Hostname: page-component-76fb5796d-9pm4c Total loading time: 0 Render date: 2024-04-26T21:10:39.925Z Has data issue: false hasContentIssue false
  • English
  • Français

Some aspects of balking and reneging in finite buffer queues

Published online by Cambridge University Press:  16 December 2011

Amit Choudhury  and
Pallabi Medhi
Amit Choudhury
Affiliation:
Dept. of Statistics, Gauhati University, Guwahati 781014, Assam, India. achoudhury@rediffmail.com ; pmedhi16@gmail.com ;
Pallabi Medhi
Affiliation:
Dept. of Statistics, Gauhati University, Guwahati 781014, Assam, India. achoudhury@rediffmail.com ; pmedhi16@gmail.com ;
Get access

Abstract

In this paper, a single server finite buffer Markovian queuing system is analyzed with the additional restriction that customers may balk as well as renege. Reneging considered in literature is usually of position independent type where the reneging rate is constant irrespective of the position of the customer in the system. However there are many real world situations where this assumption does not hold. This paper is an attempt to model balking with position dependent reneging. Explicit closed form expressions of a number of performance measures are presented. A typical problem is discussed to demonstrate the usefulness of results derived in the paper.

Keywords

Balkingfinite buffer queueimpatienceposition dependent renegingqueuingreneging
Type
Research Article
Information
RAIRO - Operations Research , Volume 45 , Issue 3 , July 2011 , pp. 223 - 240
Copyright
© EDP Sciences, ROADEF, SMAI 2011

