Application of a Particular Class of Markov Chains in the Assessment of Semi-actuated Signalized Intersections

Abstract

We investigate a queuing model for a signalized intersection regulated by semi-actuated control in a urban traffic network. Modelling the queue length and the delay of vehicles for this type of traffic, characterized 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.

An analytical model for a tandem of two traffic-light intersections under semi-actuated and fixed control

“…The length of a green period for the main direction can be fixed, while the green time of the minor roads depends on the queue. In Macedo et al (2017), the queue length at a minor lane is modelled as an M ∕D∕1 queue with deterministic vacations, during which the major road is served. The green period of the minor lane has a fixed minimum and maximum length.…”

“…Finally, the majority of the existing queueing models use the concept of the effective green time. During this time, the queued vehicles are assumed to depart at constant (saturation) rate with free-flow speed, see, e.g., Webster (1958), Macedo et al (2017). The green period in such models has a different length and is postponed compared to the real green period by the acceleration time of the first vehicle in the queue.…”