System capacity and performance modelling of finite buffer queueing networks

Abstract

Estimating the performance measures of queues and queueing networks with finite buffers and general service times is a complex and challenging problem. This paper presents an effective two-moment approach for calculating the state probability distribution of the performance measures of the queues in these systems. Performance measures of throughput (), the work-in-process (WIP) and sojourn or cycle time () are estimated. The generalised expansion method is employed to calculate the network performance measures of the topologies and extensive computational experiments are provided. It is shown that the performance measures of WIP and sojourn time for multi-server exponential systems have an s-shaped function and this measure is extended to networks. It is argued that this relates directly to the system capacity of queues in finite buffer queueing networks. Series, merge and splitting topologies of finite buffer multi-server queueing networks are then examined. Numerous experiments involving the given topological configurations are demonstrated and the s-shaped behaviour of the overall system performance measures for system capacity are explained.