Some aspects of balking and reneging in finite buffer queues
RAIRO - Operations Research - Recherche Opérationnelle, Tome 45 (2011) no. 3, pp. 223-240.

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.

DOI : 10.1051/ro/2011113
Classification : 60K25, 68M20, 90B22
Mots-clés : balking, finite buffer queue, impatience, position dependent reneging, queuing, reneging 
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Choudhury, Amit; Medhi, Pallabi. Some aspects of balking and reneging in finite buffer queues. RAIRO - Operations Research - Recherche Opérationnelle, Tome 45 (2011) no. 3, pp. 223-240. doi : 10.1051/ro/2011113. http://archive.numdam.org/articles/10.1051/ro/2011113/

[1] A. Allen, Probability, Statistics and Queuing Theory with Computer Science Application, 2nd edition. Academic Press, San Diego, California (2005). | MR | Zbl

[2] R.O. Al-Seedy and F.M. Al-Ibraheem, 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. | MR | Zbl

[3] R.O. Al-Seedy, A.A. El-Sherbiny, S.A. El-Shehawy and S.I. Ammar, Transient solution of the M/M/c queue with balking and reneging. Comput. Math. Appl. 57 (2009) 1280-1285. | MR | Zbl

[4] E. Altman and U. Yechiali, Infinite-server queues with system's additional tasks and impatient customers. Probab. Eng. Inform. Sci. 22 (2008) 477-493. | MR | Zbl

[5] C.J. Ancker Jr. and A.V. Gafarian, Queuing problems with balking and reneging I. Oper. Res. 11 (1963) 88-100. | Zbl

[6] F. Baccelli, P. Boyer and G. Hebuterne, Single server queues with impatients customers. Adv. Appl. Probab. 16 (1984) 887-905. | MR | Zbl

[7] D.Y. Barrer, Queuing with impatient customers and ordered service. Oper. Res. 5 (1957) 650-656. | MR

[8] D.Y. Barrer, Queuing with impatient customers and indifferent clerks. Oper. Res. 5 (1957) 644-649. | MR

[9] N.K. Boots and H. Tijms, An M/M/c queues with impatient customers. Top 7 (1999) 213-220. | MR | Zbl

[10] O. Boxma, D. Perry, W. Stadje and S. Zacks, The busy period of an M/G/1 queue with customer impatience. J. Appl. Prob. 47 (2008) 130-145. | MR | Zbl

[11] A. Brandt and M. Brandt, On a two-queue priority system with impatience and its application to a call centre. Methodol. Comput. Appl. Probab. 1 (1999) 191-210. | MR | Zbl

[12] B.D. Choi, B. Kim and D. Zhu, MAP/M/C queue with constant impatients times. Math. Oper. Res. 29 (2004) 309-325. | MR | Zbl

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

[14] A. Choudhury, A few words on Reneging in M/M/1/K queues. Contributions to Applied and Mathematical Statistics 4 (2009) 58-64.

[15] M.S. El-Paoumy, On Poisson bulk arrival queue: MX/M/2/N with balking, reneging and heterogeneous servers. Appl. Math. Sci. 2 (2008) 1169-1175. | MR | Zbl

[16] M.S. El-Paoumy, On a truncated Erlangian queuing system with state-dependent service rate, balking and reneging, Appl. Math. Sci. 2 (2008) 1161-1167. | MR | Zbl

[17] M.S. El-Paoumy and M.M. Ismail, On a truncated Erlang queuing system with bulk arrivals, balking and reneging. Appl. Math. Sci. 3 (2009) 1103-1113. | MR

[18] A.A. El-Sherbiny, 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. | MR | Zbl

[19] A.M. Haghighi, J. Medhi and S.G. Mohanty, On a multi server Markovian queuing system with balking and reneging. Comput. Oper. Res. 13 (1986) 421-425. | MR | Zbl

[20] F.A. Haight, Queuing with balking. Biometrika 44 (1957) 360-369. | MR | Zbl

[21] F.A. Haight, Queuing with reneging. Metrika 2 (1959) 186-197. | MR | Zbl

[22] 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).

[23] O. Jouini, Y. Dallery and Z. Aksin, Queuing models for full-flexible multi-class call centers with real-time anticipated delays. Int. J. Prod. Econ. 120 (2009) 389-399.

[24] J.C. Ke and K.-H. Wang, Cost analysis of the M/M/R machine repair problem with balking, reneging and server breakdowns. J. Oper. Res. Soc. 50 (1999) 275-282. | Zbl

[25] L. Liu, B.R.K. Kashyap and J.G.C. Templeton, The service system M/MR/∞ with impatient customers. Queuing Syst. 2 (1987) 363-372. | MR | Zbl

[26] M. Martin and J.R. Artalejo, Analysis of an M/G/1 Queue with two types of impatient units. Adv. Appl. Probab. 27 (1995) 840-861. | MR | Zbl

[27] J. Medhi, Stochastic Processes, 2nd edition. Wiley Eastern Limited, India (1994). | MR | Zbl

[28] A. Movaghar, On queuing with customer impatience until the beginning of service. Queuing Syst. 29 (1998) 337-350. | MR | Zbl

[29] A. Pazgal and S. Radas, Comparison of customer balking and reneging behavior to queuing theory predictions: An experimental study. Comput. Oper. Res. 35 (2008) 2537-2548. | Zbl

[30] A.I. Shawky, The single server machine interference model with balking, reneging and an additional server for longer queues. Microelectron. Reliab. 37 (1997) 355-357.

[31] A.I. Shawky and M.S. El-Paoumy, The interarrival hyperexponential queues: Hk/M/c/N with balking and reneging. Stochastics 69 (2000) 67-76. | MR | Zbl

[32] A.I. Shawky and M.S. El-Paoumy, 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. | MR | Zbl

[33] C.J. Singh, B. Kumar and M. Jain, Single server interdependent queuing model with controllable arrival rates and reneging. Pakistan J. Statistics 23 (2007) 171-178. | MR | Zbl

[34] 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).

[35] 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).

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