Passage time distributions for a class of queueing networks: closed, open, or mixed, with difference classes of customers with applications to computer system modeling

Networks of queues are important models of multiprogrammed time-shared computer systems and computer communication networks. Although equilibrium state probabilities of a broad class of network models have been derived in the past, analytic or approximate solutions for response time distributions or more general passage time distributions are still open problems. In this paper we formulate the passage time problem as a "hitting time" or "first passage time" problem in a Markov system and derive the analytic solution to passage time distributions of closed queueing networks. Efficient numerical approximation is also proposed. The result for closed queueing networks is further extended to obtain approximate passage time distributions for open queueing networks. Finally, we employ the techniques derived in this paper to study the interfault time and response time distribution and density functions of multiprogramming, size of main memory, service time of paging devices and rate of file I/O requests on the shape of distribution functions and density functions have been examined.