Admission control policies for two-stage tandem queues with no waiting spaces

Abstract

This study considers a two-stage no-wait tandem queueing system, in which any customer who finds all servers busy at his destination stage will be lost. If customers arrive randomly, in order to prevent the loss of customers from the second stage, an admission control is applied to determine whether a new customer shall be accepted such that all accepted customers will go through the second stage successfully. We propose an admission control policy and show that the admission conditions of this policy are the sufficient and necessary admission conditions. The rejection or loss rate of customers in such a controlled system is compared with the loss rate of a system without any admission control. It is shown that both loss rates are equal when there is only one server at the first stage. Scope and purpose Production systems, such as steel production, plastic moulding and just-in-time production lines, are often modeled as no-wait tandem queues, in which jobs must be processed from the first station to the last without any delay. If the release and processing times of jobs are known, the problem for determining the processing order of jobs is typically a scheduling problem. However, if jobs arrive randomly, in order to prevent any delay of jobs currently in the system and ensure that the new job will go through all the stages successfully, an admission control should be used to decide whether or not to accept the new job. This paper deals with the admission control policies for no-wait tandem queueing systems. We present the least strict admission control policy, which will induce the maximal throughput, for a two-stage system with parallel servers. This policy can be easily extended for multistage systems.