CICTP 2018 1607
© ASCE
Optimization Model of Signal Timing at Isolated Intersections Based on Stochastic Chance
Constrained Programing
Jingrong Chen
1
; Yaran Zhang
2
; and Yuan Bai
3
1
Professor, LanZhou Jiaotong Univ. E-mail: jrchen@mail.lzjtu.cn
2
Postgraduate, LanZhou Jiaotong Univ. E-mail: 18394161423@163.com
3
Postgraduate, LanZhou Jiaotong Univ. E-mail: baiyuan423@163.com
ABSTRACT
Most optimization models of signal timing at isolated intersections delay formulas are
designed using transient delay model or fixed number theory delay model. According to the
random characteristic that arrival rate from each entrance lane at the intersection for stochastic,
targeting at the minimum gap between green time of each phase and the actual needs of green
time, a stochastic chance constrained programing model of signal timing at isolated intersections
is proposed. A new algorithm for stochastic chance constrained programing, which uses a two-
phase signalized intersection as the simulation example, is presented using a combination of
random simulation and particle swarm optimization. The results show that the random variation
of arrival rate has an obvious effect on the parameter setting of intersection signal timing, which
illustrates the correctness of the model and the algorithm.
KEYWORDS: Chance constrained programing; Random simulation; Particle swarm
optimization; Signals timing
1. INTRODUCTION
Urban traffic problems have become a heated issue. Intersections are important nodes that
affects the overall operation efficiency of urban traffic, and their signal control scheme would be
a decisive factor in intersection operations. The most basic form of intersection traffic signal
control, isolated intersection control, puts pre-timed control as the main modes. The rationale of
pre-timed control is to determine a signal timing scheme based on road conditions, approach
directions, and volume of the isolated intersection.
Pre-timed signal controls of isolated intersection models always use traffic delays (such as
queue length and queuing time) or capability as objects, and use capability or saturation as the
evaluation indicators of an intersection’s traffic operations. These formulas of optimal isolated
intersection signal timing model are always identified by a transient delay model or fixed number
theory delay model, which are often calculated by simplifying the traffic parameters. Based on
this theory, Zhongjie Zhao et al. (Zhao Zhongjie, 2005) used the fuzzy control theory to establish
the control algorithm of which the phase and cycle changed and verified the effectiveness of the
algorithm by simulation. Rui-min Li, Hua-pu Lu (Li Rui-min, 2009) put forward a multi-layer
fuzzy control model of signal control, put the average delay and stops as the optimization goal,
adopting the random weighting method in the genetic algorithm for solving the model, and
eventually got the traffic signal control program. To study the stochastic characteristics of the
arrival rate of traffic flow, Bin Lv (Lv Bin, 2010) analyzed the random characteristics of traffic
flow, and assumed the traffic arrival rate of intersection is a random variable. By applying the
uncertainty theory, Bin Lv established the green time optimization model of isolated
intersections according to the expected queue length of the vehicle, relative deviation index line,
and by using Lagrange multiplier method for solving stochastic expected value. The algorithm
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