An analysis of oblivious and adaptive routing in optical networks with wavelength translation

We present an analysis for both oblivious and adaptive routing in regular, all-optical networks with wavelength translation. Our approach is simple, computationally inexpensive, accurate for both low and high network loads, and the first to analyze adaptive routing with wavelength translation in wavelength division multiplexed (WDM) networks while also providing a simpler formulation of oblivious routing with wavelength translation. Unlike some previous analyses which use the link independence blocking assumption and the call dropping (loss) model (where blocked calls are cleared), we account for the dependence between the acquisition of wavelengths on successive links of a session's path and use a lossless model (where blocked calls are retried at a later time). We show that the throughput per wavelength increases superlinearly (as expected) as we increase the number of wavelengths per link, due both to additional capacity and more efficient use of this capacity; however, the extent of this superlinear increase in throughput saturates rather quickly to a linear increase. We also examine the effect that adaptive routing can have on performance. The analytical methodology that we develop can be applied to any vertex and edge symmetric topology, and with modifications, to any vertex symmetric (but not necessarily edge symmetric) topology. We find that, for the topologies we examine, providing at most one alternate link at every hop gives a per wavelength throughput that is close to that achieved by oblivious routing with twice the number of wavelengths per link. This suggests some interesting possibilities for network provisioning in an all-optical network. We verify the accuracy of our analysis for both oblivious and adaptive routing via simulations for the torus and hypercube networks.