Offset optimization is of critical importance to the traffic control system, especially when spillovers appear. In order to avoid vehicle queue spillovers, an arterial offset optimization model was presented in saturated arterial intersections based on minimizing the queue length over the whole duration of the saturated traffic environment. The paper uses the shockwave theory to analyze the queue evolution process of the intersection approach under the saturated traffic environment. Then through establishing and analyzing a function relationship between offset and the maximum queue length per cycle, a mapping model of offset and maximum queue length was established in the saturated condition. The validity and sensitivity of this model were tested by the VISSIM simulation environment. Finally, results showed that when volumes ratios are 0.525–0.6, adjusting offset reasonably under the saturated condition could decrease the queue length and effectively improve the vehicle operating efficiency.
In arterials systems, reasonable adoption of the coordinated control could decrease vehicle delays and stops. Offset is an important parameter of the arterial signal coordinate control, which decides the effect of the coordinated control for adjacent intersections. Now, there are mainly two kinds of the offset optimization [
The above arterial coordination methods play an important role in the practical traffic management. However, these methods are mainly designed to the undersaturated coordination, namely, link supply can satisfy upstream input demand [
When traffic demand exceeds road capacity or intersection capacity, the saturated condition appears, and vehicle queues continue to increase. These queues can overflow the storage capacity of the road and physically block intersections and gradually spread to the surrounding intersections. Implementing signal control policies designed for the undersaturated condition is ineffective and even counters product to the saturated condition [
According to an objective of minimizing queue length over the whole duration of the saturated traffic environment, the paper presented a method to optimize offset of the saturated arterial through analyzing queue evolution process based on shockwave theory. Through establishing and analyzing functions relationship between offset and maximum queue length of single cycle, a mapping model of offset and maximum queue length is established in the saturated condition. Finally, validity and sensitivity of the model are tested in VISSIM software.
When traffic demand is much more than the capacity at saturated arterial intersections, the number of inflowing vehicles exceeds those discharging from the approach, and queue length will gradually increase at downstream intersection. Assuming the signal timing parameters remain fixed, this current state of the approach will sustainably develop, then the long queuing will spill over to the upstream intersection. Our study is based on the following basic assumptions.
(1) Saturated arterial intersections are typical four phases, and the phase sequence remains consistent and fixed. Every cycle is composed of the green time and red time without considering the yellow time. Rightturn flows at the adjacent intersection are less and without signal control, so that its effect can be neglected. Figure
Main direction of traffic flows and phasesequence at saturated arterial adjacent intersections.
As shown in Figure
(2) Coordination phase green time of upstream intersection is adequate. When green time starts, the platoon firstly discharges with saturation flow rate, and later discharges with average arrival rate. If we ignore the discreteness of platoon to reach downstream intersection, the travel platoon will be pulse arriving to downstream:
Then there are three femoral pulses of the travel platoons, as Figure
Pulse arrival flows schema of downstream intersection.
Substituting (
(3) Maximum cycle length model to determine intersection cycle [
(4) The common cycle length of the saturated arterial is determined by traditional methods [
(5) Green time of each intersection allocated by equal saturation principle.
At a signalized intersection, multiple shock waves are generated due to the stopandgo traffic caused by signal changes. As indicated in Figure
Traffic flow temporalspatial graph at saturated arterial adjacent intersections.
When arrival vehicles are of the saturation flow rate all joining the queue, the second part flows will continue to queue, forming a queuing shockwave:
Figure
The maximum queue length of intersection
(1) When
(2) When
Under the saturated condition, if the signal timing is fixed, the arrival rate and discharge rate stability, the maximum queue numbers, and original queue numbers are greater than previous cycles, and the relation of queue lengths between cycle
The maximum queue numbers and original queue numbers of intersection
Arterial traffic flow temporalspatial graph in multisaturated cycle.
An algorithm for solving the variable quantity of maximum queue numbers model is arranged in the following steps.
By introducing parameter
There are continuous vehicles from upstream joining the queue; assuming queue residence time is
The queue numbers of first part flows from upstream in cycle
By introducing parameter
The queue numbers of total flows from upstream in cycle
We can get the variable quantity of maximum queue numbers according to (
The maximum queue numbers and original queue numbers of the last saturated cycle can be represented by the following equation:
Through building a single cycle function relationship between offset and maximum queue length, a computation model of queue length diversification each cycle during duration of saturated, we propose an arterial offset optimization model based on an objective of minimizing queue length over the whole duration of the saturated traffic environment, avoiding queue spillover.
Equation (
In order to verify the application effect of the Saturated Arterial Optimization method, we simulate traffic operation state of two intersections adopting single point control (Scheme 1), coordination control (Scheme 2), and optimization coordination control (Scheme 3) by the VISSIM software, also comparative analysis of the output evaluation of these simulation scenarios.
Simulation Testing Arterial Schematic as shown in Figure
Simulation testing arterial schematic.
All entry volumes and approach lengths of arterial are showed in Table
All entry flows and approach length of the arterial.
Direction  Intersection 
Intersection 


