Optimization of road design via the use of a queueing model with transit and local users and processor sharing discipline

Abstract

A problem of the optimal choice of the number of lanes and admission control in the road that is shared by the local and transit vehicles is considered. The operation of a road is modelled by the $MMAP/M/1$ type queue with two types of customers. The service of type-2 (local) customers is mandatory. Type-1 (transit) customers can use alternative routes and, therefore, abandon or interrupt service in the considered system. All admitted customers are serviced simultaneously. A customer receives a constant part of a server bandwidth if the number of customers does not exceed a predefined in advance threshold and the reduced part, otherwise. The stability condition is derive and the stationary distribution of the system states is computed. A potential application for optimizing the number of lanes in the road is numerically illustrated.

Keywords:

• Traffic admission control
• abandonments
• processor sharing
• impatience
• optimization

2020 Mathematics Subject Classifications:

• 60K25
• 60K30
• 68M20
• 990B22

Acknowledgments

The authors express their sincere appreciation to Associate Editor Gerhard-Wilhelm Weber and the four anonymous referees for valuable constructive comments. Their account helped to essentially improve the paper.

Disclosure statement

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

Additional information

Funding

The publication was prepared with the support by the RUDN University Strategic Academic Leadership Program [5-100].