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We present a new analysis of wavelength translation in
regular, alloptical WDM networks, that is simple, computationally
inexpensive, and accurate for both low and high
network loads. In a network with
k
wavelengths per link,
we model the output link by an auxiliary
M/M/k/k
queueing
system. We then obtain a closedform expression for
the probability
P succ
that a session arriving at a node at a
random time successfully establishes a connection from its
source node to its destination node. Unlike previous analyses,
which use the link independence blocking assumption,
we account for the dependence between the acquisition of
wavelengths on successive links of the session’s path. Based
on the success probability, we show that the throughput per
wavelength increases superlinearly (as expected) as we increase
the number of wavelengths per link; however, the
extent of this superlinear increase in throughput saturates
rather quickly. This suggests some interesting possibilities
for network provisioning in an alloptical network. We verify the accuracy of our analysis via simulations for the torus
and hypercube networks.
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