We investigate a queuing model for a signalised intersection regulated by semi-actuated control in an urban traffic network. Modelling the queue length and the delay of vehicles for this type of traffic, characterised by variable durations of the green signal, is crucial to evaluate the performance of traffic intersections. Additionally, determining the size of the extensions of the green signal is also relevant. The traffic systems addressed in the paper have the particularity that the server remains active (green signal) for a period of time that depends on the number of vehicles waiting at the intersection. This gives rise to an M/D/1 queuing system with a server that occasionally takes vacations (red signal), for which we compute the long-run mean delay of vehicles, mean queue length and mean duration of the green signal. We consider a case study and compare the results obtained from the proposed queueing model with those obtained by using a microsimulation model. The formulas derived for the performance measures are of interest for traffic engineers, since the existing alternative formulas are subject to strong criticism.

CEMAT - Center for Computational and Stochastic Mathematics