We present a new analytical technique, based on the inclusion-exclusion principle from combinatorial mathematics, for the analysis of all-optical networks with no wavelength conversion and random wavelength assignment. We use this technique to propose two models of low complexity for analysing networks with arbitrary topologies and traffic patterns. The first model improves the current technique by Birman (1996) in that the complexity of calculation is independent of hop-length and scales only with the capacity of the link as against that of Birman's method which grows exponentially with hop-length. We then propose a new heuristic to account for wavelength correlation and show that the second model is accurate even for sparse networks. Our technique can also be extended to analyse fixed alternate and least loaded routing.
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