Open Access Open Access  Restricted Access Subscription Access

Time Dependent Analysis for Retrial Priority Model with Single Vacation

S. Damodaran, A. Muthu Ganapathi Subramanian, Gopal Sekar

Abstract


Transient behaviour of Single server Retrial Queueing problem with non-preemptive priority combined with single vacation is taken up for study in this paper. The arrival pattern of low priority customer follows Poisson distribution with arrival rate λ1 and that of high priority also follows Poisson distribution with arrival rate λ2. Service rates of low and high priority customers follow exponential distribution with rates μ1and μ2 respectively. Retrial rate of customers from the orbit is σ. When there are no customers in both high and low priority queues, the server will go for a vacation. The server will return to the system to provide service with rate α. The transient solution to the model is obtained using matrix exponential method. The time dependent probabilities and system performance measures are computed.


Full Text:

PDF

References


J. R. Artalejo; A classified bibliography of research on retrial queues Progress in 1990-1999, Top 7, 187-221(1999a).https://doi.org/10.1007/BF02564721

J. R. Artalejo; Accessible bibliography onretrial queues, Mathematical and Computer Modelling, 30 223-233(1999b). https://doi.org/10.1016/S08957177(99)00128-4

G. Ayyappan; A. MuthuGanapathiSubramanianandGopalsekar (2009); M/M/1 Retrial Queueing System with Non-preemptive priority Service and Single Vacation – Exhaustive Service, Pacific Asian Journal of Mathematics, 3(1-2) 307-322 (2009).

A. Azhagappan; E. Veeramani; W. Monica; K. Sonabharathi; Transient solution of an M/M/1 Retrial Queue with Reneging from Orbit; Application and Applied Mathematics, 13(2) 628-638 (2018).

A. Azhagappan; T. Deepa; Transient Analysis of a markovian Single Vacation Feedback Queue with an Interrupted Closed Down Time and Control of Admission during Vacation, Applications and Applied Mathematics, 14(1) 34-45 (2019).

S. Damodaran; A. MuthuGanapathiSubramanian;GopalSekar; Transient Behaviour of M/M/1 Retrial Queueing Model, Journal of Scientific Computing, 9(3) (2020).

S. Damodaran; A. MuthuGanapathiSubramanian;GopalSekar; Computational Approach for Transient Behaviour of Single server Retrial Queueing System with Non-pre emptive priority services, Science, Technology and Development, IX (VII) 2020.http://journalstd.com/gallery/7-july2020.pdf

B. T. Doshi; Queueing Systems with vacation – a Survey, Queueing systems, 1 29-66 (1986).

G.I Falin; A survey of retrial queues, Queueing Systems, 7(2) 127-167 (1990)

G.I. Falin; J.G.C. Templeton; Retrial Queues, Monographs on Statistics and Applied Probability, Chapman and Hall, 75 (1997).

U. Gupta; A. Banik; S. Pathak; Complete analysis of MAP/G/1/N queue with single (multiple) vacation(s) under limited service discipline, Journal of Applied Mathematics and Stochastic Analysis, 3 353–373 (2005).https://doi.org/10.1155/JAMSA.2005.353

U. C. Gupta; K. Sikdar; Computing queuelength distributions in MAP/G/1 N queue under single and multiple vacation, Applied Mathematics and Computation, 174 1498-1525 (2006).https://doi.org/10.1016/j.amc.2005.07.001

Indra; S. Bansal; The transient solution of an unreliable M/G/1 queue with vacations, International Journal of Information and Management Sciences, 21 391-406 (2010).

K. Kaliappan; J. Gananraj; S. Gopinathan; R.Kasturi; Transient analysis of an M/M/1 queue with repairable server and Multiple vacations, International Journal of Mathematics in Operations Research, 6(2) 193-216 (2014).

K. Ramanath; K.Kalidass; A two phase service M/G/1 vacation queue with general retrial times and non-persistent customers. Int. J. Open Problems Compt. Math., 3(2) (2010).

J. C. Ke; C. H.Lin;Maximum entropy approach for batch-arrival under N policy with a non-reliable server and single vacation, Journal of Computational and Applied Mathematics, 221 1-15 (2008).https://doi.org/10.1016/j.cam.2007.10.001

J. C. Ke; C. H. Wu; Z.G. Zhang; Recent developments in vacation queueing Models: A Short Survey, International Journal of Operations Research, 7(4) 3-8 (2010).

B. K. Kumar; D. Arivudainambi; The M/G/1retrial queue with Bernoulli schedules and general retrial times, Computer and Mathematics with Application, 43 15-30 (2002).https://doi.org/10.1016/S0898-1221(01)00267-X

K. LakshmI; K. Ramanath; (2013)An M/G/1RetrialQueue with a single vacation Scheme and General Retrial times, American Journal of Operational Research, 3(2A) 7-16 (2013). https://doi.org/10.5923/s.ajor.201305.02

K. C. Madan; W. Abu-Dayyeh; F. Taiyyan; Atwo server queue with Bernoulli schedules and a single vacation policy, Applied Mathematics and Computation,145 59-71(2003).https://doi.org/10.1016/S0096-3003(02)00469-1

S. MaragathaSundari; S. Srinivasan; Analysis of Transient Behaviour of M/G/1 Queue with Single Vacation, International Journal of Pure and Applied Mathematics, 76(1) 149-156 (2012).

P. R. Parthasarathy; R. Sudhesh; Time-

dependent analysis of a single-server retrial queue with state-dependent rates, Operations Research Letters, 35 601-611(2007).https://doi.org/10.1016/j.orl.2006.12.005

S. Ammar; Transient analysis of an M/ M /1queue with impatient behavior and multiple vacations, Applied Mathematics and Computational 260 97–105 (2015). https://doi.org/10.1016/j.amc.2015.03.066

S. Ammar; Transient solution of an M/M/1vacation queue with a waiting server and impatient customers, Journal of the Egyptian Mathematical Society, 25 337-342 (2017). https://doi.org/10.1016/j.joems.2016.09.002

R. Sudhesh; A. Azhagappan; Transient

analysis of M/M/1 queue with server vacation customers impatient and a waiting server timer, Asian Journal of Research in Social Sciences and Humanities, 6(9) 1096-1104 (2016). http://dx.doi.org/10.5958/2249-7315.2016.00857.1

H. Takagi; Queueing Analysis, Vacation and Priority Systems, North-Holland, Amsterdam, 1 (1991).

N. Tian; Z. G. Zhang; Vacation Queueing Models – Theory and Applications, Springer, Newyork, (2006).

M. Wozniak; M. WojciechKempa; M. Gabryel; K. Robert Nowicki; A Finite–Buffer Queue with a Single Vacation Policy: An Analytical Study with Evolutionary Positioning, International Journal of Applied Mathematics and Computer Science, 24(4) 887–900 (2014). https://doi.org/10.2478/amcs-2014-0065

X. L. Xu; Z. G. Zhang; The analysis of multi server

queue with single vacation and a (e,d) policy, Performance Evaluation, 63(8) 825-838 (2006).https://doi.org/10.1016/j.peva.2005.09.003

Z. G. Zhang; N. Tian; Analysis of queueing system with synchronous single vacation for some servers, Queueing Systems, 45 161-175 (2003a). https://doi.org/10.1023/A:1026097723093


Refbacks

  • There are currently no refbacks.




INDIAN ASSOCIATION FOR RELIABILITY AND STATISTICS

(IARS)

© 2015 IARS. All right reserved.