Single-class bounds of multi-class queuing networks

Reviewer: Guenter Haring

In building a queueing network model of a computer system, workload characterization is an important task. Part of workload characterization is determining the number and composition of the workload classes. It is often difficult to determine these features, because of measurement and assignment problems, such as the representation of system overhead. The authors have investigated the size of the error if a multiclass system is represented by a single-class model, which can be characterized more easily. The background of this investigation is multiclass, separable queueing network models with load-independent centers. Starting from the case of two centers and extending their work to an arbitrary number of centers, the authors have shown by thorough analysis that the center utilizations and the throughput in a multiclass model are higher than in the equivalent single-class model, that is, the single-class model gives pessimistic bounds. An error analysis shows that the maximum error decreases as the number of jobs increases, so careful workload characterization is important when the number of jobs is low. Furthermore, it shows that in the worst case, the single-class equivalent underestimates the multiclass throughput by, at most, 50 percent. If there are no dominating customers, the error can be reduced by not combining all classes into a single class, but only combining a subset of the errors. Finally, the authors give a relation that allows one to determine the minimum number of workload classes for a given utilization, total population, and number of centers. The paper is a valuable contribution to the modeling of computer systems. In particular, it will support workload characterization and its standard techniques, including clustering, and it may help the modeler to construct and interpret models correctly.