Processor-shared service systems with queue-dependent processors

In this investigation, we analyze the finite queue-dependent heterogeneous multiprocessor service system in which processors are shared by more than one job. Whenever, the queue length of jobs in the system reaches a threshold value Nj (j = 1,2,…,r – 1), the (j + 1)th processor starts the processing of the jobs and continues till queue length is again decreased to the same level. Steady-state queue size distribution is obtained using recursive method considering Markovian arrival and service times. We derive the system characteristics, viz. expected number of jobs in the system, throughput of the system, probability that jth (j = 2,3,…,r) processor rendering the service etc. A cost relationship is constructed to determine the optimal threshold levels for processors being active in order to gain maximum net profit. For illustration purpose, tables and graphs are also provided.