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Optimization of road design via the use of a queueing model with transit and local users and processor sharing discipline. (English) Zbl 1514.60101

Authors’ 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 derived 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.

MSC:

60K25 Queueing theory (aspects of probability theory)
60K30 Applications of queueing theory (congestion, allocation, storage, traffic, etc.)
68M20 Performance evaluation, queueing, and scheduling in the context of computer systems
90B22 Queues and service in operations research
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