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Control of G/MX/1 Queueing System with N-Policy and Customer Impatience
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 Title & Authors
Control of G/MX/1 Queueing System with N-Policy and Customer Impatience
Lim, Si-Yeong; Hur, Sun;
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 Abstract
We introduce a queueing system with general arrival stream and exponential service time under the N-policy, where customers may renege during idle period and arrival rates may vary according to the server`s status. Probability distributions of the lengths of idle period and busy period are derived using absorbing Markov chain approach and a method to obtain the optimal control policy that minimizes long-run expected operating cost per unit time is provided. Numerical analysis is done to illustrate and characterize the method.
 Keywords
Impatience;Control Policy;N-Policy;General Arrival;
 Language
English
 Cited by
 References
1.
Akcan, S. (2013), A New Approximation for Inventory Control System with Decision Variable Lead-Time and Stochastic Demand, International Journal of Industrial Engineering: Theory, Applications and Practice, 20(3/4).

2.
Altman, E. and Yechiali, U. (2006), Analysis of Customers' Impatience in Queues with Server Vacations, Queueing Systems, 52, 261-279. crossref(new window)

3.
Bae, J. and Kim, S. (2010), The Stationary Workload of the G/M/1 Queue with Impatient Customers, Queueing Systems, 64, 253-265. crossref(new window)

4.
Benjaafar, S., Gayon, J., and Tepe, S. (2010), Optimal Control of a Production-Inventory System with Customer Impatience, Operations Research Letters, 38, 267-272. crossref(new window)

5.
Blackburn, J. D. (1972), Optimal Control of a Single Server Queue with Balking and Reneging, Management Science, 19, 297-313. crossref(new window)

6.
Chae, K. C. and Kim, S. J. (2007), Busy Period Analysis for the GI/M/1 Queue with Exponential Vacations, Operations Research Letters, 35(1), 114-118. crossref(new window)

7.
Chae, K. C. and Lee, S. M. (2005), An Absorbing Markov Chain Approach to GI/M/1 Queues with Generalized Vacations, Asia Pacific Management Review, 10, 163-167.

8.
Chae, K. C. and Lim, D. E. (2008), Busy period analysis for the n-policy GI/M/c queue, Journal of the Korean Statistical Society, 37(3), 285-290. crossref(new window)

9.
Choi, B. D., Kim, B., and Zhu, D. (2004), MAP/M/c Queue with Constant Impatience Time, Mathematics of Operations Research, 29, 309-325. crossref(new window)

10.
Kao, P. C. (1997), An Introduction to Stochastic Processes, Duxbury Press, Belmont, California.

11.
Ke, J.-C. (2003), The Analysis of a General Input Queue with N Policy and Exponential Vacations, Queueing Systems, 45, 135-160. crossref(new window)

12.
Kim, K. and Yang, W. S. (2011), Busy Period Analysis for the GI/M/1 Queue with Phase-Type Vacations, Journal of the Korean Statistical Society, 40(1), 55-62. crossref(new window)

13.
Lee, H. W. and Ahn, B. Y. (2002), Operational Behavior of the MAP/G/1 Queue under N-Policy with Single Vacation and Set-Up, Journal of Applied Mathematics and Stochastic Analysis, 15, 167-196.

14.
Lee, H. W. and Park, N. I. (2004), Using Factorization for Waiting Times in BMAP/G/1 Queues with N-Policy and Vacations, Stochastic Analysis and Applications, 22, 755-773. crossref(new window)

15.
Mandelbaum, A. and Momcilovic, P. (2012), Queues with Many Servers and Impatient Customers, Mathematics of Operations Research, 37, 41-65. crossref(new window)

16.
Swensen, A. R. (1986), On a GI/M/c Queue with Bounded Waiting Times, Operations Research, 34, 895-908. crossref(new window)

17.
Tadj, L. and Choudhury, G. (2005), Optimal Design and Control of Queues, Sociedad de Estadistica e Investigacion Operativa, Top, 13, 359-412.

18.
Takacs, L. (1962), Theory of queues, Oxford: Oxford University Press, reprinted in 1982 by Greenwood Press, Westport, CT.

19.
Takagi H. (1991), Queueing Analysis: A Foundation of Performance Evaluation, North-Holland, 1.

20.
Yadin, M. and Naor, P. (1963), Queueing Systems with a Removable Service Station, Operational Research Quarterly, 14, 393-405. crossref(new window)

21.
Yue, D., Yue, W., and Li, X. (2011), Analysis of a Two-Phase Queueing System with Impatient Customers and Multiple Vacations, The Tenth International Symposium on Operations Research and Its Applications (ISORA 2011), Dunhuang, China, 292-298.

22.
Zhe George Zhang, Z. G. and Tian, N. (2004), The N threshold policy for the GI/M/1 queue, Operations Research Letters, 32, 77-84. crossref(new window)