A Tandem Queue Model for Two-Server Resequencing System∗

A two-server resequencing system has two heterogeneous servers and two buffers. One is an arrival buffer, which holds incoming jobs waiting for service. The other is a resequencing buffer, which resequences served jobs back to their arrival orders before departure. Such a system can be modeled as a two-stage tandem queue where the jobs are always kept in the arrival orders but the servers swap the positions upon any job departure. With the assumption of phase-type distributions for job interarrival and service time, the Markovian properties of the state transition is preserved in the model. The stationary probability distribution and the stationary conditions are obtained by the matrix-geometric solution approach. The performance is evaluated in five numerical experiments. The main conclusions are: a small resequencing buffer reduces the mean delay of the jobs significantly; the burstness of arrival traffic has positive influence on the mean delay; a heterogeneous system with more-balanced servers achieves better performance; and the slow server in a less-balanced system has negative effect which might eventually “starve” the fast server under heavy traffic load.