A continuous flow model for networks with finite queues, unreliable servers, and multiple customers

This paper presents a flow approximation of acyclic queueing networks with multiple classes of jobs, unreliable servers, and finite buffers. Different jobs compete for service before a server, or they may combine before service to yield a composite job. Up times and down times of servers are random and service times have gamma distributions or may be constant quantities. Random service times are approximated by piecewise deterministic variables. The model is a combination of discrete event simulation and analysis. The simulator keeps track of the queue and server states. Between two consecutive state transitions the flow rates remain constant and the model calculates the cumulative flow of each job. When a transition takes place the model modifies the flow rates of the affected servers and schedules new events. Compared to a conventional simulator, the model is quite fast and accurate