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Transient Analysis of Two-Dimensional State Markovian Queuing Model with Multiple Working Vacations and Non-Exhaustive Service

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International Journal of Computer Applications
© 2010 by IJCA Journal
Number 7 - Article 1
Year of Publication: 2010
Authors:
Indra
Ruchi
10.5120/1598-2147

Indra and Ruchi. Article:Transient Analysis of Two-Dimensional State Markovian Queuing Model with Multiple Working Vacations and Non-Exhaustive Service. International Journal of Computer Applications 11(7):1–7, December 2010. Published By Foundation of Computer Science. BibTeX

@article{key:article,
	author = {Indra and Ruchi},
	title = {Article:Transient Analysis of Two-Dimensional State Markovian Queuing Model with Multiple Working Vacations and Non-Exhaustive Service},
	journal = {International Journal of Computer Applications},
	year = {2010},
	volume = {11},
	number = {7},
	pages = {1--7},
	month = {December},
	note = {Published By Foundation of Computer Science}
}

Abstract

In the present paper, Two-dimensional state time dependent probabilities along with some interesting particular cases are obtained for single server Markovian queuing system where the service mechanism is Non-exhaustive i.e. the server may go on vacation even if there are some customers waiting for service and during a vacation (working) period the server is allowed to do an alternative job at a different rate. The interarrival time, service time, working vacation time and availability time of the server are assumed to be exponentially distributed. Sample computational representations of the solution are developed and results of a simple computation are provided and presented graphically. Finally some particular cases are derived there from.

Reference

  • Baba, Y., (2005), Analysis of a GI/M/1 queue with multiple working vacations. Oper. Res. Lett. 33, 201–209.
  • Banik, A.D., Gupta, U.C., Pathak, S.S. (2007), On the GI/M/1/N queue with multiple working vacations -analytic analysis and computation Appl. Math. Modell. 31(9), 1701–1710.
  • 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, (Mar.,1986), pp.249-255.
  • Indra, (1994), Some two-state single server queueing models with vacation or latest arrival run, Ph.D. thesis, Kurukshetra University, Kurukshetra.
  • 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, (Dec. 2009) pp. 110-128.
  • 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.
  • Kumar Vijay, (2007), Two-State Bulk Queueing models with multiple vacations, Ph.D. Thesis, K.U. Kurukshetra.
  • Pegden, C.D. and Rosenshine, M. (1982), Some new results for the M/M/1 queue, Mgt Sci 28, 821-828 (1982).
  • 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.
  • Wu, D., Takagi, H., (2006), M/G/1 queue with multiple working vacations. Perform. Eval. 63(7), 654–681.