APPROXIMATE ANALYSIS OF FORK JOIN SYNCHRONIZATION IN PARALLEL QUEUES

An approximation technique, called scaling approximation, is introduced and applied to the analysis of homogeneous fork/join queuing systems consisting of K greater than equivalent to 2 servers. The development of the scaling approximation technique is guided by both experimental and theoretical considerations. The approximation is based on the observation that there exist upper and lower bounds on the mean response time that 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% for K less than equivalent to 32.