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.

本文考虑了本地车辆与过境车辆共享道路场景下，车道数量优化与准入控制的最优选择问题。道路运行过程采用带有两类顾客的马尔可夫调制到达过程（Markov Modulated Arrival Process, MMAP）/M/1型队列进行建模。其中，类型2（本地）顾客的服务为强制服务；类型1（过境）顾客拥有备选通行路线，因此可在本系统中选择放弃服务或中断已接受的服务。所有获准接入系统的顾客可同时接受服务：当系统内顾客总数不超过预先设定的阈值时，每位顾客可获得固定份额的服务带宽；若超出该阈值，则每位顾客仅能获得缩减后的服务带宽份额。本文推导了该系统的稳定性条件，并计算得到系统状态的平稳分布。最后通过数值算例，对道路车道数量优化的潜在应用场景进行了示例性演示。