An algorithm for the computation of mean delay of traffic at pre-timed control signals

Abstract

A signalized intersection regulated by pre-timed control in an urban traffic network is considered. A method for computing the mean delay of vehicles based on the theory of queues with server vacations is adapted from the existing literature and an algorithm for numerical implementation is proposed. Arrivals are assumed to occur according to a batch Markovian arrival process (BMAP). The proposed algorithm is an alternative to the previous methods that includes a numerical improvement in the computation of the queue invariant probabilities. In the case of isolated intersections we compare the new algorithm with other traffic models, including simulation model, Webster model and the Highway Capacity Manual model. The mean delay of vehicles given by the new algorithm is a short distance away from the mean delay obtained in the simulations. The approximation for large flows given by the proposed algorithm is as good as the Highway Capacity Manual model and with no need to tune unknown parameters. Our results are of interest for traffic engineers, since other approaches have been subject to criticism when flows near capacity are involved.

Keywords:

• Queuing systems
• Queues with server vacations
• Traffic delay estimation
• Traffic models

Acknowledgments

We thank the Reviewer for pointing out to us the relevance of the extension of the model to the traffic with platoons. Formulation of the model including BMAP arrivals is due to him(her). His(Her) suggestions considerably improved the content of the paper.

Additional information

Funding

M. L. Simões was financially supported by CONSTRUCT – Institute of R&D In Structures and Construction (Project POCI-01-0145-FEDER-007457), funded by FEDER funds through COMPETE2020 - Programa Operacional Competitividade e Internacionalização (POCI) and by national funds through FCT (Portugal). P. Milheiro-Oliveira was financially supported by CMUP – Center of Mathematics of the University of Porto (UID/MAT/00144/2013), funded by FCT (Portugal) with National (MEC) and European structural funds the programs FEDER, under the partnership agreement PT2020 and Project STRIDE Ref NORTE-01-0145-FEDER-000033, supported by the Northern Regional Operational Program (NORTE2020), through the European Regional Development Fund (ERDF).