An ‘(s, S)’ inventory in a queueing system with batch service facility

This paper considers a single-server queueing model in which the customers are served in batches of varying size depending on predetermined thresholds as well as available inventory. There is a finite buffer for the inventory and the service of every customer requires an inventory item. An (s, S) -type inventory system is used for the models considered in this paper. Initially, the model is studied in detail using the matrix-analytic method by assuming all the underlying random variables to be exponentially distributed. Thereafter, an outline of the model in a more general set up is also presented. Due to complexity of the model when more general assumptions are made on the underlying random variables, simulation is opted after a satisfactory validation with the analytic counterpart of the exponential model. Finally, some illustrative numerical examples are also presented to accomplish our analysis.