Abstract
The queueing system considered in this thesis consists of N identical servers. Jobs arrive at the system according to a Poisson process. Among all the jobs in the system, a maximum of M jobs can be ready for service simultaneously. The rest of the jobs must wait in a waiting queue. When a service becomes available, one of the jobs currently ready for service is selected randomly and then one of the task belonging to the selected job is chosed for service. A job consists of one task initially. Zero or more tasks may become ready for service when a task finished service. A job completes it service when all of its tasks are completed. Exact performance analysis of a multi-server system serving parallel jobs with general task graphs is very difficult. In this thesis, we obtain an accurate approximation to the mean job response time. The effects of the characteristics of the jobs and system parameters on the system performance are also studied.