An inventory model with server interruptions

Authors:
A. Krishnamoorthy;Sajeev S. Nair;Viswanath C. Narayanan
Affiliations:
Cochin University of Science and Technology, Kochi, India;Government Womens Polytechnic College, Thrissur, India;Government Engineering College, Thrissur, India
Venue:
Proceedings of the 5th International Conference on Queueing Theory and Network Applications
Year:
2010

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Abstract

In this paper, we consider a single server queuing system with inventory where customers arrive according to a Poisson process. Inventory is served at an exponential rate provided there are customers. Inventory is replenished according to the (s, S) policy with zero lead-time. The service process is subject to interruptions, which occurs according to a Poisson process. The interrupted server is repaired at an exponential rate. We assume that during interruption, the customer being served waits there until his service is completed and also that no inventory is lost due to interruption. Stability of the above system is analyzed and steady state vector is calculated explicitly. Explicit formulas for system performance measures such as expected number of customers in the system, expected inventory size, expected interruption rate etc are also obtained.