Analysis of MAP/PH1, PH2, PH3/1 Queueing-Inventory System with Two Commodities.

In this work, a single server implements a two-commodity inventory queueing system. We assume that both commodities have a finite capacity. Customers arrive by a Markovian Arrival Process, there is a need for a single item, and either or both types of commodities are required, and this requirement is modeled using certain probabilities. The lead times are exponentially distributed, and the service times have a PH distribution. We use matrix analytical techniques to investigate the queueing inventory system and adopt an (s, S)-type replenishment policy that is dependent on the type of commodity. In the steady state, the joint and individual probability distribution of the Esystem, inventory level, and server status is obtained. A few significant performance measures are attained. Our mathematical concept is then illustrated with a few numerical examples. [ABSTRACT FROM AUTHOR]