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APPROXIMATE ANALYSIS OF M/M/c RETRIAL QUEUE WITH SERVER VACATIONS
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 Title & Authors
APPROXIMATE ANALYSIS OF M/M/c RETRIAL QUEUE WITH SERVER VACATIONS
SHIN, YANG WOO; MOON, DUG HEE;
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 Abstract
We consider the M/M/c/c queues in which the customers blocked to enter the service facility retry after a random amount of time and some of idle servers can leave the vacation. The vacation time and retrial time are assumed to be of phase type distribution. Approximation formulae for the distribution of the number of customers in service facility and the mean number of customers in orbit are presented. We provide an approximation for M/M/c/c queue with general retrial time and general vacation time by approximating the general distribution with phase type distribution. Some numerical results are presented.
 Keywords
Retrial queue;Vacation queue;Phase type distribution;Approximation;
 Language
English
 Cited by
 References
1.
J. R. Artalejo and A. Gomez-Corral, Retrial Queueing Systems, A Computational Approach, Hidelberg, Springer-Verlag, 2008.

2.
G. I. Falin and J. G. C. Templeton, Retrial Queues, London, Chapman and Hall, 1997.

3.
H. Takagi, Queueing Analysis, Vol. 1. Vacation Systems, Elsevier Science, Amsterdam, 1991.

4.
N. Tian and Z. G. Zhang, Vacation Queuing Models: Theory and Applications, Springer, New York, 2006.

5.
J. R. Artalejo, Analysis of an M/G/1 queue with constant repeated attempts and server vacations, Computers & Operations Research, 24 (1997), 493-504. crossref(new window)

6.
M. Boualem, N. Djellab and D. Aissani, Stochastic inequalities for M/G/1 retrial queues with vacations and constant retrial policy, Mathematical and Computer Modelling, 50 (2009), 207-212. crossref(new window)

7.
G. Choudhury and J. C. Ke, A batch arrival retrial queue with general retrial times under Bernoulli vacation schedule for unreliable server and delyed repair, Applied Mathematical Modelling, 36 (2012), 255-269. crossref(new window)

8.
J. C. Ke and F. M. Chang, Modified vacation policy for M/G/1 retrial queue with balking and feedback, Computers & Industrial Engineering, 57 (2009), 433-443. crossref(new window)

9.
B. K. Kummar, R. Rukmani and V. Thangaraj, An M/M/c retrial queueing system with Bernoulli vacations, Journal of Systems Science and Systems Engineering, 18(2) (2009), 222-242. crossref(new window)

10.
G. Choudhury, Steady state analysis of an M/G/1 queue with linear retrial policy and two phase service under Bernoulli vacation schedule, Applied Mathematical Modelling, 32 (2008), 2480-2489. crossref(new window)

11.
T. Phung-Duc and K. Kawanishi, Multi-server retrial queues with after-call-work, Numerical Algebra, Control and Optimization, 1(4) (2011), 639-656. crossref(new window)

12.
Y. W. Shin, Algorithmic approach to Markovian multi-server retrial queue with vacations, Applied Mathematics and Computation, 250 (2015), 287-297. crossref(new window)

13.
Y.W. Shin and D. H. Moon, Approximation of M/M/c retrial queue with PH-retrial times European Journal of Operational Research, 213 (2011), 205-209. crossref(new window)

14.
Y. W. Shin and D. H. Moon, Approximation of PH/PH/c retrial queue with PH-retrial time, Asia-Pacific Journal of Operational Research, 31(2) (2014), 140010 (21 pages).

15.
Y. W. Shin, Ergodicity of M AP/PH/c/K retrial queue with server vacations, Submitted for publication.

16.
X. Xu and Z.G. Zhang, Analysis of multiple-server queue with a single vacation (e, d)-policy, Performance Evaluation, 63 (2006), 825-838. crossref(new window)

17.
M. F. Neuts, Matrix-Geometric Solutions in Stochastic Models - An Algorithmic Approach, Baltimore, Johns Hopkins University Press, 1981.

18.
R. W. Wolff, Stochastic Modeling and the Theory of Queues, Prentice-Hall, Inc. Englewood Cliffs, 1989.

19.
H. Tijms, A First Course in Stochastic Models, Wiley, 2003.

20.
Y.W. Shin, Fundamental matrix of transientQBD generator with finite states and level dependent transitions, Asia-Pacific Journal of Operational Research, 26 (2009), 697-714. crossref(new window)

21.
S. Wolfram, Mathematica, 2nd ed. Addison-Wesley, 1991.

22.
W. D. Kelton, R. P. Sadowski and D. A. Sadowski, Simulation with ARENA, 2nd Ed., New York, McGraw-Hill, 1998.

23.
W. Whitt, Approximating a point process by a renewal process, I: two basic methods, Operations Research, 30 (1982), 125-147. crossref(new window)

24.
A. Bobbio, A. Horvath and M. Telek, Matching three moments with minimal acyclic phase type distributions, Stochastic Models, 21 (2005), 303-326. crossref(new window)