Analytical model of road bottleneck queueing system

ABSTRACT

Car drivers have been suffering from road bottlenecks due to the constant increase in the number of vehicles that are not matched by the growth of the road network. Obstacles on a road or a road narrowed to one bidirectional are an accompanying phenomenon of a congested transport network. This paper solves a queueing system generated by such a road bottleneck managed by traffic lights. Generally, the problem can be classified as a Semi-Markov process with stochastic arrivals and deterministic service with a queue of an appropriate length. In order, to allow for an analytical solution, a simplifying assumption that the incoming flow of cars has a uniform distribution is made. A complex analysis of possible scenarios is done, the efficiency and the average waiting times are calculated. The results confirm the nature of the studied system and allow an optimization of the system settings.

KEYWORDS:

• Road bottleneck
• traffic control
• system efficiency
• average time delay
• car flow density
• simulation

Acknowledgments

This work was supported by the FPEDAS, University of Zilina under Grant 2/KKMHI/2020.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the FPEDAS, University of Zilina [2/KKMHI/2020].