Queueing Theory Based Vehicular Traffic Management System Through Jackson Network Model and Optimization

Abstract

Traffic congestion is increasing in over populated urban areas, our traditional traffic management system can no longer solve this problem. However, this problem can be solved by converting our road networks into queueing networks. This paper proposes, the use of an open Jackson Queueing Model which can be equated with our existing road network to calculate the waiting time of vehicles in the network, which can be further processed to put the network into an optimized state. In this model, the waiting time depends on both arrival rate and service rate. Our implementation designates a set of service rates from a range of possible service rates for each road within the network and these designated service rates are used to calculate waiting time. As these various combinations of service rates of different roads produce multiple waiting times, we select the combination set of service rates which has the lowest set of waiting times. This set of service rates is also compared with quadratic optimization problem of the same road network to evaluate implementation’s accuracy.

Keywords

• Traffic congestion
• queueing model
• Jackson queueing network
• optimization theory
• quadratic programming
• quadratic optimization