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

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.