Transient analysis of M/M/1 queue with working vacation, heterogeneous service and customers’ impatience
RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 3, pp. 591-606.

This paper studies the time-dependent behavior of a single server queueing model with slow service during single and multiple working vacations, and customers’ impatience due to slow service. The time-dependent system size probabilities for the underlying model are obtained in closed form. Further, time-dependent mean and variance are deduced. Finally, numerical illustrations are shown to visualize the system effect for various values of parameters.

Reçu le :
Accepté le :
DOI : 10.1051/ro/2016046
Classification : 60K25, 33C15
Mots clés : Single server queue, multiple and single working vacation, impatient customers, continued fractions, confluent hypergeometric functions
Sudhesh, R. 1 ; Azhagappan, A. 2 ; Dharmaraja, S. 3

1 Department of Mathematics, Bharathidasan Institute of Technology (BIT) Campus, Anna University, Tiruchirappalli, 620024 Tamilnadu, India.
2 Department of Mathematics, St. Anne’s College of Engineering and Technology, Anna University, Panruti, Cuddalore district, 607110 Tamilnadu, India.
3 Department of Mathematics, Indian Institute of Technology Delhi, Haus Khas, 110016 New Delhi, India.
@article{RO_2017__51_3_591_0,
     author = {Sudhesh, R. and Azhagappan, A. and Dharmaraja, S.},
     title = {Transient analysis of {M/M/1} queue with working vacation, heterogeneous service and customers{\textquoteright} impatience},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {591--606},
     publisher = {EDP-Sciences},
     volume = {51},
     number = {3},
     year = {2017},
     doi = {10.1051/ro/2016046},
     mrnumber = {3880514},
     zbl = {1382.60120},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ro/2016046/}
}
TY  - JOUR
AU  - Sudhesh, R.
AU  - Azhagappan, A.
AU  - Dharmaraja, S.
TI  - Transient analysis of M/M/1 queue with working vacation, heterogeneous service and customers’ impatience
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2017
SP  - 591
EP  - 606
VL  - 51
IS  - 3
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ro/2016046/
DO  - 10.1051/ro/2016046
LA  - en
ID  - RO_2017__51_3_591_0
ER  - 
%0 Journal Article
%A Sudhesh, R.
%A Azhagappan, A.
%A Dharmaraja, S.
%T Transient analysis of M/M/1 queue with working vacation, heterogeneous service and customers’ impatience
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2017
%P 591-606
%V 51
%N 3
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ro/2016046/
%R 10.1051/ro/2016046
%G en
%F RO_2017__51_3_591_0
Sudhesh, R.; Azhagappan, A.; Dharmaraja, S. Transient analysis of M/M/1 queue with working vacation, heterogeneous service and customers’ impatience. RAIRO - Operations Research - Recherche Opérationnelle, Tome 51 (2017) no. 3, pp. 591-606. doi : 10.1051/ro/2016046. http://archive.numdam.org/articles/10.1051/ro/2016046/

E. Altman and U. Yechiali, Analysis of customers’ impatience in queues with server vacation. Queueing Syst. 52 (2006) 261–279. | DOI | MR | Zbl

S.I. Ammar, Transient analysis of an M/M/1 queue with impatient behavior and multiple vacations. Appl. Math. Comput. 260 (2015) 97–105. | MR | Zbl

B.D. Choi, B. Kim and J. Chung, M/M/1 queue with impatient customers of higher priority. Queueing Syst. 38 (2001a) 49–66. | DOI | MR | Zbl

A. Choudhury, Impatience in single server queuing model. Am. J. Math. Manage. Sci. 28 (2008) 177–211. | MR | Zbl

B.T. Doshi, Queueing Syst. with vacations – A survey. Queueing Syst. 1 (1986) 29–66. | DOI | MR | Zbl

I. Gradshteyn, I. Ryzhik, A. Jeffrey and D. Zwillinger, Table of Integrals, Series and Products, 7th edn. Academic Press, Elsevier (2007). | MR

W.B. Jones and W.J. Thron, Continued Fractions: Analytic Theory and Applications, Vol. 2 of Encyclopedia of Mathematics and its Applications. Addison Wesley, New York (1980). | MR

K. Kalidass and K. Ramanath, Transient analysis of an M/M/1 queue with multiple vacations. Pakistan J. Stat. Oper. Res. 10 (2014) 121–130. | DOI | MR | Zbl

B. Kim and J. Kim, A single server queue with Markov modulated service rates and impatient customers. Perform. Eval. 83–84 (2015) 1–15. | DOI

J. Li and N. Tian, The M/M/1 queue with working vacations and vacation interruptions. J. Syst. Sci. Syst. Eng. 16 (2007). 121–127.

L. Lorentzen and H. Waadeland, Continued Fractions with Applications, in Vol. 3 of Studies in Computational Mathematics. Elsevier, Amsterdam (1992). | MR | Zbl

N. Perel and U. Yechiali, Queues with slow servers and impatient customers. Eur. J. Oper. Res. 201 (2010) 247–258. | DOI | MR | Zbl

L.D. Servi and S.G. Finn, M/M/1 queue with working vacations(M/M/1/WV). Perform. Eval. 50 (2002) 41–52. | DOI

R. Sudhesh, Transient analysis of a queue with system disasters and customer impatience. Queueing Syst. 66 (2010) 95–105. | DOI | MR | Zbl

N. Tian, X. Zhao and K. Wang, The M/M/1 queue with single working vacation. Int. J. Inf. Manage. Sci. 19 (2008) 621–634. | MR | Zbl

P. Vijayalaxmi and K. Jyothsna, Analysis of finite buffer renewal input queue with balking and multiple working vacations. Opsearch 50 (2013) 548–565. | DOI | MR | Zbl

U. Yechiali, Queues with system disasters and impatient customers when system is down. Queueing Syst. 56 (2007) 195–202. | DOI | MR | Zbl

D. Yue, W. Yue and G. Xu, Analysis of a queueing system with impatient customers and working vacations, in Proc. of the 6th International Conference on Queueing Theory and Network Applications (2011) 208–211.

D. Yue, W. Yue, Z. Saffer and X. Chen, Analysis of an M/M/1 queueing system with impatient customers and a variant of multiple vacation policy. J. Ind. Manag. Optim. 10 (2014) 89–112. | DOI | MR | Zbl

D. Yue, W. Yue and G. Zhao, Analysis of an M/M/1 queue with vacations and impatience timers which depend on the server’s states. J. Ind. Manag. Optim. 12 (2016) 653–666. | DOI | MR | Zbl

Cité par Sources :