AN APPROXIMATE PRODUCT SOLUTION FOR QUEUING-INVENTORY SYSTEM WITH FINITE WAITING ROOM AND CATASTROPHES

Abstract

In this paper, the Markovian model of queuing-inventory system with finite waiting room and catastrophes is considered. As a result of the catastrophes, all stocks in the warehouse are destroyed instantly. In addition to consumer customers, the system also takes into account customers who do not require service or inventory, but who displace one customer from the system. Replenishment of fixed volume stocks is carried out with random delays. To mathematically analyze this system, a two-dimensional Markov chain is constructed, and an approximate product solution is developed to calculate its steady state probabilities. The high accuracy of the developed approximate formulas is confirmed by numerical experiments. The behavior of the performance measures versus on the initial parameters is demonstrated, and carried out optimization of the studied system. Keywords: queuing-inventory system, finite waiting room, catastrophes, two-dimensional Markov chain, approximate product solution.