Parameter Tolerance in Queueing Models

Analytical models based on queueing theory have been widely used in analyzing the dynamic behavior of manufacturing and service systems. Such models allow the user to easily experiment with different system designs or configurations for a given set of input parameters. However, an input parameter of the model could be inaccurate, due to, for example, estimation difficulties. In some cases a parameter may not be known (e.g., the customer order arrival rate for a new product) and we can only provide a good guess. In order to determine if the analysis results (and hence the system design) are robust to estimation errors, sensitivity analysis can be performed, using an analytical derivation or a numerical estimation.

In this paper we propose an alternative to the traditional approach of sensitivity analysis. We select a subset of the model parameters as the uncertain set and specify a tolerance range of a system performance measure, such as within 10% of the nominal value resulting from the baseline estimates of the parameters. We then calculate a feasible region of the uncertain parameters for which the performance measure will be within the tolerance limits. This is more convenient in cases where the system performance measure is required to be within a target range, or when it is an interface parameter to other models. We illustrate this approach by analyzing the basic exponential queues and then apply it to a more realistic model – a queueing model of a typical order fulfillment process in a distribution center