Hostname: page-component-586b7cd67f-g8jcs Total loading time: 0 Render date: 2024-11-24T05:54:58.343Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on single server loss systems with a superposition of inputs

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Helmut Willie
Helmut Willie*
Affiliation:
Deutsche Telekom
*
∗Postal address: Deutsche Telekom, Research and Technology Center, Postfach 100003, D-64276 Darmstadt, Germany.
Get access Rights & Permissions [Opens in a new window]

Abstract

Explicit formulas for the time congestion and the call blocking probability are derived in a single server loss system whose total input consists of a finite superposition of independent general stationary traffic streams with exponentially distributed service times. The results are used for studying to what extent two arrival processes with coinciding customer-stationary state distributions are similar or even identical, and whether an arrival process with coinciding customer-stationary and time-stationary state distributions is of the Poisson type.

Keywords

G1 + ···+ GN/M/1 LOSS SYSTEMTIME CONGESTIONCALL BLOCKING PROBABILITYARRIVAL PROCESS IDENTIFICATION

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60G55: Point processes
Type
Research Papers
Information
Journal of Applied Probability , Volume 34 , Issue 1 , March 1997 , pp. 213 - 222
Copyright
Copyright © Applied Probability Trust 1997 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

[1] Franken, P., König, D., Arndt, U. and Schmidt, V. (1982) Queues and Point Processes. Wiley, New York.Google Scholar
[2] Gnedenko, B. V. and König, D. (1983) Handbuch der Bedienungstheorie I. Akademie, Berlin.Google Scholar
[3] Hewitt, E. and Stromberg, K. (1969) Real and Abstract Analysis. Springer, Berlin.Google Scholar
[4] Kerstan, J., Matthes, K. and Mecke, J. (1978) Infinitely Divisible Point Processes. Wiley, New York.Google Scholar
[5] König, D., Miyazawa, M. and Schmidt, V. (1983) On the identification of Poisson arrivals in queues with coinciding time-stationary and customer-stationary state distributions. J. Appl. Prob. 20, 860–871.Google Scholar
[6] Lam, C. Y. T. (1993) Superposition of Markov renewal processes and applications. Adv. Appl. Prob. 25, 585–606.Google Scholar
[7] Lam, C. Y. T. and Lehoczky, J. P. (1991) Superposition of renewal processes. Adv. Appl. Prob. 23, 64–85.Google Scholar
[8] Ross, S. M. (1983) Stochastic Processes. Wiley, New York.Google Scholar
[9] Takács, L. (1962) Introduction to the Theory of Queues. Oxford University Press, New York.Google Scholar
[10] Willie, H. (1988) Individual call blocking probabilities in the loss systems SM+ M/M/N and G + M/M/N. J. Inf. Process. Cybern. EIK 24, 601–612.Google Scholar
[11] Willie, H. (1990) Individual blocking probabilities in the loss system G1 + + GN/M/1/0. Queueing Systems 6, 109–112.Google Scholar
[12] Willie, H. (1991) Steady state of loss systems with a superposition of inputs. Queueing Systems 9, 441–160.Google Scholar