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Extended and conditional versions of the PASTA property

Published online by Cambridge University Press:  01 July 2016

Dieter König  and
Volker Schmidt
Dieter König*
Affiliation:
Mining Academy of Freiberg
Volker Schmidt*
Affiliation:
Mining Academy of Freiberg
*
∗Postal address for both authors: Bergakademie Freiberg, Sektion Mathematik, Bernhard-von-Cotta-Str. 2, Freiburg, 9200, GDR.
∗Postal address for both authors: Bergakademie Freiberg, Sektion Mathematik, Bernhard-von-Cotta-Str. 2, Freiburg, 9200, GDR.
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Abstract

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Two types of conditions are discussed ensuring the equality between long-run time fractions and long-run event fractions of stochastic processes with embedded point processes. Modifications of this equality statement are considered.

Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 22 , Issue 2 , June 1990 , pp. 510 - 512
Copyright
Copyright © Applied Probability Trust 1990 

References

[1] Bremaud, P. (1989) Characteristics of queueing systems observed at events and the connection between stochastic intensity and Palm probability. Queueing Systems 5.Google Scholar
[2] 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
[3] König, D. and Schmidt, V. (1989) EPSTA. The coincidence of time-stationary and customer-stationary distributions. Queueing Systems 5, 247–264.Google Scholar
[4] König, D., Schmidt, V. and Van Doorn, E. A. (1989) On the ‘PASTA’ property and a further relationship between customer and time averages in stationary queueing systems. Stochastic Models 5, 261–272.Google Scholar
[5] Makowski, A., Melamed, B. and Whitt, W. (1989) On averages seen by arrivals in discrete time. Proc. 28th IEEE Conference on Decision and Control, Tampa, Florida.Google Scholar
[6] Melamed, B. and Whitt, W. (1989) On arrivals that see time averages: A martingale approach. J. Appl. Prob. 26.Google Scholar
[7] Melamed, B. and Whitt, W. (1990) On arrivals that see time averages. Operat. Res. 37.Google Scholar
[8] Regterschot, G. J. K. and Van Doorn, E. A. (1988) Conditional PASTA. Operat. Res. Letters 7, 229–232.Google Scholar
[9] Stidham, S. Jr. and El Taha, M. (1989) Sample-path analysis of processes with embedded point processes. Queueing Systems 5.Google Scholar