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Two - Dimensional State M/G/1 Queuing System with Working Vacations under Non-Exhaustive Service

Indra, Ruchi Published in

International Journal of Applied Information Systems
Year of Publication 2012
© 2010 by IJAIS Journal
Info Co-published with IJCA
Authors Indra, Ruchi
10.5120/ijais12-450212
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  1. Indra and Ruchi. Article: Two - Dimensional State M/G/1 Queuing System with Working Vacations under Non-Exhaustive Service. International Journal of Applied Information Systems 1(8):36-44, April 2012. BibTeX

    @article{key:article,
    	author = "Indra and Ruchi",
    	title = "Article: Two - Dimensional State M/G/1 Queuing System with Working Vacations under Non-Exhaustive Service",
    	journal = "International Journal of Applied Information Systems",
    	year = 2012,
    	volume = 1,
    	number = 8,
    	pages = "36-44",
    	month = "April",
    	note = "Published by Foundation of Computer Science, New York, USA"
    }
    

Abstract

This paper studies the two-dimensional state M/G/1 queue with multiple working vacations in which the server works with different service rate rather than completely terminating the service during a working vacation period, also the server is following non-exhaustive service policy i. e. the server may go on vacation even if there are some customers present in the system. We assume that the server begins the working vacation when the system is empty. The service time during busy period is having general distribution whereas the service time during working vacation period, working vacation time and vacation time of the server are assumed to be exponentially distributed. Explicit probabilities of exact number of arrivals & departures by a given time are obtained. Number of units arrive by time t, number of units depart by time t, waiting time distribution, cumulative distribution for sojourn time, server's utilization time are also presented numerically and graphically both. Some particular cases are derived there from.

Reference

  1. Baba, Y. , 2005. Analysis of a GI/M/1 queue with multiple working vacations. Oper. Res. Lett. 33, 201–209.
  2. Hubbard, J. R. , Pegden, C. D. and Rosenshine, M. , 1986. The departure process for the M/M/1 queue, Journal of Applied Probability, Vol. 23, No. 1, pp. 249-255.
  3. Indra, 1994. Some two-state single server queueing models with vacation or latest arrival run, Ph. D. thesis, Kurukshetra University, Kurukshetra.
  4. Indra and Ruchi, 2009. Transient Analysis of Two-Dimensional M/M/1 Queueing System with working vacations, Journal of Mathematics and System Science, Vol. 5, No. 2, pp. 110-128.
  5. Indra and Vijay, 2005. A two-state queueing model with intermittent available server and departures in batches of variable size, Vision 2020: The Strategic Role of Operational Research, Allied publishers, pp. 222-232.
  6. Kim, J. D. , Choi, D. W. , Chae, K. C, 2003. Analysis of queue-length distribution of the M/G/1 queue with working vacations In: Hawaii International Conference on Statistics and Related Fields.
  7. Pegden, C. D. and Rosenshine, M. , 1982. Some new results for the M/M/1 queue, Mgt Sci Vol. 28, pp. 821-828.
  8. Servi, L. D. and Finn, S. G. , 2002. M/M/1 queues with working vacations (M/M/1/WV), Performance Evaluation, Vol. 50, pp 41-52.
  9. Sharda and Indra, 1995. Explicit transient and steady state queue length probabilities of a queueing model with server on vacation providing service intermittently, Microelectronic Reliab. Vol. 35, No. 1, pp-13-23.
  10. Takagi, H. , 1991. Vacation and Priority Systems, Part 1. Queueing Analysis: A Foundation of Performance Evaluation, vol. 1. North-Holland/Elsevier, Amsterdam.
  11. Tian, N. , Zhang, Z. G. , 2006. Vacation Queueing Models: Theory and Applications. Springer, New York.
  12. Wu, D. , Takagi, H. , 2006. M/G/1 queue with multiple working vacations. Perform. Eval. 63(7), pp. 654–681.

Keywords

Two-dimensional State Model, Multiple Working Vacation, Non-exhaustive Service, Laplace Transform, Supplementary Variable Technique