Approximation of single-class queueing networks with downtime-induced traffic variability

Queuing networks have been used with partial success for analytical modelling of manufacturing systems. In this paper, we consider a tandem system with high traffic variability caused by downtime events in the first queue. We propose improved approximation for departure variability in order to predict the waiting duration at the bottleneck queue located last in the line. We demonstrate that existing methods do not properly approximate such systems and provide some reasons and insights. Thus, a new decomposition method which employs the variability function principles is proposed. We differentiate between two components of the departure variability in multi-class systems: the ‘within-class effect’ – the variability caused by the class’ own inter-arrival and service time distributions – and the ‘between-class effect’ – the variability caused by interactions with other classes. Our analysis shows that the first effect can be approximated by existing multi-class decomposition methods, while the second effect requires a new development. Our proposed approximation for between-class effect is based on simulating a proper sub-system. The method enables modelling different policies of downtimes (e.g. FCFS, Priority). Numerical experiments show relative errors much smaller vs. existing procedures.