Mean value technique for closed fork-join networks

Abstract

A simple technique for computing mean performance measures of closed single-class fork-join networks with exponential service time distribution is given here. This technique is similar to the mean value analysis technique for closed product-form networks and iterates on the number of customers in the network. Mean performance measures like the mean response times, queue lengths, and throughput of closed fork-join networks can be computed recursively without calculating the steady-state distribution of the network. The technique is based on the mean value equation for fork-join networks which relates the response time of a network to the mean service times at the service centers and the mean queue length of the system with one customer less. Unlike product-form networks, the mean value equation for fork-join networks is an approximation and the technique computes lower performance bound values for the fork-join network. However, it is a good approximation since the mean value equation is derived from an equation that exactly relates the response time of parallel systems to the degree of parallelism and the mean arrival queue length. Using simulation, it is shown that the relative error in the approximation is less than 5% in most cases. The error does not increase with each iteration.