Allocation of service time in a two-server system

Abstract

Consider a two-server FCFS queueing model where servers are arranged in series. All arrivals join the first service center where they receive a maximum of T units of service. Arrivals with service requirements that exceed the threshold T join the second queue where they receive their remaining service. We show that when the service requirements have hyper-exponential service times with large coefficient of variation our scheme provides better system performance than the standard two parallel server model in the sense of reducing the mean delay per customer in the system. Our model is likely to be useful in systems where high variability is a cause of performance degradation and where numerous service interruptions are not desirable. Scope and purpose Reducing congestion is a primary concern in the design and analysis of queueing models, especially in systems where the distribution of service times is characterized by high variability. As an example consider a two server repair facility where job arrivals have one of two types of defects and where the type of defect is not known a priori. Each type of defect requires an exponential service, but with different service rate. Thus, the overall repair time has a hyper-exponential distribution. The purpose of this article is to present a model that is likely to be useful in systems where high variability is a cause of performance degradation. Our policy is to arrange servers in series and to service an arrival by the first server for a maximum of T units of service. Arrivals join the second queue, if necessary, where they receive their remaining service. It is shown that this simple scheme outperforms the standard two parallel server model.