Two remarks on insensitive stochastic models

This paper contains two contributions to the insensitivity theory for generalized semi-Markov schemes, namely (1) a detailed account of a close relationship between insensitive schemes and partially balanced discrete-state Markov chains, and (2) an extension of the notion of an insensitive scheme in order to incorporate insensitivity phenomena not previously covered.

[1]  Dénes König,et al.  Verallgemeinerungen der Erlangschen und Engsetschen Formeln : Eine Methode in der Bedienungstheorie , 1967 .

[2]  H. Geiringer.  On the Foundations of Probability Theory , 1967 .

[3]  K. Mani Chandy,et al.  Open, Closed, and Mixed Networks of Queues with Different Classes of Customers , 1975, JACM.

[4]  R. Schassberger.  Insensitivity of Steady-state Distributions of Generalized Semi-Markov Processes. Part II , 1977 .

[5]  Uwe Jansen,et al.  Stochastic Processes and Properties of Invariance for Queueing Systems with Speeds and Temporary Interruptions , 1977 .

[6]  R. Schassberger.  Insensitivity of steady-state distributions of generalized semi-Markov processes by speeds , 1978, Advances in Applied Probability.

[7]  U. Jansen,et al.  A criterion of insensitivity for a class of queueing systems with random marked point processes , 1979 .

[8]  Ward Whitt,et al.  Continuity of Generalized Semi-Markov Processes , 1980, Math. Oper. Res..

[9]  Anthony Unwin,et al.  Reversibility and Stochastic Networks , 1980 .

[10]  A. Barbour,et al.  INSENSITIVE AVERAGE RESIDENCE TIMES IN GENERALIZED SEMI-MARKOV PROCESSES , 1981 .

[11]  A. Barbour.  Generalized semi-Markov schemes and open queueing networks , 1982 .

[12]  W. Henderson.  Insensitivity and reversed Markov processes , 1983 .

[13]  R. Schassberger,et al.  Decomposable stochastic networks: Some observations , 1984 .

[14]  U. Jansen.  Conditional expected sojourn times in insensitive queueing systems and networks , 1984, Advances in Applied Probability.

[15]  P. Whittle.  Partial balance and insensitivity , 1985, Journal of Applied Probability.