arXiv subjects

Rik W. Timmerman

Publications and source records attributed to Rik W. Timmerman.

3 recordsLinked to original sources

arXiv2022

The Fixed-Cycle Traffic-Light queue with multiple lanes and temporary blockages

Traffic-light modelling is a complex task, because many factors have to be taken into account. In particular, capturing all traffic flows in one model can significantly complicate the model. Therefore, several realistic features are typically omitted from most models. We introduce a mechanism to include pedestrians and focus on situations where they may block vehicles that get a green light simultaneously. More specifically, we consider a generalization of the Fixed-Cycle Traffic-Light (FCTL) queue. Our framework allows us to model situations where (part of the) vehicles are blocked, e.g. by pedestrians that block turning traffic and where several vehicles might depart simultaneously, e.g. in case of multiple lanes receiving a green light simultaneously. We rely on probability generating function and complex analysis techniques which are also used to study the regular FCTL queue. We study the effect of several parameters on performance measures such as the mean delay and queue-length distribution.

math.PR↗

arXiv2020

New vehicle-actuated access algorithms for intersections close to oversaturation

Optimal traffic-light settings are generally hard to obtain, certainly for actuated access control of an intersection. Typically, computationally expensive (microscopic) simulations or complicated optimization schemes are required to find those optimal settings. Based on recent developments regarding the Fixed-Cycle Traffic-Light (FCTL) queue, we propose a new allocation scheme for actuated access control at isolated intersections. Our scheme allows for very easy computations and an intuitive explanation, which are both based on the Central Limit Theorem, a key tool in probability theory. The desirable properties observed for the FCTL queue can also be achieved in case of actuated access control of an intersection. We show this by means of simulation of the underlying queueing model, because the actuated control defies an exact analysis so far. We also observe the same type of results employing the microscopic traffic simulator SUMO. The intuition and insights obtained might also open up new possibilities for obtaining optimal actuated access control for a network of intersections.

eess.SP↗

arXiv2018

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

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

math.PR↗