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Reseach Article

A View of Queue Analysis with Customer Behaviour and Priorities

Published on May 2012 by Neetu Gupta
National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011
Foundation of Computer Science USA
RTMC - Number 4
May 2012
Authors: Neetu Gupta
2ed0c853-75f2-4bcc-a62c-1a74b5d1d8ac

Neetu Gupta . A View of Queue Analysis with Customer Behaviour and Priorities. National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011. RTMC, 4 (May 2012), 9-15.

@article{
author = { Neetu Gupta },
title = { A View of Queue Analysis with Customer Behaviour and Priorities },
journal = { National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011 },
issue_date = { May 2012 },
volume = { RTMC },
number = { 4 },
month = { May },
year = { 2012 },
issn = 0975-8887,
pages = { 9-15 },
numpages = 7,
url = { /proceedings/rtmc/number4/6644-1027/ },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Proceeding Article
%1 National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011
%A Neetu Gupta
%T A View of Queue Analysis with Customer Behaviour and Priorities
%J National Workshop-Cum-Conference on Recent Trends in Mathematics and Computing 2011
%@ 0975-8887
%V RTMC
%N 4
%P 9-15
%D 2012
%I International Journal of Computer Applications
Abstract

This paper presents an analysis for an queueing system with customer behaviour and priorities. Arriving customers balk (do not enter) with a probability and renege (leave the queue after entering) according to some distribution. The priority discipline followed may be either non-preemptive or preemptive in nature. When the priority discipline is non-preemptive in nature, a job in service is allowed to complete its service normally even if a job of higher priority enters the queue while its service is going on. In the preemptive case, the service to the ongoing job will be preempted by the new arrival of higher priority. At the end of paper benefits and limitations of queueing theory is also given.

References
  1. Abou El-Ata M. O. , Hariri A. M. A. , "The M/M/C/N queue with balking and reneging" Computers and Operations Research 19, pp. 713-716, 1992.
  2. Ancker Jr. C. J. , Gafarian A. V. , "Some queueing problems with balking and reneging", I. Operations Research 11, pp. 88-100, 1963.
  3. Ancker Jr. C. J. , Gafarian A. V. , "Some queueing problems with balking and reneging", II. Operations Research 11, pp. 928-937, 1963.
  4. Ancker Jr. C. J. , Gafarian A. V. , "Queueing with Impatient Customers who Leave at Random", J. Indust. Eng. 13, pp. 86-87, 1962.
  5. Ancker Jr. C. J. , Gafarian A. V. , "Queueing with Reneging and Multiple Hetero-geneous servers", Naval Res. Log. Quart. 10, pp. 137-139, 1963.
  6. . Ancker Jr. C. J. , Gafarian A. V. , "Queuing with Reneging and Multiple Heterogeneous Servers", SP-372, System Development Corporation, pp. 16-18, 1961.
  7. Avi-Itzhak B. , Naor P. , "Some queueing problems with the service station subject to breakdown", Oper. Res. , 11, pp. 303-320, 1963.
  8. Barrer D. Y. , "Queuing with impatient customers and ordered service", Oper. Res. 5, pp. 650-656, 1957.
  9. Bbocmeyer E. , Halstrom H. L. , Jensen A. , "The Life and Works of A. K. Erlang", Copenhagen Telephone Company, 1948.
  10. Boots N. K. , Tijms H. , "A multiserver queueing system with impatient customers",Management Sci. 45, pp. 444-448, 1999.
  11. Choi B. D. , Kim B. , Chung J. , "M/M/1 queue with impatient customers of higher priority", Queueing Systems 38, pp. 49-66. 2001.
  12. Crommelin C. D. , "Delay Probability Formulae When the Holding Times Are Constant", P. O. Elec. Eng. J. 25, pp. 41-50, 1932.
  13. Erlang A. K. , "The Theory of Probabilities and Telephone Conservations", Nyt Tidsskrift Mat. B 20, pp. 33-39, 1909.
  14. Gaver D. P. , Junior, "A waiting line with interrupted service, including priorities", J. Roy. Stat. Soc. , B 24, pp. 73-90, 1962.
  15. Gupta N. , Mishra G. D. , Choubey A. , "Performance analysis of an queueing model M/M/c/N with balking andreneging", International Journal of Computer Mathematical Sciences and Applications, Vol 2, No. 4, pp. 335-339, October-December 2008.
  16. Gupta N. , Mishra G. D. , Choubey A. , "Performance analysis of An M/M/1/K Queue with Non-Preemptive Priority", International Journal of Mathematical Sciences and Engineering Applications, Vol 3, No. 2, pp. 191-197, 2009.
  17. Gupta N. , Mishra G. D. , Choubey A. , "Performance analysis of queueing model M/M/I/N with balking and reneging", International Journal of Pure Applied Mathematical Sciences, Vol. LXX, No. 1-2, pp. 59-65, September 2009.
  18. Gupta N. , Mishra G. D. , Choubey A. , "Performance Analysis of An M/M/1/K Queue with Preemptive Priority", International journal of Business Research, Vol. July, pp. 50-57, 2009.
  19. Haight F. A. , "Queueing with balking", Biometrika 44, pp. 360-369, 1957.
  20. Homma T. , "On a Certain Queuing Process", Rept. Statist. Application Research, Union Japanese Scientists and Engrs. 4, No. 1, 1955.
  21. Jaiswal N. K. ,"Priority Queues", New York, Academic Press, 1968.
  22. Keilson J. , "Queues subject to service interruption", Ann. Math. Statist. , 33, pp. 1314-1322, 1962.
  23. Kendall D. G. , "Stochastic Processes Occuring in the Theory of Queues and Their Analysis by the Method of Imbedded Markov Chains", Ann. Math. Statist. 24, pp. 338-354,1953.
  24. Kendall D. G. , Reuter G. E. H. , "The calculation of the ergodic projection for Markov chains and processes with a countable infinity of states", Acta Mathematica, 97, pp. 103—144, 1957.
  25. Khintchine A. Y. , "Mathematisches ?ber die Erwortung vor einemöffenthchen Schalter", Mat. Sb. 39, pp. 73-84, 1932.
  26. Kolmogorov A. N. , "Sur le problem d'attente", Mat. Sb. 8, pp. 101-106, 1932.
  27. Palm C. , "Analysis of the Erlang Traffic Formulae for Busy Signal Arrangements", Ericsson Tech. 6, pp. 39-58, 1938.
  28. Pollaczek F. , "Lösung eines Geometrischen Wahrsceinlichkeits-problems", Math. Z. 35, pp. 230-278, 1932.
  29. Takine T. , Hasegawa T. , "The workload in the MAP/G/l queue with state dependent services: Its application to a queue with preemptive resume priority'", Comm. Statist. Stochastic Models, 10, pp. 183-221, 1994.
  30. Welch P. D. , "On preemptive resume priority queues", Ann. Math. Statist. , 35, pp. 600-612, 1964.
Index Terms

Computer Science
Information Sciences

Keywords

Balking And Reneging Preemptive And Non-preemptive Priority Queueing System