Allocation of service time in a two-server system

Consider a two-server first-come-first-served 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.