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Tail asymptotics for waiting time distribution of an M/M/s queue with general impatient time
1. | Department of Distribution and Information Engineering, Hiroshima National College of Maritime Technology, Osakikamijima-Town, 725-0231, Japan |
2. | Department of Information Network and Communication, Kanagawa Institute of Technology, Atsugi-City, 243-0292, Japan |
3. | Department of Computer Science, Gunma University, Kiryu-City, 376-8515, Japan |
4. | Department of Information Sciences, Tokyo University of Science, Noda-City, 278-8510, Japan |
References:
[1] |
S. Asmussen, "Applied Probability and Queues," 2nd ed.,, Applications of Mathematics (New York), 51 (2003).
|
[2] |
F. Baccelli, P. Boyer and G. Hebuterne, Single-server queues with impatient customers,, Advances in Applied Probability, 16 (1984), 887.
doi: 10.2307/1427345. |
[3] |
F. Baccelli and G. Hebuterne, On queues with impatient customers,, in, 32 (1981), 159.
|
[4] |
D. Y. Barrer, Queueing with impatient customers and indifferent clerks,, Operations Research, 4 (1957), 644. Google Scholar |
[5] |
D. Y. Barrer, Queueing with impatient customers and ordered service,, Operations Research, 4 (1957), 650.
doi: 10.1287/opre.5.5.650. |
[6] |
A. Brandt and M. Brandt, On the $M(n)$/$M(n)$/$s$ queue with impatient calls,, Performance Evaluation, 35 (1999), 1.
doi: 10.1016/S0166-5316(98)00042-X. |
[7] |
A. Brandt and M. Brandt, Asymptotic results and a Markovian approximation for the $M(n)$/$M(n)$/$s+GI$ system,, Queueing Systems, 41 (2002), 73.
doi: 10.1023/A:1015781818360. |
[8] |
L. Brown, N. Gans, A. Mandelbaum, A. Sakov, H. Shen, S. Zeltyn and L. Zhao, Statistical analysis of a telephone call center: A queueing-science perspective,, Journal of the American Statistical Association, 100 (2005), 36.
doi: 10.1198/016214504000001808. |
[9] |
B. D. Choi and B. Kim, $MAP$/$M$/$c$ queue with constant impatient time,, Mathematics of Operations Research, 29 (2004), 309.
doi: 10.1287/moor.1030.0081. |
[10] |
D. J. Daley, General customer impatience in the queue $GI$/$G$/$1$,, Journal of Applied Probability, 2 (1965), 186.
doi: 10.2307/3211884. |
[11] |
A. G. de Kok and H. C. Tijms, A queueing system with impatient customers,, Journal of Applied Probability, 22 (1985), 688.
doi: 10.2307/3213871. |
[12] |
G. Evans, "Practical Numerical Analysis,", John Wiley & Sons, (1996). Google Scholar |
[13] |
P. D. Finch, Deterministic customer impatience in the queueing system $GI$/$M$/$1$,, Biometrika, 47 (1960), 45.
|
[14] |
N. Gans, G. Koole and A. Mandelbaum, Telephone call centers: Tutorial, review, and research prospects,, Manufacturing and Service Operations Management, 5 (2003), 79.
doi: 10.1287/msom.5.2.79.16071. |
[15] |
O. Garnett, A. Mandelbaum and M. Reiman, Designing a call center with impatient customers,, Manufacturing & Service Operations Management, 4 (2002), 208.
doi: 10.1287/msom.4.3.208.7753. |
[16] |
R. B. Haugen and E. Skogan, Queueing systems with stochastic time out,, IEEE Transactions on Communications, 28 (1980), 1984.
doi: 10.1109/TCOM.1980.1094632. |
[17] |
G. Latouche and V. Ramaswami, "Introduction to Matrix Analytic Methods in Stochastic Modeling,", American Statistical Association and the Society for Industrial and Applied Mathematics, (1999).
doi: 10.1137/1.9780898719734. |
[18] |
A. Movaghar, On queueing with customer impatience until the beginning of service,, Queueing Systems Theory Appl., 29 (1998), 337.
doi: 10.1023/A:1019196416987. |
[19] |
C. Palm, Methods of judging the annoyance caused by congestion,, Tele (English ed.), 2 (1953), 1. Google Scholar |
[20] |
R. E. Stanford, Reneging phenomena in single server queues,, Mathematics of Operations Research, 4 (1979), 162.
doi: 10.1287/moor.4.2.162. |
[21] |
W. Xiong, D. Jagerman and T. Altiok, $M$/$G$/$1$ queue with deterministic reneging times,, Performance Evaluation, 65 (2008), 308.
