Single-Class Bounds of Multi-Class Queuing Networks

In a closed, separable, queuing network model of a computer system, the number of customer classes is an input parameter. The number of classes and the class compositions are assumptions regarding the characteristics of the system's workload. Often, the number of customer classes and their associated device demands are unknown or are unmeasurable parameters of the system. However, when the system is viewed as having a single composite customer class, the aggregate single-class parameters are more easily obtainable. This paper addresses the error made when constructing a single-class model of a multi-class system. It is shown that the single-class model pessimistically bounds, the performance of the multi-class system. Thus, given a multi-class system, the corresponding single-class model can be constructed with the assurance that the actual system performance is better than that given by the single-class model. In the worst case, it is shown that the throughput given by the single-class model underestimates the actual multi-class throughput by, at most, 50%. Also, lower bounds are provided for the number of necessary customer classes, given observed device utilizations. This information is useful to clustering analysis techniques as well as to analysts who must obtain class-specific device demands.