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Analysis of customers' impatience in an M/M/1 queue with working vacations
1. | Department of Statistics, College of Sciences, Yanshan University, Qinhuangdao 066004, China |
2. | Department of Intelligence and Informatics, Konan University, 8-9-1 Okamoto, Kobe 658-8501 |
References:
[1] |
R. O. Al-Seedy, S. A. El-Shehawy, A. A. El-Sherbiny and S. I. Ammar, Transient solution of the M/M/c queue with balking and reneging, Computers and Mathematics with Applications, 57 (2009), 1280-1285.
doi: 10.1016/j.camwa.2009.01.017. |
[2] |
E. Altman and U. Yechiali, Analysis of customers' impatience in queues with server vacations, Queueing Systems, 52 (2006), 261-279.
doi: 10.1007/s11134-006-6134-x. |
[3] |
E. Altman and U. Yechiali, Infinite-server queues with systems' additional task and impatient customers, Probability in the Engineering and Informational Sciences, 22 (2008), 477-493.
doi: 10.1017/S0269964808000296. |
[4] |
Y. Baba, Analysis of a GI/M/1 queue with multiple working vacations, Operations Research Letters, 33 (2005), 201-209.
doi: 10.1016/j.orl.2004.05.006. |
[5] |
F. Baccelli, P. Boyer and G. Hebuterne, Single-server queues with impatient customers, Advances in Applied Probability, 16 (1984), 887-905.
doi: 10.2307/1427345. |
[6] |
A. D. Banik, U. C. Gupta and S. S. Pathak, On the GI/M/1/N queue with multiple vacation-analytic analysis and computation, Applied Mathematical Modelling, 31 (2007), 1701-1710.
doi: 10.1016/j.apm.2006.05.010. |
[7] |
S. Benjaafar, J. Gayon and S. Tepe, Optimal control of a production-inventory system with customer impatience, Operations Research Letters, 38 (2010), 267-272.
doi: 10.1016/j.orl.2010.03.008. |
[8] |
T. Bonald and J. Roberts, Performance modeling of elastic traffic in overload, ACM Sigmetrics Performance Evaluation Review, 29 (2001), 342-343.
doi: 10.1145/384268.378845. |
[9] |
O. J. Boxma and P. R. de Waal, Multiserver queues with impatient customers, in "The Fundamental Role of Teletraffic in the Evolution of Telecommunications Networks" (eds. J. Labetouille and J. W. Roberts), North-Holland, Amsterdam, (1994), 743-756. |
[10] |
D. J. Daley, General customer impatience in the queue GI/G/1, Journal of Applied Probability, 2 (1965), 186-205. |
[11] |
S. Economou and S. Kapodistria, Synchronized abandonments in a single server unreliable queue, European Journal of Operational Research, 203 (2010), 143-155.
doi: 10.1016/j.ejor.2009.07.014. |
[12] |
N. Gans, G. Koole and A. Mandelbaum, Telephone call centers: Tutorial, review, and research prospects, Manufacturing and Service Operations Management, 5 (2003), 79-141. |
[13] |
E. R. Obert, Reneging phenomenon of single channel queues, Mathematics of Operations Research, 4 (1979), 162-178. |
[14] |
C. Palm, Methods of judging the annoyance caused by congestion, Tele., 4 (1953), 189-208. |
[15] |
N. Perel and U. Yechiali, Queues with slow servers and impatient customers, European Journal of Operational Research, 201 (2010), 247-258.
doi: 10.1016/j.ejor.2009.02.024. |
[16] |
Y. Sakuma, A. Inoie, K. Kawanishi and M. Miyazawa, Tail asymptotics for waiting time distribution of an M/M/$s$ queue with general impatient time, Journal of Industrial and Management Optimization, 7 (2011), 593-606. |
[17] |
L. D. Servi and S. G. Finn, M/M/1 queues with working vacations (M/M/1/WV), Performance Evaluation, 50 (2002), 41-52.
doi: 10.1016/S0166-5316(02)00057-3. |
[18] |
L. Takacs, A single-server queue with limited virtual waiting time, Journal of Applied Probability, 11 (1974), 612-617.
doi: 10.2307/3212710. |
[19] |
B. Van Houdt, R. B. Lenin and C. Blonia, Delay distribution of (im)patient customers in a discrete time D-MAP/PH/1 queue with age-dependent service times, Queueing Systems, 45 (2003), 59-73.
doi: 10.1023/A:1025695818046. |
[20] |
D. Wu and H. Takagi, M/G/1 queue with multiple working vacations, Performance Evaluation, 63 (2006), 654-681.
doi: 10.1016/j.peva.2005.05.005. |
[21] |
U. Yechiali, Queues with system disasters and impatient customers when system is down, Queueing Systems, 56 (2007), 195-202.
doi: 10.1007/s11134-007-9031-z. |
[22] |
D. Yue and W. Yue, Analysis of M/M/$c$/N queueing system with balking, reneging and synchronous vacations, in "Advanced in Queueing Theory and Network Applications" (eds. W. Yue et al.), Springer-Verlag, New York, (2009), 165-180. |
[23] |
D. Yue and W. Yue, Block-partioning matrix solution of M/M/R/N queueing system with balking, reneging and server breakdowns, Journal of Industrial and Management Optimization, 5 (2009), 417-430. |
[24] |
M. Zhang and Z. Hou, Performance analysis of MAP/G/1 queue with working vacations and vacation interruption, Applied Mathematical Modelling, 35 (2011), 1551-1560.
