Sojourn time distributions in queuing networks seldom possess closed-form analytical solutions.When overtaking is permitted, the sojourn times at indlwdual nodes are usually dependent, in which case the attendant distribution is mathematically intractable.In a previous paper the authors proposed a methodology utihzing randomization procedures to approximate sojourn time distributions in arbitrary discrete-state Markovian queuing networks.Th~s paper addresses the computational aspects of the methodology pertaining to implementation.Ways of improving the accuracy ofthe approximated distribution functions are also discussed.

A demand-interrupting device is any attachment to a computer which, when busy, blocks a processor that reqmres further service from it In this paper there is considered a system with a processor rendering two types of serwce, so as to be able to take advantage of enforced idle times, which is connected to one or two demand-interrupting devices that feed back the programs to the processor.The dlstrzbution of the holding time in the processor and the utilization figures for all the components are computed under several assumptmns on the distributions of the serwces performed by the demand interrupting devices and the delay-type service performed by the processor The principal processor serwce duration is assumed to be exponentially distributed throughout the dlscussmn.

A simple computer system is described, which consists of a CPU and I/O unit and which works in a multiprogramming manner.The model assumes that the system works under heavy load so that the incoming queue is never empty, that the service times at the two units are exponentially distributed independent random variables, and that the number of iterations of the programs is geometrically distributed.Head of the line priority of programs which are being processed over newcomers is considered.Steady state distribution of the states of the system is numerically solved under the assumption of a finite waiting room.The suggested system is compared with one working in "batch mode" and with an equivalent multiprogramming system with a constant number of programs.The latter comparison shows that the suggested priority rule improves the expected response time without affecting the throughput and the utilizations of the CPU and the I/O unit.The model induces an interesting dependence phenomenon which is discussed at length.