This paper analyses an M/G/1 retrial queue with working vacation and constant retrial policy. As soon as the system becomes empty, the server begins a working vacation. The server works with different service rates rather than completely stopping service during a vacation. We construct the mathematical model and derive the steady-state queue distribution of number of customer in the retrial group. The effects of various performance measures are derived.
Mots-clés : retrial queue, working vacation, constant retrial policy
@article{RO_2014__48_3_381_0, author = {Jailaxmi, V. and Arumuganathan, R. and Senthil Kumar, M.}, title = {Performance analysis of single server non-markovian retrial queue with working vacation and constant retrial policy}, journal = {RAIRO - Operations Research - Recherche Op\'erationnelle}, pages = {381--398}, publisher = {EDP-Sciences}, volume = {48}, number = {3}, year = {2014}, doi = {10.1051/ro/2014013}, mrnumber = {3264385}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ro/2014013/} }
TY - JOUR AU - Jailaxmi, V. AU - Arumuganathan, R. AU - Senthil Kumar, M. TI - Performance analysis of single server non-markovian retrial queue with working vacation and constant retrial policy JO - RAIRO - Operations Research - Recherche Opérationnelle PY - 2014 SP - 381 EP - 398 VL - 48 IS - 3 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ro/2014013/ DO - 10.1051/ro/2014013 LA - en ID - RO_2014__48_3_381_0 ER -
%0 Journal Article %A Jailaxmi, V. %A Arumuganathan, R. %A Senthil Kumar, M. %T Performance analysis of single server non-markovian retrial queue with working vacation and constant retrial policy %J RAIRO - Operations Research - Recherche Opérationnelle %D 2014 %P 381-398 %V 48 %N 3 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ro/2014013/ %R 10.1051/ro/2014013 %G en %F RO_2014__48_3_381_0
Jailaxmi, V.; Arumuganathan, R.; Senthil Kumar, M. Performance analysis of single server non-markovian retrial queue with working vacation and constant retrial policy. RAIRO - Operations Research - Recherche Opérationnelle, Tome 48 (2014) no. 3, pp. 381-398. doi : 10.1051/ro/2014013. http://www.numdam.org/articles/10.1051/ro/2014013/
[1] Retrial queues, Chapman and Hall, London (1997). | Zbl
and ,[2] Accessible bibliography on retrail queues. Math. Comput. Model. 30 (1999) 1-6. | Zbl
,[3] A classified bibliography of research on retrial queues: Progress in 1990, Top 7 (1999) 187-211. | MR | Zbl
,[4] The M/G/1 Retrial queue with Bernoulli schedule. Queueing Syst. 7 (1990) 219-227. | MR | Zbl
and ,[5] M/G/1 Retrial queueing system with two types of calls and finite capacity. Queueing Syst. 19 (1995) 215-229. | MR | Zbl
, and ,[6] Single server retrial queues with priority calls. Math. Comput. Model. 30 (1999) 7-32. | MR | Zbl
and ,[7] J.R. Artalejo and Gomez-Corral, Retrial queueing systems. A Comput. Approach. Springer-Verlag, Berlin (2008). | MR | Zbl
[8] Vacation and priority systems, Part I, Queueing analysis. A foundation of performance evaluation, Vol. 1, North-Holland, Amsterdam (1991). | MR | Zbl
,[9] A single server retrial queue with server vacation and a finite number of input sources. Eur. J. Oper. Res. 85 (1995) 149-160. | Zbl
and ,[10] Analysis of an M/G/1 queue with constant repeated attempts and server vacations. Comput. Oper. Res. 24 (1997) 493-504. | MR | Zbl
,[11] Queueing systems with vacations a survey. Queueing Syst. 1 (1986) 29-66. | MR | Zbl
,[12] An M/G/1 queue with variable vacation. Proc. Int. Conf. Performance Model., Sophia Antipolis, France (1985).
,[13] On the MX/G/1 queue with vacation time. Oper. Res. Lett. 5 (1986) 93-98. | MR | Zbl
,[14] On the single server batch arrival retrial queue with general vacation time under Bernoulli schedule and two phases of heterogeneous service. Quality Technology and Quantitative Management 5 (2008) 145-160. | MR
and ,[15] Analysis of MX/G/1 queue with N-policy and multiple vacations. J. Appl. Prob. 31 (1994) 467-496. | MR | Zbl
, , and ,[16] Batch arrival queue with N-policy and single vacation. Comput. Oper. Res. 22 (1995) 173-189. | Zbl
, and ,[17] Analysis of a bulk queue with N- policy multiple vacations and setup times. Comput. Oper. Res. 25 (1998) 957-967. | MR | Zbl
, and ,[18] Steady state analysis of non-Markorian bulk queueing system with N-Policy and different types of vacations. Int. J. Modern Math. 3 (2008) 47-66. | MR | Zbl
, and .[19] Analysis of a MX/G/1 queueing system with vacation interruption. RAIRO-Oper. Res. 46 (2012) 304-334. | Numdam | MR | Zbl
and ,[20] M/M/1 queues with working vacation (M/M/1/Wv). Performance Evaluation 50 (2002) 41-52.
and ,[21] D. Choi and K. Chae, Analysis of queue length distribution of the M/G/1 queue with working vacations, Int. Conf. Statistics and related fields, Hawaii (2003).
[22] D. Wu. and H. Takagi, M/G/1 queue with multiple working vacations. Performance Evaluations 63 (2006) 654-681.
[23] Analysis of the M/G/1 queue with exponentially distributed working vacations a matrix analytic approach. Queueing Syst. 61 (2009) 139-166. | MR | Zbl
, and ,[24] Do. Tien Van, M/M/1 retrial queue working vacation. Acta Inf. 47 (2009) 67-75. | MR | Zbl
[25] Semi-Markov Process and Reliability-Statistics for Industry and Technology, Birkhauser Boston, Springer (2001). | MR | Zbl
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