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Stationary representation of queues. II

Published online by Cambridge University Press:  01 July 2016

Władysław Szczotka
Władysław Szczotka*
Affiliation:
Wrocław University
*
∗Postal address: Mathematical Institute, Wrocław University, pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland.
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Abstract

The paper is a continuation of [7]. One of the main results is as follows: if the sequence (w, v, u) is asymptotically stationary in some sense then (l, w, v, u) is asymptotically stationary in the same sense. The other main result deals with an asymptotic behaviour of the vector of the queue size and the waiting time in the heavy-traffic situation. This result resembles a formula of the Little type.

Keywords

FIFO SINGLE-SERVER QUEUEWAITING TIMEQUEUE SIZEHEAVY TRAFFICLITTLE&S FORMULAASYMPTOTIC STATIONARITY
Type
Research Article
Information
Advances in Applied Probability , Volume 18 , Issue 3 , September 1986 , pp. 849 - 859
Copyright
Copyright © Applied Probability Trust 1986 

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References

1. Borovkov, A. A. (1972) Stochastic Processes in Queueing Theory (in Russian) Nauka, Moscow.Google Scholar
2. Breiman, L. (1968) Probability. Addision-Wesley, Reading, Mass.Google Scholar
3. Szczotka, W. (1973) M/G/1 queueing system with ‘fagging’ service channel. Zast. Mat. 13, 439–463.Google Scholar
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6. Szczotka, W. (1986) Joint distribution of waiting time and queue size for single server queues, Dissertationes Math. 248.Google Scholar
7. Szczotka, W. (1986) Stationary representation of queues I. Adv. Appl. Prob. 18, 815–848.CrossRefGoogle Scholar