Volumes (veh/h)  Approach length (m)  Volumes (veh/h)  Approach length (m)  
East approach  
Through  —  325  1738  400 
Left turn  —  —  242  — 
 
West approach  
Through  1794  400  —  400 
Left turn  269  —  —  — 
 
North approach  
Through  298  275  400  425 
Left turn  128  —  171  — 
 
South approach  
Through  272  300  498  355 
Left turn  119  —  213  — 
Assume the saturated duration of two intersections is 1200 s, total loss time
Signal timing parameters of the 3 simulated schemes.
Scheme 1  Scheme 2  Scheme 3  

Intersection  Intersection  Intersection  Intersection  Intersection  Intersection  





 
Cycle length (m)  193  176  193  193  193  193 
WE through green (s)  102  91  102  93  102  93 
WE leftturn green (s)  31  27  31  28  31  28 
NS through green (s)  34  41  34  42  34  42 
NS leftturn green (s)  15  17  15  18  15  18 
Offset (s)  —  36  −31 
Output the maximum queue length, and mean queue length, mean vehicle delays of two intersections with the three timing schemes in the last saturated cycle.
As shown in Table
Outputs parameters of the simulations.
Scheme 1  Scheme 2  Scheme 3  

Intersection 

Coordination phase  
Maximum queue length (m)  221  208  202 
Mean queue length (m)  113  101  96 
Mean vehicle delays (s)  108  100  88 
Mean value of noncoordination phase  
Maximum queue length (m)  121  98  82 
Mean queue length (m)  64  42  35 
Mean vehicle delays (s)  78  64  58 
 
Intersection 

Coordination phase  
Maximum queue length (m)  289  295  263 
Mean queue length (m)  162  170  134 
Mean vehicle delays (s)  125  127  128 
Mean value of noncoordination phase  
Maximum queue length (m)  141  132  122 
Mean queue length (m)  89  75  66 
Mean vehicle delays (s)  88  83  80 
Simulation results of link maximum queue length.
There is a function of offset and maximum queue length, and determining the offset reasonably can reduce the maximum queue length. Whether this optimization of different arrival rates significant or not, which requires the sensitivity analysis.
As the shown in Figure
The relation between offset and maximum queue length.
We have presented a method of offset optimization based on queue length constraint for the saturated arterial, whose objective is to minimize queue length and avoid queue spillback over the whole duration of saturated. To avoid secondary queues, in algorithm development we assume that through flows from upstream are pulse discharge to downstream. VISSIM simulation results show the follwing: to ensure the operation parameters of the competitive phase to not be deteriorated, the offset which is calculated by our optimization method can effectively reduce the maximum queue length and prevent queuing spillover. In addition, sensitivity analysis of the model shows that, before the volumes ratios exceed the threshold, the effectiveness by adjusting offset to reduce maximum queue length is less significant when volumes increase. The next step will be focused on an indepth study timing parameter of coordinated optimization strategy for the saturated arterial.
This work was supported by the National Science Foundation of China (Grant no. 50908100, Grant no. 51278520, and Grant no. 51278220) and China Postdoctoral Science Foundation funded project (Grant no. 20110491307). The authors thank anonymous reviewers for their valuable input and suggestions.