Queuing networks are frequently used to model the performance of complex systems such as production job shops, service systems, and communication networks. Yet, existing queuing network approximations cannot cope with some of the manufacturing lines’ complexities. Scenarios of multi-product types, deterministic route per type, bottlenecks, maintenance, setups, batching and breakdowns, present notable challenge. Such situations involve significant interference among products’ flows and the above events, while causing non-renewable flows with very high variability. Hence, existing queuing network approximations can’t properly predict: tool utilization, work-in-process, and flow-time. Consequently, simulation models are frequently used in such practical situations. Yet, they are expensive and time-consuming to model, update and run.
In this research decomposition methods are used to develop better approximations suitable for queuing network models of multi-class systems with very high flow variability. We consider an open and tandem queuing network with multi-class dependent service, where the routing of each class is deterministic. Each queue has an unlimited waiting line. The nodes are single-server queues with a first-come-first-serve discipline in each of the classes, prioritizing one of the classes over the other. General distributions for inter-arrival and service times are allowed and assumed i.i.d. Since analysis of any multi-class system can be reduced to the two-class case, where one class is the class of interest and the other class is an aggregated class of the rest of the classes, two-class systems are considered.
Our analysis illustrates that the departure variability can be expressed as the sum of two components. The first component reflects the within-class effect while the second reflects the between-class interference effect, demonstrating a novel approximation approach. The proposed development relies in addition on modifying the variability functions for multi-class systems. The within-class variability function is class-dependent, while the between-class variability function is a result of non-renewal processes. The proposed approximation has been validated via simulation, demonstrating a relative error five times smaller than the best relevant existing procedures in the literature.
