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 />
1/µ for each machine <strong>and</strong> each operator. The service times are mutually<br />
independent <strong>and</strong> also independent of the number of down machines.<br />
Then<br />
Prob [one of the n down machines is fixed in an interval ∆t]<br />
�<br />
nµ∆t + o(∆t), for 1 ≤ n ≤ r<br />
=<br />
rµ∆t + o(∆t), for r < n ≤ N<br />
3. The machines are served in the order od <strong>their</strong> beakdowns.<br />
Let<br />
<strong>and</strong><br />
L(t) = the number of down machines at time t<br />
Pn(t) = P rob(L(t) = n|L(0) = i), n = 0, . . . , N.<br />
Then the stochastic process, (L(t), t ≥ 0), is a birth-<strong>and</strong>-death process, with<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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