Waiting times at periodically switched one-way traffic lanes – a periodic, two-queue polling system with random setup times

We study vehicle waiting times at a traffic lane that is shared by traffic from two directions. In contrast to crossovers, we focus on instances where the vehicle passing time of the shared infrastructure can be large. The motivation for this model arises from our research on underground transportation systems. We examine vehicle waiting times under periodic control rules (i.e., the driving direction on the infrastructure is switched between two directions according to a fixed time schedule). We analyze both symmetric and asymmetric systems (i.e., vehicle arrival rates as well as effective green and red periods may be different for both directions). In fact, we are dealing with a single server, two-queue polling system with random setup times and periodic (nonexhaustive) service discipline. We develop approximations for the mean waiting time and we show by comparison to simulation results that the accuracy is usually in the range of 1–2% for Poisson arrivals. Also, we indicate how our approximations can be generalized to compound Poisson arrivals.