Cascades of queues

This paper presents results from a bulk service queueing system, where the main service takes place at fixed time intervals, but where back-up (or relief) services may be introduced in times of heavy demand on the system. On occasions the back-up service itself may receive further back-up services, thus leading to the concept of a cascade of queues flowing from the original main service. Analytic expressions are derived for the mean queue lengths at the points of delivery of service, and the computational requirements are discussed in detail. Sample numerical results and a simple cost analysis are provided.