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H = λG and the Palm transformation

Part of: Special processes Stochastic processes

Published online by Cambridge University Press:  01 July 2016

Ward Whitt
Ward Whitt*
Affiliation:
AT&T Bell Laboratories
*
∗Postal address: Room 2C-178, AT&T Bell Laboratories, Murray Hill, NJ 07974-0636, USA.
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Abstract

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We show that the stationary version of the queueing relation H = λG is equivalent to the basic Palm transformation for stationary marked point processes.

Keywords

CONSERVATION LAWSCAMPBELL'S FORMULAPALM INVERSION FORMULASTATIONARY MARKED POINT PROCESS

MSC classification

Primary: 60K25: Queueing theory
Secondary: 60G55: Point processes
Type
Letters to the Editor
Information
Advances in Applied Probability , Volume 24 , Issue 3 , September 1992 , pp. 755 - 758
Copyright
Copyright © Applied Probability Trust 1992 

References

Baccelli, F. and Bremaud, P. (1987) Palm Probabilities and Stationary Queueing Systems. Lecture Notes in Statistics 41, Springer-Verlag, New York.Google Scholar
Brandt, A., Franken, P. and Lisek, B. (1990) Stationary Stochastic Models. Wiley, Chichester.Google Scholar
Bremaud, P. (1991) An elementary proof of Sengupta's invariance relation and a remark on Miyazawa's conservation principle. J. Appl. Prob. 28, 950–954.Google Scholar
Bremaud, P. (1993) A Swiss army formula of Palm calculus. J. Appl. Prob. 30(1).Google Scholar
Franken, P. (1976) Some applications of the theory of point processes in queueing theory. Math. Nachr. 70, 303–319 (in German).Google Scholar
Franken, P., König, D., Arndt, U. and Schmidt, V. (1981) Queues and Point Processes . Akademie-Verlag, Berlin.Google Scholar
Glynn, P. W. and Whitt, W. (1989) Extensions of the queueing relations L = ?W and H = ?G. Operat. Res. 37, 634–644.Google Scholar
Miyazawa, M. (1979) A formal approach to queueing processes in the steady state and their applications. J. Appl. Prob. 16, 332–346.Google Scholar
Miyazawa, M. (1983) The derivation of invariance relations in complex queueing systems with stationary inputs. Adv. Appl. Prob. 15, 874–885.Google Scholar
Miyazawa, M. (1985) The intensity conservation law for queues with randomly changed service rate. J. Appl. Prob. 22, 408–418.Google Scholar
Miyazawa, M. (1990) Derivation of Little's and related formulas by rate conservation law with multiplicity. Department of Information Sciences, Science University of Tokyo.Google Scholar
Rolski, T. (1981) Stationary Random Processes Associated with Point Processes. Springer-Verlag, New York.CrossRefGoogle Scholar
Sigman, K. (1991) A note on a sample-path rate conservation law and its relationship with H = ?G. Adv. Appl. Prob. 23, 662–665.Google Scholar
Stidham, S. Jr. (1979) On the relation between time averages and customer averages in stationary random marked point processes. Department of Industrial Engineering, North Carolina State University, Raleigh.Google Scholar
Stidham, S. Jr. (1982) Sample-path analysis of queues. In Applied Probability–Computer Science: The Interface , Vol. II, pp. 41–70, ed. Disney, R. L. and Ott, T. J., Birkhäuser, Boston.Google Scholar
Walrand, J. (1988) An Introduction to Queueing Networks. Prentice Hall, Englewood Cliffs, NJ.Google Scholar
Whitt, W. (1991) A review of L = ?W and extensions. QUESTA 9, 235–268 (Correction 11, to appear).Google Scholar