Sensitivity analysis for queuing equilibrium network flow and its application to traffic control

Vehicle queuing often forms at a controlled access ramp to an expressway or at a saturated approach to a signalized intersection, and the queue size depends highly on the traffic control pattern. An efficient control scheme should, therefore, take into account the effects of the altered network flow pattern due to traffic control to achieve a global optimal solution. In this paper, a queuing network equilibrium assignment model is introduced to describe driversʹ route choice behavior under conditions of both queuing and congestion for a given traffic control pattern. A sensitivity analysis is then performed for the queuing network equilibrium assignment problem to derive the explicit expressions of the derivatives of equilibrium link flows and equilibrium queuing times with respect to traffic control parameters. This derivative information is shown to have many important applications. It indicates the ramp metering rates or signal splits to which the queuing equilibrium flow pattern is the most sensitive, and therefore, the traffic control that deserves the most consideration to improve the current operation of the congested traffic systems. The derivative information also allows one to estimate a nearby solution for any combination of changes in traffic control parameters once an equilibrium solution has been calculated. Numerical examples are presented to illustrate the sensitivity analysis method and its application to the evaluation of traffic control schemes.