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WROCŁAW UNIVERSITY
OF SCIENCE AND
TECHNOLOGY

Contents of PMS, Vol. 17, Fasc. 1,
pages 47 - 63
 

ASYMPTOTIC STATIONARITY OF TANDEM OF QUEUES

Władysław Szczotka

Abstract: In [12] it was proved that the process of waiting times for single server queues is asymptotically stationary if

  1. a generic process X = (Xk,k > 1) is asymptotically stationary,
  2. X satisfies condition AB and
  3. the two-sided stationary extension X* = (X* ,- oo < k < oo ) k of the stationary representation of X is such that sum 0 * j=-nX j-- > - oo a.e.

The paper gives a detailed characterization of condition AB. Next, the sufficient conditions on the input to a tandem of queues are given under which the inputs to the nodes in that tandem satisfy conditions (l)-(3).

2000 AMS Mathematics Subject Classification: Primary: -; Secondary: -;

Key words and phrases: -

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