Queuing Models with Lane Selection: A New Class of Problems

Abstract

This paper presents a new class of queuing models. There are n distinct types of customers and n distinct types of service facilities. Some customers can be processed at any service facility, but other customer types can only use selected ones among the service-facility types. This class of model is named “lane selection,” abbreviated LS, since the arriving customers with some freedom of choice must select the queue, or lane, in which they are to be processed through the system. It is shown by example that many physical situations are represented more accurately by this model than by more conventional ones. However, in analysis, the LS concept raises many theoretical difficulties. For a number of special cases, this paper obtains in explicit form as functions of the model parameters the mean queue lengths and waiting times for the different classes of customers.