Aspects of Impatience in a Finite Buffer Queue
RAIRO - Operations Research - Recherche Opérationnelle, Tome 46 (2012) no. 3, pp. 189-209.

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 while waiting for service. Additionally, they may also become impatient if service is not offered at the desired rate. This paper analyses a finite buffer multi server queuing system with the additional restriction that customers may balk as well as renege. Closed form expressions of a number of performance measures are presented. A design problem is discussed to demonstrate the results derived.

DOI : 10.1051/ro/2012014
Classification : 60K25, 68M20, 90B22
Mots clés : balking, finite buffer, impatience, reneging, queuing
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Pallabi, Medhi; Choudhury, Amit. Aspects of Impatience in a Finite Buffer Queue. RAIRO - Operations Research - Recherche Opérationnelle, Tome 46 (2012) no. 3, pp. 189-209. doi : 10.1051/ro/2012014. http://archive.numdam.org/articles/10.1051/ro/2012014/

[1] E. Altman and U. Yechiali, Analysis of customer impatience in queue with server vacations. Queuing Syst. 52 (2006) 261-279. | MR | Zbl

[2] 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

[3] 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

[4] 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

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

[6] J. Bae and S. Kim, The stationary workload of the G/M/1 queue with impatient customers. Queuing Syst. 64 (2010) 253-265. | MR | Zbl

[7] J. Bae, S. Kim and E.Y. Lee, The virtual waiting time of the M/G/1 queue with impatient customers. Queuing Syst. 38 (2001) 485-494. | MR | Zbl

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

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

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

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

[12] O. Boxma, D. Perry, W. Stadje and S. Zacks, The busy period of an M/G/1 queue with customer impatience. J. Appl. Probab. 47 (2010) 130-145. | MR | Zbl

[13] 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

[14] B.D. Choi, B. Kim and J. Chung, M/M/1 queue with impatient customers of higher priority. Queuing Syst. 38 (2001) 49-66. | MR | Zbl

[15] 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

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

[17] A. Choudhury and P. Medhi, Balking and reneging in multiserver Markovian queuing system. Int. J. Math. Oper. Res. 3 (2011) 377-394. | MR | Zbl

[18] A. Choudhury and P. Medhi, Some aspects of balking and reneging in finite buffer queues. RAIRO Oper. Res. 45 (2011) 223-240. | Numdam | Zbl

[19] J.K. Cochran and J.R. Broyles, Developing non-linear queuing regressions to increase emergency department patient safety : approximating reneging with balking. Comput. Ind. Eng. 59 (2010) 378-386.

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

[21] 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

[22] 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

[23] 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

[24] B. Gavish and P.J. Schweitzer, The Markovian queue with bounded waiting time. Manage. Sci. 23 (1977) 1349-1357. | MR | Zbl

[25] A. Ghosal, Queues with finite waiting time. Oper. Res. 11 (1963) 919-921. | MR | Zbl

[26] 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

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

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

[29] 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).

[30] 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.

[31] 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

[32] A.G.D. Kok and H. Tijms, A queuing system with impatient customers. J. Appl. Probab. 22 (1985) 688-696. | MR | Zbl

[33] L. Liu and V.G. Kulkarni, Busy period analysis for M/PH/1 queues with workload dependent balking. Queuing Syst. 59 (2008) 37-51. | MR | Zbl

[34] L. Liu and V.G. Kulkarni, Balking and reneging in M/G/s system exact analysis and approximations. Probab. Eng. Inform. Sci. 22 (2008) 355-371. | MR | Zbl

[35] 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

[36] 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

[37] 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

[38] A. Ravindran, D.T. Phillips and J.J. Solberg, Operations research, principles and practice, 2nd edition. John Wiley and Sons, New York (1987). | MR | Zbl

[39] 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.

[40] A.I. Shawky and M.S. El-Paoumy, The interarrival hyperexponential queues : Hk/M/c/N with balking and reneging. Stochastics An Int. J. of Probability & Stochastic Processes 69 (2000) 67-76. | MR | Zbl

[41] 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

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

[43] W. Xiong and T. Altiok, An approximation for multi-server queues with deterministic reneging times. Ann. Oper. Res. 172 (2009) 143-151. | MR | Zbl

[44] W. Xiong, D. Jagerman and T. Altiok, M/G/1 queue with deterministic reneging times. Perform. Eval. 65 (2008) 308-316.

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

[46] D. Yue and W. Yue, A heterogeneous two-server network system with balking and a Bernoulli vacation schedule. J. Ind. Manag. Optim. 6 (2010) 501-516. | MR | Zbl

[47] 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.

[48] 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.

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