| Abstract |
Summary form only given. Circuit switching networks under Poissonian traffic have been extensively investigated in $mid-20^{th}$ century, and then somewhat "forgotten" when packet switching emerged. Interest on circuit switching theory is now revived by the first generation of optical networks, but with new features and constraints concerning new issues such as wavelength continuity, non-Poissonian traffic, poorly connected topologies, and survivability requirements, that demand new analytical models and approaches. The physical and technological environments also offer unique challenges in the optical domain that stress the design of new network architectures. Transition toward an optical packet switching network architecture is not as straightforward as it has been in the electrical domain, due to both lack of appropriate means for optical storage and excessive burstiness in traffic patterns generated by Internet applications in both time and space. These difficulties have led to a focus on optical burst switching (OBS) networks. Characterization of blocking performance on such networks are of paramount importance in the evaluation of their efficiency. Given the peculiar way in which bursts occupy network resources in time and space, new blocking models must be devised for this purpose. This paper discusses new analytical approaches for performance characterization of optical networks, including the calculation of blocking probabilities in poorly connected topologies, with a special emphasis on the case of slotted line topologies with single-circuit links, for which exact asymptotic results have been derived [1]. The new approach deals effectively with link dependence in this environment, thus obviating the need for the usual assumption of link independence, which is a source of large errors in the estimation of blocking probability, especially in such poorly connected topologies. Furthermore, extension to multiple wavelength environments is also possible through reduced load approximations [2]. The underlying idea of the new approach is the assumption of object independence in lieu of the simpler but less effective link independence assumption. In principle, object independence may be assumed in any topology, but applying this assumption to meshed topologies is more difficult due to the explosion in the number of routes and the possibilities of interference between them. The results obtained for slotted line topologies can be extended to "unslotted" asymptotic limits [3], with possible extensions in other frameworks, such as scheduling performance over continuous media (e.g., as in OBS networks). However, extension of this approach to scheduling environments requires two steps. Firstly, the model must be made to deal with non-uniform traffic patterns, since resources are to be reserved on a finite period from the reservation time until a maximum lead time, and with non-uniform rates in this period. Second, as time goes by, scheduled times move with respect to real time, so the reservation log moves with respect to reservation time, so the blocking model must be able to deal with this feature. At least under a "slotted-time approximation", these challenges seem to be approachable by Markovian modeling. The old emphasis on the blocking performance under stationary, dynamic traffic, although still important, is not anymore able to characterize appropriate performance in current business environment. In practice, many connections are active for a long time. For this reason, we are interested in the extension of current models to deal with incremental traffic, in which new connections are accommodated or blocked, but never torn up. In such networks, the steady-state blocking probability is not a good metric, because equilibrium is reached only when the whole network is blocked. Instead, we propose to focus on network resource utilization. |
