Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-28T00:43:41.907Z Has data issue: false hasContentIssue false
  • English
  • Français

An MX/G/1 unreliable retrial queuewith two phase service and persistence behaviour of customers in service

Published online by Cambridge University Press:  11 February 2013

M. Senthil Kumar  and
R. Arumuganathan
M. Senthil Kumar
Affiliation:
Department of Applied Mathematics and Computational Sciences, PSG College of Technology, Coimbatore 641004, India.. ms_kumar_in@yahoo.com
R. Arumuganathan
Affiliation:
Department of Mathematics, PSG College of Technology, 641004 Coimbatore, India.; ran_psgtech@yahoo.co.in
Get access

Abstract

This paper describes an unreliable server batch arrival retrial queue with two types ofrepair and second optional service. The server provides preliminary first essentialservice (FES) to the primary arriving customers or customers from retrial group. Onsuccessful completion of FES, the customer may opt for second optional service (SOS) withprobability α. The server is subject to active break downs. The customerunder FES (or SOS) during the failure decides, with probability q, tojoin the orbit(impatientcustomer) and, with complementary probabilityp, to remain in the server for repair in order to conclude hisremaining service (patientcustomer). Both service and repair times areassumed to have general distribution. It is considered that the repair time of serverduring the presence of patient customer and the repair time of the server while thecustomer (impatientcustomer) joining the orbit due to failure, aredifferent. For this queueing system, the orbit and system size distributions are obtained.Reliability of the proposed model is analysed. Some particular cases are also discussed.Other performance measures are also obtained. The effects of several parameters on thesystem are analysed numerically.

Keywords

First essential servicereliability measuressecond optional serviceunreliable serverpersistent customers
Type
Research Article
Information
RAIRO - Operations Research , Volume 47 , Issue 1 , January 2013 , pp. 9 - 32
Copyright
© EDP Sciences, ROADEF, SMAI, 2013

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Références

Aissani, A., Unreliable queueing with repeated orders. Microelectr. Reliab. 33 (1993) 2093–2106. Google Scholar
Aissani, A., A retrial queue with redundancy and unreliable server. Queueing Syst. 17 (1994) 431–449. Google Scholar
Aissani, A. and Artalejo, J., On the single server retrial queue subject to breakdowns. Queueing Syst. 30 (1998) 309–321. Google Scholar
Artalejo, J.R., Accessible bibliography on retrial queues. Math. Comput. Model. 30 (1999a) 1–6. Google Scholar
Artalejo, J.R., A classified bibliography of research on retrial queues : progress in 1990-1999 Top 7 (1999b) 187–211. Google Scholar
Artalejo, J.R. and Choudhury, G., Steady state analysis of an M/G/1 queue with repeated attempts and two phase service. Quality Technol. Quantitat. Manag. 1 (2004) 189–199. Google Scholar
Atencia, I., Fortes, I., Morena, P. and Sanchez, S., An M/G/1 retrial queue with active breakdowns and Bernoulli schedule in the server. Informat. Manag. Sci. 17 (2006) 1–17. Google Scholar
Atencia, I., Bouza, G. and Morena, P., An retrial queue with server breakdowns and constant rate of repeated attempts. Annal. Operat. Res. 157 (2008) 225–243. Google Scholar
Atencia, I. and Moreno, P., A single server retrial queue with general retrial times and Bernoulli Schedule. Appl. Math. Comput. 162 (2005) 855–880. Google Scholar
Avi-Itzhak, B. and Naor, P.P., Some queueing problems with the service station subject to breakdown. Operat. Res. 11 (1963) 303–320. Google Scholar
Choudhury, G., Some aspects of an M/G/1 queueing system with optional second service. Top 11 (2003) 141–150. Google Scholar
Choudhury, G. and Madan, Kailash, A batch arrival Bernoulli Vacation queue with a random setup time under restricted admissibility policy. Int. J. Oper. Res. 2 (2007) 81–97. Google Scholar
Choudhury, G. and Kandarpa, D., An M/G/1 retrial queue with two phases of service subject to the server breakdowns and repair. Performance Evaluation 65 (2008) 714–724. Google Scholar
Falin, G.I., Aggregate arrival of customers in one line queue with repeated calls. Ukrainian Math J. 28 (1976) 437–440. Google Scholar
Falin, G.I., A survey of retrial queues. Queueing Syst. 7 (1990) 127–168. Google Scholar
G.I. Falin and J.G.C. Templeton, Retrial Queues. Chapman and Hall, London (1997).
Ke., J.C., Batch Arrival queues under vacation policies with server breakdowns and start-up /close-down times. Appl. Math. Model. 31 (2007) 1282–1292. Google Scholar
Ke., J.C., An M x/G/1 system with second optional service and J additional options for Service. Appl. Math. Model. 32 (2008) 443–458. Google Scholar
Krishnakumar, B., Vijayakumar, A. and Arivudainambi, D., An M/G/1 retrial queueing system with two-phase service and preemptive resume. Annal. Operat. Res. 113 (2002) 61–79. Google Scholar
Krishnakumar, B., S. Madheswari, Pavai and Vijayakumar, A., The M/G/1 retrial queue with feedback and starting failures. Appl. Math. Model. 26 (2002) 1057–1076. Google Scholar
Li, H. and Zhao, Y.Q., A retrial queue with constant retrial rate, server downs and impatient customers. Stoch. Models 21 (2005) 531–550. Google Scholar
Madan, K.C., An M/G/1 queue with second optional service. Queueing Syst. 34 (2000) 37–46. Google Scholar
Medhi, J., A single server Poisson input queue with a second optional channel. Queueing Syst. 42 (2002) 239–242. Google Scholar
Senthil Kumar, M. and Arumuganathan, R., On the single server Batch Arrival Retrial Queue with General vacation Time under Bernoulli schedule and two phases of Heterogeneous service. Quality Technol. Quantit. Manag. 5 (2008) 145–160. Google Scholar
Senthil Kumar, M. and Arumuganathan, R., An M X/G/1 retrial queue with two-phase service subject to active server breakdowns and two types of repair. Int. J. Oper. Res. 8 (2010) 261–291. Google Scholar
Senthil Kumar, M., A discrete-time Ge o [ X ] /G/1 retrial queue with general retrial time and M-additional options for service. RAIRO Operat. Res. 45 (2011) 131–152. Google Scholar
Tang, Y.H., A single server M/G/1 queueing system subject to breakdowns. Some reliability and queueing problems. Microelectr. Reliab. 37 (1997) 315–321. Google Scholar
Wang, J., Cao, J. and Li, Q., Reliability analysis of the retrial queue with server breakdowns and repairs. Queueing Syst. 38 (2001) 363–380. Google Scholar
Wang, J. and Li, J., A Repairable M/G/1 retrial queue with Bernoulli vacation and Two Phase service. Quality Technol. Quantit. Manag. 5 (2008) 179–192. Google Scholar
Xiaoyong, Wu, Percy, Brill, Hlynka Myron and Wang Jinting, An M/G/1 retrial queue with balking and retrials during service. Int. J. Oper. Res. 1 (2005) 30–57. Google Scholar
Yang, T. and Li, H., The M/G/1 retrial queue with the server subject to starting failures. Queueing Syst. 16 (1994) 83–96. Google Scholar
Yue, D. and Cao, J., Reliability analysis of a \hbox{$M_1^x$}M1x, \hbox{$M_2^x/G_1$}M2x/G1, G 2/1 queueing system with a repairable service station. Microelect. Reliab. 37 (1997) 1225–1231. Google Scholar