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The fixed-cycle traffic-light (FCTL) queue is the standard model forintersections with static signaling, where vehicles arrive, form a queue anddepart during cycles controlled by a traffic light. Classical analysis of theFCTL queue based on transform methods requires a computationally challengingstep of finding the complex-valued roots of some characteristic equation.Building on the recent work of Oblakova et al. (Exact expected delay anddistribution for the fixed-cycle traffic-light model and similar systems inexplicit form, 2016), we obtain a contour-integral expression, reminiscent ofPollaczek integrals for bulk-service queues, for the probability generatingfunction of the steady-state FCTL queue. We also show that similar contourintegrals arise for generalizations of the FCTL queue introduced in Oblakova etal. (2016) that relax some of the classical assumptions. Our results allow tocompute the queue-length distribution and all its moments using algorithms thatrely on contour integrals and avoid root-finding procedures.

Pollaczek contour integrals for the fixed-cycle traffic-light queue