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Aspects of Impatience in a Finite Buffer Queue

Published online by Cambridge University Press:  07 September 2012

Medhi Pallabi  and
Amit Choudhury
Medhi Pallabi
Affiliation:
Department of statistics, Guwahati university, Guwahati-781014 Assam, India. [email protected]
Amit Choudhury
Affiliation:
Department of statistics, Guwahati university, Guwahati-781014 Assam, India. [email protected]
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Abstract

In a multi server queuing system, buffer size is often larger than the number of servers.This necessitates queuing and waiting for some customers. Customers become impatient whilewaiting for service. Additionally, they may also become impatient if service is notoffered at the desired rate. This paper analyses a finite buffer multi server queuingsystem with the additional restriction that customers may balk as well as renege. Closedform expressions of a number of performance measures are presented. A design problem isdiscussed to demonstrate the results derived.

Keywords

Balkingfinite Bufferimpatiencerenegingqueuing
Type
Research Article
Information
RAIRO - Operations Research , Volume 46 , Issue 3 , July 2012 , pp. 189 - 209
Copyright
© EDP Sciences, ROADEF, SMAI, 2012

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References

Altman, E. and Yechiali, U., Analysis of customer impatience in queue with server vacations. Queuing Syst. 52 (2006) 261–279. 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
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
Ancker, C.J. Jr. and Gafarian, A.V., Queuing problems with balking and reneging I. Oper. Res. 11 (1963) 88–100. Google Scholar
Bae, J. and Kim, S., The stationary workload of the G/M/1 queue with impatient customers. Queuing Syst. 64 (2010) 253–265. Google Scholar
Bae, J., Kim, S. and Lee, E.Y., The virtual waiting time of the M/G/1 queue with impatient customers. Queuing Syst. 38 (2001) 485–494. 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. Probab. 47 (2010) 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 Chung, J., M/M/1 queue with impatient customers of higher priority. Queuing Syst. 38 (2001) 49–66. 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. Manag. Sci. 28 (2008) 177–211. Google Scholar
Choudhury, A. and Medhi, P., Balking and reneging in multiserver Markovian queuing system. Int. J. Math. Oper. Res. 3 (2011) 377–394. Google Scholar
Choudhury, A. and Medhi, P., Some aspects of balking and reneging in finite buffer queues. RAIRO Oper. Res. 45 (2011) 223–240. Google Scholar
Cochran, J.K. and Broyles, J.R., Developing non-linear queuing regressions to increase emergency department patient safety : approximating reneging with balking. Comput. Ind. Eng. 59 (2010) 378–386. Google Scholar
El-Paoumy, M.S., On Poisson 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
Gavish, B. and Schweitzer, P.J., The Markovian queue with bounded waiting time. Manage. Sci. 23 (1977) 1349–1357. Google Scholar
Ghosal, A., Queues with finite waiting time. Oper. Res. 11 (1963) 919–921. 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
Kok, A.G.D. and Tijms, H., A queuing system with impatient customers. J. Appl. Probab. 22 (1985) 688–696. Google Scholar
Liu, L. and Kulkarni, V.G., Busy period analysis for M/PH/1 queues with workload dependent balking. Queuing Syst. 59 (2008) 37–51. Google Scholar
Liu, L. and Kulkarni, V.G., Balking and reneging in M/G/s system exact analysis and approximations. Probab. Eng. Inform. Sci. 22 (2008) 355–371. 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
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
A. Ravindran, D.T. Phillips and J.J. Solberg, Operations research, principles and practice, 2nd edition. John Wiley and Sons, New York (1987).
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 An Int. J. of Probability & Stochastic Processes 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. Stat. 23 (2007) 171–178. Google Scholar
Xiong, W. and Altiok, T., An approximation for multi-server queues with deterministic reneging times. Ann. Oper. Res. 172 (2009) 143–151. Google Scholar
Xiong, W., Jagerman, D. and Altiok, T., M/G/1 queue with deterministic reneging times. Perform. Eval. 65 (2008) 308–316. Google Scholar
Yechiali, U., Queues with system disasters and impatient customers when system is down. Queueing Syst. 56 (2007) 195–202. Google Scholar
Yue, D. and Yue, W., A heterogeneous two-server network system with balking and a Bernoulli vacation schedule. J. Ind. Manag. Optim. 6 (2010) 501–516. Google Scholar
D. Yue, W. Yue, J. Yu and R. Tian, A heterogeneous two-server queuing system with balking and server breakdowns. Paper presented in the Eight International Symposium on Operations Research and its Applications (ISORA’09). Zhangjiajie, Chaina (2009). Downloaded from the site www.aporc.org/LNOR/10/ISORA 2009 F31.pdf 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. Paper presented in the Vth. International Symposium on OR and its Application (2005). Downloaded from www.aporc.org/LNOR/6/ISORA 2006F10.pdf on 04.08.2010.