the proposed model, a   Table 1 and Table 2, respectively.   random phase sequence group, as shown in Table 3

Conclusions
In this paper, a split allocation model of intersection group oriented to the network carrying capacity limit is