Two server Markovian inventory systems with server interruptions: Heterogeneous vs. homogeneous servers.

Abstract This paper discusses about Markovian (s , Q) inventory-queueing system with server interruptions of two heterogeneous servers. Matrix method is applied to obtain the steady state joint probability distribution of customers level in the queue, retrial group, status of the servers and stock level of heterogeneous system. This paper studies the significant effect of heterogeneous system (each server work with different service rate) as compared with homogeneous system (all servers work with same service rate). Performance measures are derived for heterogeneous system and homogeneous system. Appropriate cost functions for both models are defined. Numerical examples are used to compare the total expected cost rates of both systems. Heterogeneous system yields the minimum total expected cost value and therefore the heterogeneous system is effective. Highlights • This paper investigates the Markovian (s , Q) inventory system with server interruptions and two heterogeneous servers. • One important feature is that our paper makes comparison of the systems with homogeneous servers and heterogeneous servers with server interruptions and obtained the heterogeneous system to be better than the corresponding homogeneous system. • Our paper gives the better solution for heterogeneous servers based on the numerical examples corresponding to the homogeneous system. • Mr.V.P.Singh (1970) in his paper "Two Server Markovian queues with Balking: Heterogeneous Vs Homogeneous", Operations Research Vol. 18, 1, 145–149, had obtained solution to Queueing system (without Inventory) with two heterogeneous servers and had compared the heterogeneous servers with the corresponding homogeneous servers and obtained results under which the queueing system with heterogeneous servers is better than the corresponding homogeneous system. Our result with inventory is consistent with the result of Mr. V.P. Singh. [ABSTRACT FROM AUTHOR]