Approximate solutions for M/G/1 fork/join synchronization
Alexander Thomasian, Asser N. Tantawi · NCSU Libraries Repository (North Carolina State University Libraries) · 1994
Approximation techniques are developed to evaluate the performance of symmetric fork-join synchronization delays for K M/G/1 queues. For a server utilization /spl rho/, the mean response time for fork-join requests is expressed as the sum of the mean response time at one of the queues and the mean synchronization delay as follows: R/sub K//sup F/1/(/spl rho/)=R/sub 1/(/spl rho/)+F/sub K//spl alpha//sub K/(/spl rho/)/spl sigma//sub 1/(/spl rho/), where F/sub K/ is obtained from the previous equation at /spl rho/=0, R/sub 1/(/spl rho/) and /spl sigma//sub 1/(/spl rho/) are the mean and the standard deviation of response time at any one of the queues, respectively, and /spl alpha//sub K/(/spl rho/) is a low-degree service-time distribution dependent polynomial in /spl rho/, whose coefficients are determined from simulation results. We also use simulation results to show that when fork-join requests share the servers with local requests, a good approximation (and an upper bound) to the fork-join response time is obtained by treating the components of fork-join response time as independent, i.e., the mean fork-join response time can be approximated by the expected value of the maximum of the response times at the K queues.