Co axian - 2 General Service Queuing Model with Restricted Admissibility

Authors(2) :-P. Suthersan, S. Maragathasundari

We explore the steady state conduct of a bulk arrival queuing model with compulsory vacation. Here the arrival follows a poisson distribution. Service following a general service distribution is rendered in two stages in which the second stage is optional. After the completion of service, the server has to undergo a compulsory vacation. An important phenomenon of restricted admissibility is carried out in this model which plays a wide role in all the categories of system which are following the queuing strategy. We obtain in closed form, the steady state probability generating functions for the number of customers in the queue for various states of the server, the average number of customers as well as their average waiting time in the queue and the system.

Authors and Affiliations

P. Suthersan
Department of Mathematics, Kalasalingam University, Tamilnadu, India
S. Maragathasundari
Department of Mathematics, Kalasalingam University, Tamilnadu, India

Bulk arrival, optional second stage, compulsory vacation, restricted admissibility.

  1. Chae.K.C, Lee H.W and Ahn. C.W (2001), “An arrival time approach to M/G/1- type queues with generalized vacations”, Queueing Systems, Vol.38, pp. 91-100.
  2. Choi. B.D., Kim. B. and Choi. S.H., (2003), “A M/G/1 queue with multiple types of feedback, gated vacations and FCFS policy”, Computers and Operations Research, Vol.30, No.9, pp.1289-1309.
  3. Choudhury, G., (2002), “A batch arrival queue with a vacation time under single vacation policy”, Computers and Operations Research, Vol.29, No.14, pp.1941-1955.
  4. Cox. D.R (1955), “The analysis of Non-Markovian Stochastic Processes by the inclusion of Supplementary Variables”, Proceedings of the Cambridge Philosophical Society, Vol.51, pp.433-441.
  5. Haridass M.and Arumuganathan R.(2015), “Analysis of a single server batch arrival retrial queueing system with modified vacations and N-policy, RAIRO-Oper. Res. 49, pp. 279-296
  6. Jain. M & Jain. A (2010), “Working vacation queueing model with multiple types of server breakdowns”, Applied Mathematical Modelling, Vol.34, pp.1-13.
  7. Kella.O, Zwart. B & Boxma. O (2005), “Some time-dependent properties of symmetric M/G/1 queues”, Journal of Applied Probability, Vol.42, No.1, pp.223-234.
  8. Kumar.R  and Sharma . S.K (2012), “A Markovian Feedback Queue with Retention of Reneged Customers and Balking”, AMO-Advanced Modeling and Optimization, Vol.14, No.3, pp.681-688.
  9. Karthikeyan.K and Maragathasundari.S (2015), Batch arrival of two stages with standby server during general vacation time & general repair time”, International Journal of Mathematical archive, Vol.6, No.4, pp.43-48.
  10. Kavitha. K and Maragathasundari.S (2012),“Analysis of Non Markovian queue with restricted admissibility and optional types of repair”, International journal of scientific research and management studies, Vol.2, No.5, pp.244-252.
  11. Kendall. D.G (1953), “Stochastic Processes occurring in the theory of queues and their analysis by the method of embedded Markov chain”, Annals of Mathematical Statistics, Vol.24.
  12. Madan. K.C and Abu-Dayyeh. A.Z (2004), “On a single server queue with optional phase type server vacations based on exhaustive deterministic service and a single vacation policy”, Applied Mathematics and Computation, Vol.149, No.3, pp. 723-734.
  13. Madan. K.C. and Chodhury. G (2004), “An Mx/G/1 queue with Bernoulli vacation schedule under restricted admissibility policy”,Sankhaya,Vol.66, pp.172-193.
  14. Madan. K.C and Anabosi. R.F (2003), “A single server queue with two types of service, Bernoulli schedule server vacations and a single vacation policy”, Pakistan Journal of Statistics, Vol.19, pp.331-442.
  15. Maragathasundari.S (2015), “A bulk arrival queuing model of three stages of service with different vacation policies, service interruption and delay time”, American International Journal of Research in Science, Technology, Engineering& Mathematics, Vol.11, No.1, pp.52-56.
  16. Maragathasundari.S and Srinivasan.S (2012), “Analysis of M/G/1 feedback queue with three stage and multiple server vacation”, Applied mathematical sciences, Vol.6, No.125, pp.6221-6240.
  17. Maragathasundari.S and Srinivasan.S (2015), “A Non-Markovian Multistage Batch arrival queue with breakdown and reneging”, Mathematical problems in engineering, Volume 2014/16 pages/ Article ID 519579/ http: // dx. Doi.  Org / 10.1155/2014/ 519579.
  18. Maragathasundari.S and Mirian cathy joy (2017), Queueing model of optional type of services with service stoppage and revamp process in web hosting (2017), Int. J. Knowledge Management in Tourism and Hospitality, Vol. 1, No. 2, 2017 241Copyright © 2017 Inderscience Enterprises Ltd
  19. Maraghi. F. A, Madan. K.C and Darby-Dowman. K (2010), “Batch Arrival vacation queue with second optional service and Random Breakdowns”, International Journal of Statistical Theory and Practice, Vol.4, No.1, pp.137-153.
  20. Maraghi. F.A, Madan. K.C and Darby-Dowman. K (2009), “Batch Arrival queuing system with Random Breakdowns and Bernoulli Schedule server vacations having General vacation Time Distribution”, International Journal of Information and Management Sciences, Vol.20, pp.55-70.
  21. Ranjitham .A. and Maragathasundari .S (2014), “Batch arrival queueing system with two      stages of service”, International journal of Math.Analysis, Vol.8 (6), pp.247-258
  22. Srinivasan.  S  and  Maragathasundari.S  (2017),  “Optional  services  in  a  Non  Markovian Queue”, International Journal of Operational Research, Vol.28, No.1, pp.1-17.
  23. Sowmiah. S and Maragathasundari. S (2015), “M/G/1 queueing system with extended    vacation, service interruption, Delay time and stages in repair”, Journal of Computer and Mathematical Sciences, Vol.6 (7), 363-370, July 2015
  24. Vignesh  and  Maragathasundari.S  (2017) “Analysis of Non Markovian Single server Batch arrival queueing system of compulsory three stages of service and fourth optional stage service service interruptions and deterministic server vacations, International Journal of Operational Research(article in press)
  25. Vignesh  and  Maragathasundari.S  (2017) “Analysis of non-Markovian batch arrival queueing model with multi stages of service of restricted admissibility, feedback service and three optional vacations in production and manufacturing” Int. J. Mathematics in Operational Research, Vol. 11, No. 3, 2017 285Copyright © 2017 Inderscience Enterprises Ltd.

Publication Details

Published in : Volume 3 | Issue 6 | September-October 2017
Date of Publication : 2017-10-31
License:  This work is licensed under a Creative Commons Attribution 4.0 International License.
Page(s) : 860-866
Manuscript Number : IJSRSET1736227
Publisher : Technoscience Academy

Print ISSN : 2395-1990, Online ISSN : 2394-4099

Cite This Article :

P. Suthersan, S. Maragathasundari, " Co axian - 2 General Service Queuing Model with Restricted Admissibility, International Journal of Scientific Research in Science, Engineering and Technology(IJSRSET), Print ISSN : 2395-1990, Online ISSN : 2394-4099, Volume 3, Issue 6, pp.860-866, September-October-2017.
Journal URL : http://ijsrset.com/IJSRSET1736227

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