Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T08:20:56.569Z Has data issue: false hasContentIssue false
  • English
  • Français

DECOMPOSITION PROPERTY FOR MARKOV-MODULATED QUEUES WITH APPLICATIONS TO WARRANTY MANAGEMENT

Published online by Cambridge University Press:  30 April 2009

Nan Liu  and
Vidyadhar G. Kulkarni
Nan Liu
Affiliation:
Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599 E-mail: [email protected]; [email protected]
Vidyadhar G. Kulkarni
Affiliation:
Department of Statistics and Operations Research, University of North Carolina, Chapel Hill, NC 27599 E-mail: [email protected]; [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

In this article we study Markov-modulated queues with and without jumps. These queuing models arise naturally in production-inventory systems with and without an external supplier. We show an interesting decomposition property that relates the equilibrium state distributions in these two systems and present an integrated warranty-inventory management model as an application.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 23 , Issue 3 , July 2009 , pp. 433 - 447
Copyright
Copyright © Cambridge University Press 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Blischke, W.R. & Murthy, D.N.P. (1994). Warranty cost analysis. New York: Marcel Dekker, Inc.Google Scholar
2.Browne, S. & Zipkin, P.H. (1991). Inventory models with continuous, stochastic demands. Annals of Applied Probability 1(3): 419–435.CrossRefGoogle Scholar
3.Eisen, M. & Tainiter, M. (1963). Stochastic variations in queuing processes. Operations Research 11(6): 922–927.CrossRefGoogle Scholar
4.Fuhrmann, S. & Cooper, R. (1985). Stochastic decomposition in the M/G/1 queue with generalized vacations. Operations Research 33(5): 1117–1129.CrossRefGoogle Scholar
5.Ja, S.S. (1998). Computation of warranty reserves for non-stationary sales processes. Ph.D. dissertation, Unversity of North Carolina, Chapel Hill.Google Scholar
6.Kulkarni, V.G. (1995). Modeling and analysis of stochastic systems. London: Chapman & Hall/CRC.Google Scholar
7.Kulkarni, V.G., Tzenova, E. & Adan, I. (1995). Fluid model with jumps. Stochastic Models 21: 37–55.Google Scholar
8.Kulkarni, V.G. & Yan, K. (2007). A fluid model with upward jumps at the boundary. Queueing Systems: Theory and Applications 56(2): 103–117.CrossRefGoogle Scholar
9.Mitrany, I.L. & Avi-Itzhak, B. (1968). A many-server queue with service interruptions. Operations Research 16(3): 628–638.CrossRefGoogle Scholar
10.Neuts, M.F. (1971). A queue subject to extraneous phase changes. Advances in Applied Probability 3(1): 78–119.CrossRefGoogle Scholar
11.Neuts, M.F. (1981). Matrix-geometric solutions in stochastic models. Baltimore, MD: Johns Hopkins University Press.Google Scholar
12.Schwarz, M., Sauer, C., Daduna, H., Kulik, R. & Szekli, R. (2006). M/M/1 queueing systems with inventory. Queueing Systems: Theory and Applications 54: 55–78.CrossRefGoogle Scholar
13.Shanthikumar, J. (1986). On stochastic decomposition in M/G/1 type queues with generalized server vacations. Operations Research 36(4): 566–569.CrossRefGoogle Scholar
14.Song, J. & Zipkin, P.H. (1993). Inventory control in a fluctuating demand environment. Operations Research 41(2): 351–370.CrossRefGoogle Scholar
15.Yan, K. & Kulkarni, V.G. (2008). Optimal inventory policies under stochastic production and demand rates. Stochastic Models 24(2): 173–190.CrossRefGoogle Scholar
16.Yechiali, U. (1973). A queueing-type birth-and-death process defined on a continuous-time Markov chain. Operations Research 21: 604–609.CrossRefGoogle Scholar
17.Yechiali, U. & Naor, P. (1971). Queueing problems with heterogeneous arrivals and service. Operations Research 19(3): 722–734.CrossRefGoogle Scholar
18.Zipkin, P.H. (2000). Foundations of inventory management. Boston: McGraw-Hill.Google Scholar