| This work studies the stochastic modeling and performance analysis of all-optical networks with a focus on closed-form analytical solutions. For the modeling and performance analysis, extensive research has been done in wavelength-routed networks, some in optical burst-switched networks and in optical packet-switched networks. However, most of them are based on an approximate stationary analysis, only a few apply time-dependent transient analysis which may be appropriate for today's dynamically changing traffic load environment. Therefore, we introduce unified product-form methods based on time reversibility of Markov chains for stationary and transient analysis. For the stationary analysis, we introduce exact Markovian analytical tools to calculate blacking probabilities for short hop path and medium size networks in the literature; and then we propose the reduced-load approximation to large capacity loss networks. For the transient analysis, we propose methods which include exact and approximate solutions for the time-dependent blocking analysis of single link, single route and arbitrary network topologies. We consider the case there is full wavelength conversion in wavelength-routed networks. While modeling, we provide the dimensioning approaches where blocking probability is used as one of the QoS requirements. |
