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Generalized model with repeated calls in case of extreme load

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S. N. StepanovAuthors Info & Claims

Queueing Systems: Theory and Applications, Volume 27, Issue 1/2

Pages 131 - 151

https://doi.org/10.1023/A:1019110030674

Published: 14 December 1997 Publication History

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Abstract

Recurrence formulas for finding any desired number of terms in the asymptotic expansion of basic stationary performance measures of a generalized full-available system with repeated calls into a power series of the intensity of primary calls as it tends to infinity are derived. The first 3-4 terms of the expansion are found in explicit form. Other coefficients can be found numerically. It is shown that a number of interesting particular cases can be obtained from the model by proper choice of the values of input parameters. Among them it is worth mentioning models with possibility of call repetitions because of unsuccessful finishing of waiting time, inner blocking or unsuccessful finishing of service time.

References

[1]

[1] S.N. Stepanov, Asymptotic analysis of models with repeated calls for a large value of losses, Preprint, Moscow, Institute for Problems of Information Transmission (1987).

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[2]

[2] S.N. Stepanov, Asymptotic analysis of models with repeated calls in case of extreme load, in: Proc. of the 13th Int. Teletraffic Congress , Copenhagen (1991) pp. 21-26.

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[3]

[3] S.N. Stepanov, Asymptotic analysis of models with repeated calls in case of extreme load, Problems of Information Transmission 29 (1993) 54-75.

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[4]

[4] S.N. Stepanov, The Numerical Methods of Analyzing the Models with Repeated Calls (Nauka, Moscow, 1983).

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[5] G.I. Falin, Survey of retrial queues, Queueing Systems 7(2) (1990) 127-167.

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[6] N. Deul, Stationary conditions for multi-server queueing systems with repeated calls, Elektronische Informationsverarbeitung und Kybernetik 16(10-12) (1980) 607-613.

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[7] M. Abramowitz and I.A. Stegun, Handbook of Mathematical Functions , Applied Mathematics Series, Vol. 55 (National Bureau of Standards, Washington, DC, 1964).

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Stepanov MStepanov SKroshin F(2022)Effective Algorithm of Estimation the Performance Measures of Group of Servers with Dependence of Call Repetition on the Type of Call BlockingDistributed Computer and Communication Networks: Control, Computation, Communications10.1007/978-3-031-23207-7_25(324-337)Online publication date: 26-Sep-2022
https://dl.acm.org/doi/10.1007/978-3-031-23207-7_25
Stepanov SStepanov MShishkin M(2020)Performance Measures of Emergency Services in Case of OverloadDistributed Computer and Communication Networks10.1007/978-3-030-66471-8_33(436-449)Online publication date: 14-Sep-2020
https://dl.acm.org/doi/10.1007/978-3-030-66471-8_33
Stepanov SStepanov MZhurko H(2019)The Modeling of Call Center Functioning in Case of OverloadDistributed Computer and Communication Networks10.1007/978-3-030-36614-8_30(391-406)Online publication date: 23-Sep-2019
https://dl.acm.org/doi/10.1007/978-3-030-36614-8_30
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cover image Queueing Systems: Theory and Applications

Queueing Systems: Theory and Applications Volume 27, Issue 1/2

1997

199 pages

ISSN:0257-0130

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J. C. Baltzer AG, Science Publishers

United States

Publication History

Published: 14 December 1997

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Stepanov MStepanov SKroshin F(2022)Effective Algorithm of Estimation the Performance Measures of Group of Servers with Dependence of Call Repetition on the Type of Call BlockingDistributed Computer and Communication Networks: Control, Computation, Communications10.1007/978-3-031-23207-7_25(324-337)Online publication date: 26-Sep-2022
https://dl.acm.org/doi/10.1007/978-3-031-23207-7_25
Stepanov SStepanov MShishkin M(2020)Performance Measures of Emergency Services in Case of OverloadDistributed Computer and Communication Networks10.1007/978-3-030-66471-8_33(436-449)Online publication date: 14-Sep-2020
https://dl.acm.org/doi/10.1007/978-3-030-66471-8_33
Stepanov SStepanov MZhurko H(2019)The Modeling of Call Center Functioning in Case of OverloadDistributed Computer and Communication Networks10.1007/978-3-030-36614-8_30(391-406)Online publication date: 23-Sep-2019
https://dl.acm.org/doi/10.1007/978-3-030-36614-8_30
Breuer LDudin AKlimenok V(2002)A Retrial BMAP/PH/N SystemQueueing Systems: Theory and Applications10.1023/A:101504160294640:4(433-457)Online publication date: 1-May-2002
https://dl.acm.org/doi/10.1023/A%3A1015041602946

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Asymptotic relations between the Hahn-type polynomials and Meixner-Pollaczek, Jacobi, Meixner and Krawtchouk polynomials

Asymptotic relations in the Askey scheme for hypergeometric orthogonal polynomials

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Asymptotic expansions of the Lauricella hypergeometric function F_D