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

A. Allen, Probability, Statistics and Queuing Theory with Computer Science Application, 2nd edition. Academic Press, San Diego, California (2005).
Al-Seedy, R.O. and Al-Ibraheem, F.M., An interarrival hyperexponential machine interference with balking, reneging, state-dependent, spares and an additional server for longer queues. Int. J. Math. Math. Sci. 27 (2001) 737–747. Google Scholar
Al-Seedy, R.O., El-Sherbiny, A.A., El-Shehawy, S.A. and Ammar, S.I., Transient solution of the M/M/c queue with balking and reneging. Comput. Math. Appl. 57 (2009) 1280–1285. Google Scholar
Altman, E. and Yechiali, U., Infinite-server queues with system’s additional tasks and impatient customers. Probab. Eng. Inform. Sci. 22 (2008) 477–493. Google Scholar
Ancker Jr., C.J. and Gafarian, A.V., Queuing problems with balking and reneging I. Oper. Res. 11 (1963) 88–100. Google Scholar
Baccelli, F., Boyer, P. and Hebuterne, G., Single server queues with impatients customers. Adv. Appl. Probab. 16 (1984) 887–905. Google Scholar
Barrer, D.Y., Queuing with impatient customers and ordered service. Oper. Res. 5 (1957) 650–656. Google Scholar
Barrer, D.Y., Queuing with impatient customers and indifferent clerks. Oper. Res. 5 (1957) 644–649. Google Scholar
Boots, N.K. and Tijms, H., An M/M/c queues with impatient customers. Top 7 (1999) 213–220. Google Scholar
Boxma, O., Perry, D., Stadje, W. and Zacks, S., The busy period of an M/G/1 queue with customer impatience. J. Appl. Prob. 47 (2008) 130–145. Google Scholar
Brandt, A. and Brandt, M., On a two-queue priority system with impatience and its application to a call centre. Methodol. Comput. Appl. Probab. 1 (1999) 191–210. Google Scholar
Choi, B.D., Kim, B. and Zhu, D., MAP/M/C queue with constant impatients times. Math. Oper. Res. 29 (2004) 309–325. Google Scholar
Choudhury, A., Impatience in single server queuing model. Am. J. Math. Manage. Sci. 28 (2008) 177–211. Google Scholar
Choudhury, A., A few words on Reneging in M/M/1/K queues. Contributions to Applied and Mathematical Statistics 4 (2009) 58–64. Google Scholar
El-Paoumy, M.S., On Poisson bulk arrival queue: MX/M/2/N with balking, reneging and heterogeneous servers. Appl. Math. Sci. 2 (2008) 1169–1175. Google Scholar
El-Paoumy, M.S., On a truncated Erlangian queuing system with state-dependent service rate, balking and reneging, Appl. Math. Sci. 2 (2008) 1161–1167. Google Scholar
El-Paoumy, M.S. and Ismail, M.M., On a truncated Erlang queuing system with bulk arrivals, balking and reneging. Appl. Math. Sci. 3 (2009) 1103–1113. Google Scholar
El-Sherbiny, A.A., The non-truncated bulk arrival queue MX/M/1 with reneging, balking, state-dependent and an additional server for longer queues. Appl. Math. Sci. 2 (2008) 747–752. Google Scholar
Haghighi, A.M., Medhi, J. and Mohanty, S.G., On a multi server Markovian queuing system with balking and reneging. Comput. Oper. Res. 13 (1986) 421–425. Google Scholar
Haight, F.A., Queuing with balking. Biometrika 44 (1957) 360–369. Google Scholar
Haight, F.A., Queuing with reneging. Metrika 2 (1959) 186–197. Google Scholar
O. Jouini, Z. Aksin and Y. Dallery, Call centers with delay information: models and insights (2008). Downloaded from the site www.uclouvain.be/cps/ucl/doc/core/documents/Jouini.pdf (accessed on 03.08.2010).
Jouini, O., Dallery, Y. and Aksin, Z., Queuing models for full-flexible multi-class call centers with real-time anticipated delays. Int. J. Prod. Econ. 120 (2009) 389–399. Google Scholar
Ke, J.C. and Wang, K.-H., Cost analysis of the M/M/R machine repair problem with balking, reneging and server breakdowns. J. Oper. Res. Soc. 50 (1999) 275–282. Google Scholar
Liu, L., Kashyap, B.R.K. and Templeton, J.G.C., The service system M/MR/∞ with impatient customers. Queuing Syst. 2 (1987) 363–372. Google Scholar
Martin, M. and Artalejo, J.R., Analysis of an M/G/1 Queue with two types of impatient units. Adv. Appl. Probab. 27 (1995) 840–861. Google Scholar
J. Medhi, Stochastic Processes, 2nd edition. Wiley Eastern Limited, India (1994).
Movaghar, A., On queuing with customer impatience until the beginning of service. Queuing Syst. 29 (1998) 337–350. Google Scholar
Pazgal, A. and Radas, S., Comparison of customer balking and reneging behavior to queuing theory predictions: An experimental study. Comput. Oper. Res. 35 (2008) 2537–2548. Google Scholar
Shawky, A.I., The single server machine interference model with balking, reneging and an additional server for longer queues. Microelectron. Reliab. 37 (1997) 355–357. Google Scholar
Shawky, A.I. and El-Paoumy, M.S., The interarrival hyperexponential queues: Hk/M/c/N with balking and reneging. Stochastics 69 (2000) 67–76. Google Scholar
Shawky, A.I. and El-Paoumy, M.S., The truncated hyper-Poisson queues: Hk/Ma,b/c/N with balking, reneging and general bulk-service rule. Yugosl. J. Oper. Res. 8 (2008) 23–36. Google Scholar
Singh, C.J., Kumar, B. and Jain, M., Single server interdependent queuing model with controllable arrival rates and reneging. Pakistan J. Statistics 23 (2007) 171–178. Google Scholar
D. Yue, W. Yue, J. Yu and R. Tian, A heterogeneous two-server queuing system with balking and server breakdowns, in the Eight International Symposium on Operations Research and its Applications (ISORA’09). Zhangjiajie, China (2009). www.aporc.org/LNOR/10/ISORA2009F31.pdf (accessed on 04.08.2010).
Y. Zhang, D. Yue and W. Yue, Analysis of an M/M/1/N queue with balking, reneging and server vacations, in the Vth. International Symposium on OR and its Application (2005). www.aporc.org/LNOR/6/ISORA 2006F10.pdf (accessed on on 04.08.2010).