Approximate Analysis of Fork/Join Synchronization in Parallel Queues

Abstract

A new approximation technique, called the scaling approximation, is introduced and applied to the analysis of homogeneous fork/ join queueing systems consisting of K ≥ 2 servers. The development of the scaling approximation technique is guided by both experimental and theoretical considerations. The essence of the approximation stems from an interesting observation that there exist upper and lower bounds on the mean response time which grow at the same rate as a function of K. Simple, closed-form approximate expressions for the mean response time are derived and compared to simulation results. The relative error in the approximation is less than 5 percent for K ≤ 32. © 1988 IEEE