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 />
This finite system of ordinary differential equations can be solved <strong>and</strong> we get<br />
the transient probabiliies.<br />
For the equilibrium values of Pn by setting these derivatives equal to zero<br />
while noting that the equilibrium (or stationary or steady state) values are<br />
Pn = lim<br />
t→∞ Pn(t)<br />
The flow balance equations ( steady-state equations ) become<br />
NλP0 = µP1<br />
{(N − n)λ + nµ}P0 = (N − n + 1)λPn−1 + (n + 1)µPn+1, 1 < n < r<br />
{(N − n)λ + rµ}P0 = (N − n + 1)λPn−1 + rµPn+1, r ≤ n < N<br />
rµPN = λPN−1<br />
These equations are solved recursively using the relationship<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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