Congestion in a system of N service centers with interference.

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Author
Lee, Kheng Nam
Date
1974-09Advisor
Milch, Paul R.
Second Reader
Gaver, Donald P.
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Show full item recordAbstract
We have a system of N sendox machines (service centers)
which can transmit or receive (but not simultaneously) photocopies
to and from each other. The stochastic process
{X(M)(t),t ≥ 0}, where X(M)(t) is the number of messages undergoing transmission in the system at epoch t, is selected to
be the measure of system congestion. Under the assumptions
of exponential inter-arrival and transmission times and that
messages not transmitted immediately are lost, X(M)(t) is a
birth and death process. We call the model under these assumptions
the "loss" model. It is shown that X(M)(t) can be
approximated by a diffusion process. The steady state results
of the diffusion model can be calculated with ease and
are in close agreement with those of the birth and death
model and the simulation "loss" model. A more realistic "no
loss" model is also developed where messages that are not
transmitted immediately are allowed to queue up. It is shown,
however, that this "no loss" model can be quite accurately
approximated by an appropriate "loss" model.
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