Finite-Source Queueing Systems and their Applications
Finite-Source Queueing Systems and their Applications
Finite-Source Queueing Systems and their Applications
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János Sztrik 2001/08/05<br />
Analytical Results<br />
Homogeneous M/M/r systems, the classical model<br />
This section presents the classical queuing theory approach to solving a<br />
machine interference problem. It should be noted that this system is analyzed<br />
by many authors in different books. It is a classical example for queueing<br />
systems with state-dependent arrival rates <strong>and</strong> it can be treated in the<br />
framework of the so-called birth-<strong>and</strong>-death processes. The present problem is<br />
descibed in several classical books on queueing systems, for example<br />
[2, 12, 15, 41, 29, 33, 79] suct to mention the basic ones. Our aim is to show<br />
the form of the steady-state probabilities of stopped machines. In the above<br />
mentioned works one can find the detailed analysis of waiting time, down<br />
time distibution of machines, too. Several numerical examples from real life<br />
situations illustrates this interesting system.<br />
It is also proved that in steady-state the arriving machines’s distribution in<br />
system containing N machines is the same as the outside observer’s<br />
<strong>Finite</strong>-<strong>Source</strong> <strong>Queueing</strong> <strong>Systems</strong> <strong>and</strong> <strong>their</strong> <strong>Applications</strong>
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