doi: 10.1016/j.apm.2010.09.031. |
show all references
References:
[1] |
R. O. Al-Seedy, S. A. El-Shehawy, A. A. El-Sherbiny and S. I. Ammar, Transient solution of the M/M/c queue with balking and reneging, Computers and Mathematics with Applications, 57 (2009), 1280-1285.
doi: 10.1016/j.camwa.2009.01.017. |
[2] |
E. Altman and U. Yechiali, Analysis of customers' impatience in queues with server vacations, Queueing Systems, 52 (2006), 261-279.
doi: 10.1007/s11134-006-6134-x. |
[3] |
E. Altman and U. Yechiali, Infinite-server queues with systems' additional task and impatient customers, Probability in the Engineering and Informational Sciences, 22 (2008), 477-493.
doi: 10.1017/S0269964808000296. |
[4] |
Y. Baba, Analysis of a GI/M/1 queue with multiple working vacations, Operations Research Letters, 33 (2005), 201-209.
doi: 10.1016/j.orl.2004.05.006. |
[5] |
F. Baccelli, P. Boyer and G. Hebuterne, Single-server queues with impatient customers, Advances in Applied Probability, 16 (1984), 887-905.
doi: 10.2307/1427345. |
[6] |
A. D. Banik, U. C. Gupta and S. S. Pathak, On the GI/M/1/N queue with multiple vacation-analytic analysis and computation, Applied Mathematical Modelling, 31 (2007), 1701-1710.
doi: 10.1016/j.apm.2006.05.010. |
[7] |
S. Benjaafar, J. Gayon and S. Tepe, Optimal control of a production-inventory system with customer impatience, Operations Research Letters, 38 (2010), 267-272.
doi: 10.1016/j.orl.2010.03.008. |
[8] |
T. Bonald and J. Roberts, Performance modeling of elastic traffic in overload, ACM Sigmetrics Performance Evaluation Review, 29 (2001), 342-343.
doi: 10.1145/384268.378845. |
[9] |
O. J. Boxma and P. R. de Waal, Multiserver queues with impatient customers, in "The Fundamental Role of Teletraffic in the Evolution of Telecommunications Networks" (eds. J. Labetouille and J. W. Roberts), North-Holland, Amsterdam, (1994), 743-756. |
[10] |
D. J. Daley, General customer impatience in the queue GI/G/1, Journal of Applied Probability, 2 (1965), 186-205. |
[11] |
S. Economou and S. Kapodistria, Synchronized abandonments in a single server unreliable queue, European Journal of Operational Research, 203 (2010), 143-155.
doi: 10.1016/j.ejor.2009.07.014. |
[12] |
N. Gans, G. Koole and A. Mandelbaum, Telephone call centers: Tutorial, review, and research prospects, Manufacturing and Service Operations Management, 5 (2003), 79-141. |
[13] |
E. R. Obert, Reneging phenomenon of single channel queues, Mathematics of Operations Research, 4 (1979), 162-178. |
[14] |
C. Palm, Methods of judging the annoyance caused by congestion, Tele., 4 (1953), 189-208. |
[15] |
N. Perel and U. Yechiali, Queues with slow servers and impatient customers, European Journal of Operational Research, 201 (2010), 247-258.
doi: 10.1016/j.ejor.2009.02.024. |
[16] |
Y. Sakuma, A. Inoie, K. Kawanishi and M. Miyazawa, Tail asymptotics for waiting time distribution of an M/M/$s$ queue with general impatient time, Journal of Industrial and Management Optimization, 7 (2011), 593-606. |
[17] |
L. D. Servi and S. G. Finn, M/M/1 queues with working vacations (M/M/1/WV), Performance Evaluation, 50 (2002), 41-52.
doi: 10.1016/S0166-5316(02)00057-3. |
[18] |
L. Takacs, A single-server queue with limited virtual waiting time, Journal of Applied Probability, 11 (1974), 612-617.
doi: 10.2307/3212710. |
[19] |
B. Van Houdt, R. B. Lenin and C. Blonia, Delay distribution of (im)patient customers in a discrete time D-MAP/PH/1 queue with age-dependent service times, Queueing Systems, 45 (2003), 59-73.
doi: 10.1023/A:1025695818046. |
[20] |
D. Wu and H. Takagi, M/G/1 queue with multiple working vacations, Performance Evaluation, 63 (2006), 654-681.
doi: 10.1016/j.peva.2005.05.005. |
[21] |
U. Yechiali, Queues with system disasters and impatient customers when system is down, Queueing Systems, 56 (2007), 195-202.
doi: 10.1007/s11134-007-9031-z. |
[22] |
D. Yue and W. Yue, Analysis of M/M/$c$/N queueing system with balking, reneging and synchronous vacations, in "Advanced in Queueing Theory and Network Applications" (eds. W. Yue et al.), Springer-Verlag, New York, (2009), 165-180. |
[23] |
D. Yue and W. Yue, Block-partioning matrix solution of M/M/R/N queueing system with balking, reneging and server breakdowns, Journal of Industrial and Management Optimization, 5 (2009), 417-430. |
[24] |
M. Zhang and Z. Hou, Performance analysis of MAP/G/1 queue with working vacations and vacation interruption, Applied Mathematical Modelling, 35 (2011), 1551-1560.
doi: 10.1016/j.apm.2010.09.031. |
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