×
Sherman, Nathan P.; Kharoufeh, Jeffrey P.; Abramson, Mark A.

An \(M/G/1\) retrial queue with unreliable server for streaming multimedia applications. (English) Zbl 1178.60066

Probab. Eng. Inf. Sci. 23, No. 2, 281-304 (2009).
Summary: As a model for streaming multimedia applications, we study an unreliable retrial queue with infinite-capacity orbit and normal queue for which the retrial rate and the server repair rate are controllable. Customers join the retrial orbit if and only if their service is interrupted by a server failure. Interrupted customers do not rejoin the normal queue but repeatedly attempt to access the server at independent and identically distributed intervals until it is found functioning and idle. We provide stability conditions, queue length distributions, stochastic decomposition results, and performance measures. The joint optimization of the retrial and server repair rates is also studied.

Cited in 1 Review
Cited in 13 Documents

MSC:

60K25 Queueing theory (aspects of probability theory)
90B22 Queues and service in operations research
PDF BibTeX XML Cite
\textit{N. P. Sherman} et al., Probab. Eng. Inf. Sci. 23, No. 2, 281--304 (2009; Zbl 1178.60066)
Full Text: DOI

References:

[1] DOI: 10.1016/0305-0548(94)00038-A · Zbl 0838.90047
[2] DOI: 10.1023/A:1019125323347 · Zbl 0918.90073
[3] DOI: 10.1016/j.ejor.2003.11.033 · Zbl 1077.90014
[4] DOI: 10.1016/S0307-904X(02)00061-6 · Zbl 1018.60088
[5] DOI: 10.1007/BF01158474 · Zbl 0727.60110
[6] DOI: 10.1016/j.amc.2003.12.128 · Zbl 1063.60129
[7] DOI: 10.1016/0167-6377(83)90019-6 · Zbl 0523.60095
[8] DOI: 10.1016/S0377-2217(00)00330-1 · Zbl 0989.90028
[9] Hassin, Probability in the Engineering and Informational Sciences 10 pp 223– (1996)
[10] DOI: 10.1016/S0305-0548(96)00076-7 · Zbl 0882.90048
[11] Falin, Retrial queues (1997)
[12] DOI: 10.1007/BF01158703 · Zbl 0817.60093
[13] DOI: 10.1016/0026-2714(93)90003-H
[14] Aissani, Journal of Technology 6 pp 98– (1988) · Zbl 0659.60097
[15] DOI: 10.1007/BF01158950 · Zbl 0810.90046
[16] DOI: 10.1504/IJOR.2005.007432 · Zbl 1100.90015
[17] Wang, Quality Technology and Quantitative Management 1 pp 325– (2004)
[18] DOI: 10.1023/A:1010918926884 · Zbl 1028.90014
[19] DOI: 10.1080/15326349608807394 · Zbl 0858.60086
[20] Liang, Applied probability and stochastic processes pp 203– (1999)
[21] DOI: 10.1081/STM-200056021 · Zbl 1069.60076
[22] DOI: 10.1016/0377-2217(94)E0358-I · Zbl 0912.90139
[23] DOI: 10.1111/j.1467-9574.1994.tb01429.x · Zbl 0829.60087
[24] DOI: 10.1051/ro:2003007 · Zbl 1037.90005
[25] DOI: 10.1007/BF01252189
[26] DOI: 10.1007/BF01158476 · Zbl 0706.60089
[27] DOI: 10.1007/BF01245324 · Zbl 0847.90059
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.