Response time analysis of parallel computer and storage systems

Fork-join structures have gained increased importance in recent years as a means of modeling parallelism in computer and storage systems. The basic fork-join model is one in which a job arriving at a parallel system splits into K independent tasks that are assigned to K unique, homogeneous servers. In the paper, a simple response time approximation is derived for parallel systems with exponential service time distributions. The approximation holds for networks modeling several devices, both parallel and nonparallel. (In the case of closed networks containing a stand-alone parallel system, a mean response time bound is derived.) In addition, the response time approximation is extended to cover the more realistic case wherein a job splits into an arbitrary number of tasks upon arrival at a parallel system. Simulation results for closed networks with stand-alone parallel subsystems and exponential service time distributions indicate that the response time approximation is, on average, within 3 percent of the seeded response times. Similarly, simulation results with nonexponential distributions also indicate that the response time approximation is close to the seeded values. Potential applications of our results include the modeling of data placement in disk arrays and the execution of parallel programs in multiprocessor and distributed systems.