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, c omputationally inexpensive, accurate for both low and high network loads, a nd the first to analyze adaptive routing with wavelength translation in wav elength division multiplexed (WDM) networks while also providing a simpler formulation of oblivious routing with wavelength translation. Unlike some p revious analyses which use the link independence blocking assumption and th e call dropping (loss) model (where blocked calls are cleared), we account for the dependence between the acquisition of wavelengths on successive lin ks of a session's path and use a lossless model (where blocked calls are re tried at a later time). We show that the throughput per wavelength increase s superlinearly (as expected) as we increase the number of wavelengths per link, due both to additional capacity and more efficient use of this capaci ty; however, the extent of this superlinear increase in throughput saturate s rather quickly to a linear increase. We also examine the effect that adap tive routing can have on performance. The analytical methodology that we de velop can be applied to any vertex and edge symmetric topology, and with mo difications, to any vertex symmetric (but not necessarily edge symmetric) t opology. We find that, for the topologies we examine, providing at most one alternate link at every hop gives a per-wavelength throughput that is clos e to that achieved by oblivious routing with twice the number of wavelength s per link. This suggests some interesting possibilities for network provis ioning in an all-optical network. We verify the accuracy of our analysis fo r both oblivious and adaptive routing via simulations for the torus and hyp ercube networks.