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 />
obviously have π0 = 1 <strong>and</strong> E[T ] = b. As N → ∞, we have π0 → 0 <strong>and</strong> so<br />
E[T ] ≈ Nb − 1<br />
λ<br />
as N → ∞ (20)<br />
The value of N, denoted by N ∗ , at which two straight lines E[T ] = b <strong>and</strong> the<br />
one in (20) as a function of N intersect each other is called the saturation<br />
number by [42] (sec.4.12). It is given by<br />
N ∗ = 1 + 1<br />
λb<br />
(21)<br />
Note that this can be written as N ∗ = (b + 1/λ)/b. Therefore, if nature were<br />
kind <strong>and</strong> all messages required exactly b service time <strong>and</strong> exactly 1/λ<br />
generation time(a deterministic system), then N ∗ would be the maximum<br />
number of messages that could be scheduled without causing mutual<br />
interference [42] page 209.<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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