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（local）车辆与过境（transit）车辆共享道路场景下，车道数量最优选择与准入控制的优化问题。该道路的运行过程采用两类顾客的MMAP/M/1型排队模型进行建模。二类（Type-2）顾客的服务为强制要求；一类（Type-1）顾客可选择替代路径，因此可在本研究考虑的系统中放弃服务或中断正在进行的服务。所有获准接入的顾客可同时接受服务。当系统内顾客数量不超过预先设定的阈值时，每位顾客可获得服务器带宽的固定份额；反之则获得缩减后的带宽份额。本文推导得到系统的稳定性条件，并计算出系统状态的平稳分布。最后通过数值算例展示了该模型在道路车道数量优化中的潜在应用价值。