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AN M/G/1 VACATION QUEUE UNDER THE $P_{\lambda}^M-SERVICE$ POLICY  

Lee, Ji-Yeon (Department of Statistics, Yeungnam University)
Publication Information
Journal of the Korean Statistical Society / v.36, no.2, 2007 , pp. 285-297 More about this Journal
Abstract
We consider the $P_{\lambda}^M-service$ policy for an M/G/1 queueing system in which the workload is monitored randomly at discrete points in time. If the level of the workload exceeds a threshold ${\lambda}$ when it is monitored, then the service rate is increased from 1 to M instantaneously and is kept as M until the workload reaches zero. By using level-crossing arguments, we obtain explicit expressions for the stationary distribution of the workload in the system.
Keywords
M/G/1 queues; multiple vacations; $P_{\lambda}^M-service$ policy; stationary distributions;
Citations & Related Records
Times Cited By KSCI : 1  (Citation Analysis)
Times Cited By Web Of Science : 0  (Related Records In Web of Science)
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1 LEE, J. AND KIM, J. (2007). 'Workload analysis of an M/G/1 queue under the $P^M_\lambda$ policy with a set-up time', Applied Mathematical Modelling, 31, 236-244   DOI   ScienceOn
2 Ross, S. M. (1996). Stochastic Processes, 2nd ed., John Wiley & Sons, New York
3 COHEN, J. W. (1982). The Single Server Queue, revised ed., North-Holland, Amsterdam
4 BOXMA, O. J., PERRY, D. AND STADJE, W. (2001). 'Clearing models for M/G/1 queues', Queueing Systems, 38, 287-306   DOI
5 COHEN, J. W. (1977). 'On up- and downcrossings', Journal of Applied Probability, 14, 405-410   DOI   ScienceOn
6 BRILL, P. H. AND POSNER, M. J. M. (1977). 'Level crossings in point processes applied to queues: single-server case', Operations Research, 25, 662-674   DOI   ScienceOn
7 COHEN, J. W. (1978). 'Properties of the process of level crossings during a busy cycle of the M/G/1 queueing system', Mathematics of Operations Research, 3, 133-144   DOI
8 FADDY, M. J. (1974). 'Optimal control of finite dams: discrete (2-stage) output procedure', Journal of Applied Probability, 11, 111-121   DOI   ScienceOn
9 KIM, N. K., PARK, Y. I. AND CHAE, K. C. (2004). 'A simple approach to the workload analysis of M/G/1 vacation queues', Journal of the Korean Statistical Society, 33, 159-167
10 TAKAGI, H. (1991). Queueing Analysis, Volume 1: Vacation and Priority Systems, NorthHolland, Amsterdam
11 LEE, E. Y. AND AHN, S. K. (1998). '$P^M_\lambda$-policy for a dam with input formed by a compound Poisson process', Journal of Applied Probability, 35, 482-488   DOI   ScienceOn
12 KIM, J., BAE, J. AND LEE, E. Y. (2006). 'An optimal $P^M_\lambda$-service policy for an M/G/1 queueing system', Applied Mathematical Modelling, 30, 38-48   DOI   ScienceOn
13 BAE, J., KIM, S. AND LEE, E. Y. (2002). 'A $P^M_\lambda$-policy for an M/G/1 queueing system', Applied Mathematical Modelling, 26, 929-939   DOI   ScienceOn
14 WOLFF, R. W. (1989). Stochastic Modeling and the Theory of Queues, Prentice Hall, New Jersey