Modeling overflow queues on urban signalized intersections

Much effort has been spent in developing more efficient control systems for signalized intersections to adapt the capacity of the network to the variability of the demand. This variability is partly due to time-dependent factors but also to the stochastic nature of the demand itself. The available formulae can still be successfully adopted in undersaturated conditions, where the stochastic effects fade into one green phase, or in highly oversaturated cases, where the queues aren't comparable with their portions caused by these uncertainties. In cases where the value of the degree of saturation is close to one the stochastic effect plays a relevant role. This paper provides a novel heuristic formula able to model the transition phase when the study involves a variable demand. It particularly solves the queuing behavior of an oversaturated period on the successive undersaturated ones. The delay experienced by the users is modeled using a Markov Chain process. Based on this data the novel model is calibrated. The new model for queues is further applied in two case studies. The first involves a two arms intersection where users of the two OD pairs can only choose between different times of departure. The second involves one OD pair and two parallel routes, one faster but ending with a traffic light while the other is unsignalised. The paper discusses the change in users' decisions with respect to the travel times and the delays they perceive at signalized intersections both from the route choice and the departure time choice point of view. In this sense a Dynamic Traffic Assignment problem in an extended network can be applied and solved. From this research we gained a deeper knowledge of the relevant role played by the random nature of the queue evolution in time for the delay experienced by the users. By acquiring this knowledge a time-dependent queue function has been provided. It is now possible to model the queue as a continuous function with more accurate results than the ones provided by the simple deterministic method.