Two-Moment Analysis of Open Queueing Networks with General Workstation Capabilities

Abstract

The QNET method for two-moment analysis of multiclass open networks is extended to allow complex workstations of various types. For example, the extension described here allows one to treat stations where several unreliable machines are tended by a small number of repair technicians, or stations where several machines that require setups are tended by a small number of operators. To illustrate the general concepts, a four-station manufacturing example is discussed in detail. In the QNET method, one first replaces the original queueing network by an approximating Brownian system model. The Brownian approximation is motivated by heavy traffic theory, and to achieve a unified treatment of complex workstations within the QNET framework we apply the following principle: For purposes of heavy traffic analysis, a workstation can be characterized by just two parameters, the asymptotic mean and asymptotic variance of its cumulative potential output process. This heavy traffic principle has long been known to researchers in the field, but we show that it has power and utility even in circumstances where the mean and variance parameters cannot be determined analytically. We explain how the heavy traffic principle can be applied successfully under certain conditions, and show by example that those conditions are not always met.

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