Optimization of road design via the use of a queueing model with transit and local users and processor sharing discipline. (2nd November 2022)

• Record Type: Journal Article
• Authors: Dudin, A. N.; Dudina, O. S.; Dudin, S. A.; Kostyukova, O. I.
• Is Part Of: Optimization. Volume 71:Number 11(2022)
• Page Start: 3147
• Page End: 3164
• Publication Date: 2022-11-02
• Subjects: Traffic admission control -- abandonments -- processor sharing -- impatience -- optimization; 60K25 -- 60K30 -- 68M20 -- 990B22; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2021.2009827
• Languages: English
• ISSNs: 0233-1934

Abstract

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 M M A P / 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.