doi: 10.1016/j.peva.2007.07.003. |
[22] |
S. Zeltyn and A. Mandelbaum, Call centers with impatient customers: Many-server asymptotics of the M/M/$n$ + G queue,, Queueing Systems, 51 (2005), 361.
doi: 10.1007/s11134-005-3699-8. |
show all references
References:
[1] |
S. Asmussen, "Applied Probability and Queues," 2nd ed.,, Applications of Mathematics (New York), 51 (2003).
|
[2] |
F. Baccelli, P. Boyer and G. Hebuterne, Single-server queues with impatient customers,, Advances in Applied Probability, 16 (1984), 887.
doi: 10.2307/1427345. |
[3] |
F. Baccelli and G. Hebuterne, On queues with impatient customers,, in, 32 (1981), 159.
|
[4] |
D. Y. Barrer, Queueing with impatient customers and indifferent clerks,, Operations Research, 4 (1957), 644. Google Scholar |
[5] |
D. Y. Barrer, Queueing with impatient customers and ordered service,, Operations Research, 4 (1957), 650.
doi: 10.1287/opre.5.5.650. |
[6] |
A. Brandt and M. Brandt, On the $M(n)$/$M(n)$/$s$ queue with impatient calls,, Performance Evaluation, 35 (1999), 1.
doi: 10.1016/S0166-5316(98)00042-X. |
[7] |
A. Brandt and M. Brandt, Asymptotic results and a Markovian approximation for the $M(n)$/$M(n)$/$s+GI$ system,, Queueing Systems, 41 (2002), 73.
doi: 10.1023/A:1015781818360. |
[8] |
L. Brown, N. Gans, A. Mandelbaum, A. Sakov, H. Shen, S. Zeltyn and L. Zhao, Statistical analysis of a telephone call center: A queueing-science perspective,, Journal of the American Statistical Association, 100 (2005), 36.
doi: 10.1198/016214504000001808. |
[9] |
B. D. Choi and B. Kim, $MAP$/$M$/$c$ queue with constant impatient time,, Mathematics of Operations Research, 29 (2004), 309.
doi: 10.1287/moor.1030.0081. |
[10] |
D. J. Daley, General customer impatience in the queue $GI$/$G$/$1$,, Journal of Applied Probability, 2 (1965), 186.
doi: 10.2307/3211884. |
[11] |
A. G. de Kok and H. C. Tijms, A queueing system with impatient customers,, Journal of Applied Probability, 22 (1985), 688.
doi: 10.2307/3213871. |
[12] |
G. Evans, "Practical Numerical Analysis,", John Wiley & Sons, (1996). Google Scholar |
[13] |
P. D. Finch, Deterministic customer impatience in the queueing system $GI$/$M$/$1$,, Biometrika, 47 (1960), 45.
|
[14] |
N. Gans, G. Koole and A. Mandelbaum, Telephone call centers: Tutorial, review, and research prospects,, Manufacturing and Service Operations Management, 5 (2003), 79.
doi: 10.1287/msom.5.2.79.16071. |
[15] |
O. Garnett, A. Mandelbaum and M. Reiman, Designing a call center with impatient customers,, Manufacturing & Service Operations Management, 4 (2002), 208.
doi: 10.1287/msom.4.3.208.7753. |
[16] |
R. B. Haugen and E. Skogan, Queueing systems with stochastic time out,, IEEE Transactions on Communications, 28 (1980), 1984.
doi: 10.1109/TCOM.1980.1094632. |
[17] |
G. Latouche and V. Ramaswami, "Introduction to Matrix Analytic Methods in Stochastic Modeling,", American Statistical Association and the Society for Industrial and Applied Mathematics, (1999).
doi: 10.1137/1.9780898719734. |
[18] |
A. Movaghar, On queueing with customer impatience until the beginning of service,, Queueing Systems Theory Appl., 29 (1998), 337.
doi: 10.1023/A:1019196416987. |
[19] |
C. Palm, Methods of judging the annoyance caused by congestion,, Tele (English ed.), 2 (1953), 1. Google Scholar |
[20] |
R. E. Stanford, Reneging phenomena in single server queues,, Mathematics of Operations Research, 4 (1979), 162.
doi: 10.1287/moor.4.2.162. |
[21] |
W. Xiong, D. Jagerman and T. Altiok, $M$/$G$/$1$ queue with deterministic reneging times,, Performance Evaluation, 65 (2008), 308.
doi: 10.1016/j.peva.2007.07.003. |
[22] |
S. Zeltyn and A. Mandelbaum, Call centers with impatient customers: Many-server asymptotics of the M/M/$n$ + G queue,, Queueing Systems, 51 (2005), 361.
doi: 10.1007/s11134-005-3699-8. |
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