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Networks with cascading overloads
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.
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.
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.
doi: 10.1017/S0269964808000296. |
[4] |
Y. Baba, Analysis of a GI/M/1 queue with multiple working vacations,, Operations Research Letters, 33 (2005), 201.
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.
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.
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.
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.
doi: 10.1145/384268.378845. |
[9] |
O. J. Boxma and P. R. de Waal, Multiserver queues with impatient customers,, in, (1994), 743. Google Scholar |
[10] |
D. J. Daley, General customer impatience in the queue GI/G/1,, Journal of Applied Probability, 2 (1965), 186.
|
[11] |
S. Economou and S. Kapodistria, Synchronized abandonments in a single server unreliable queue,, European Journal of Operational Research, 203 (2010), 143.
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. Google Scholar |
[13] |
E. R. Obert, Reneging phenomenon of single channel queues,, Mathematics of Operations Research, 4 (1979), 162.
|
[14] |
C. Palm, Methods of judging the annoyance caused by congestion,, Tele., 4 (1953), 189.
|
[15] |
N. Perel and U. Yechiali, Queues with slow servers and impatient customers,, European Journal of Operational Research, 201 (2010), 247.
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.
|
[17] |
L. D. Servi and S. G. Finn, M/M/1 queues with working vacations (M/M/1/WV),, Performance Evaluation, 50 (2002), 41.
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.
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.
doi: 10.1023/A:1025695818046. |
[20] |
D. Wu and H. Takagi, M/G/1 queue with multiple working vacations,, Performance Evaluation, 63 (2006), 654.
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.
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, (2009), 165.
|
[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.
|
[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.
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.
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.
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.
doi: 10.1017/S0269964808000296. |
[4] |
Y. Baba, Analysis of a GI/M/1 queue with multiple working vacations,, Operations Research Letters, 33 (2005), 201.
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.
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.
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.
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.
doi: 10.1145/384268.378845. |
[9] |
O. J. Boxma and P. R. de Waal, Multiserver queues with impatient customers,, in, (1994), 743. Google Scholar |
[10] |
D. J. Daley, General customer impatience in the queue GI/G/1,, Journal of Applied Probability, 2 (1965), 186.
|
[11] |
S. Economou and S. Kapodistria, Synchronized abandonments in a single server unreliable queue,, European Journal of Operational Research, 203 (2010), 143.
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. Google Scholar |
[13] |
E. R. Obert, Reneging phenomenon of single channel queues,, Mathematics of Operations Research, 4 (1979), 162.
|
[14] |
C. Palm, Methods of judging the annoyance caused by congestion,, Tele., 4 (1953), 189.
|
[15] |
N. Perel and U. Yechiali, Queues with slow servers and impatient customers,, European Journal of Operational Research, 201 (2010), 247.
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.
|
[17] |
L. D. Servi and S. G. Finn, M/M/1 queues with working vacations (M/M/1/WV),, Performance Evaluation, 50 (2002), 41.
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.
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.
doi: 10.1023/A:1025695818046. |
[20] |
D. Wu and H. Takagi, M/G/1 queue with multiple working vacations,, Performance Evaluation, 63 (2006), 654.
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.
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, (2009), 165.
|
[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.
|
[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.
doi: 10.1016/j.apm.2010.09.031. |
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