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An inventory model with server interruptions and retrials

Content Provider	Springer Nature Link
Author	Krishnamoorthy, A. Nair, Sajeev S. Narayanan, Viswanath C.
Copyright Year	2011
Abstract	In this paper we consider a single server queueing system to which customers arrive according to a Poisson process, each demanding exactly one unit of the inventoried item. Service time duration is exponentially distributed. Inventory is replenished according to (s, S) policy, with lead time following exponential distribution. The service may be interrupted according to a Poisson process in which case the service restarts after an exponentially distributed time. Upon arrival if a customer finds the server busy, it leaves the service area to join an orbit and retries for service from there. The interval between two successive repeated attempts is exponentially distributed. We assume that while the server is under interruption an arriving customer joins the system with some probability or leaves for ever with complementary probability. Further it is assumed that while the server is on interruption a retrying customer goes back to the orbit with a certain probability and with complementary probability leaves the system for ever. No arrival or retrial is entertained when the inventory level is zero. We model the above system as a level dependent quasi birth death process (LIQBD). The stability of the system has been studied using matrix analytic method and the steady state vector is obtained applying Neuts-Rao truncation procedure. Several system performance measures, including the waiting time of a customer in the orbit, has been derived and their dependence on different system parameters has been extensively investigated numerically.
Starting Page	151
Ending Page	171
Page Count	21
File Format	PDF
ISSN	11092858
Journal	Operational Research
Volume Number	12
Issue Number	2
e-ISSN	18661505
Language	English
Publisher	Springer-Verlag
Publisher Date	2011-09-04
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	(s, S) inventory with random service time Service interruption Matrix geometric method Queueing theory Queues and service Inventory, storage, reservoirs Operations Research, Management Science Computational Intelligence Operations Research/Decision Theory
Content Type	Text
Resource Type	Article
Subject	Management Science and Operations Research Strategy and Management Management of Technology and Innovation Computational Theory and Mathematics Statistics, Probability and Uncertainty Modeling and Simulation Numerical Analysis

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