Markov models for a multiple processor system with a shared bus

A finite population queueing model applicable to a class of real-time multiple processor systems with a shared bus is developed and analysed. It assumes Poisson arrivals and services, and its service discipline is FIFO, with the restriction that a customer cannot be served for the (k + l)st time unless all customers have been served k times. The performance of the system is studied by evaluating its throughput. In the special case of equal arrival and service rates, the model reduces to a simpler one, whose solution is obtained by a recursive technique that reduces significantly the computation time. Under certain conditions, the simplified model provides a good approximation to the throughput predicted by the general model.