Tandem queues with general blocking: A unified model and comparison results

Abstract

We study tandem queues with finite intermediate buffers and develop a general blocking scheme that unifies and generalizes various blocking schemes previously studied in the literature, such as manufacturing blocking, communication blocking, kanban blocking and its variations. In the general blocking scheme, job movement and service at each stage are controlled by three parameters, which represent, respectively, the upper limits (at that stage) on work-in-process inventory, finished goods inventory, and buffer space. We derive a set of recursive equations that characterize the dynamics of the system, in terms of the job completion and departure processes, and establish comparison results for these processes in the settings of stochastic ordering, variability ordering and stochastic convexity. Free of distributional assumptions, the results provide characterization of system behavior with respect to the control parameters as well as to the arrival and service processes. We also compare system performance under two different modes of operation: make-to-order versus make-to-stock, and demonstrate the trade-off between improving service and reducing inventory. Numerical studies are also presented to illustrate the diversity of performance trade-off, including composition of inventory, offered by the general model.