Network global expectation model of routing and grooming in multilayer service transport

We present an analytical model to estimate the expected minimum numbers of network elements required to support traffic demands in a multilayer service transport network for the case where grooming of demands into channels is permitted at all nodes. This new scalable formulation expands upon earlier models and makes use of global expectation values, the concept of maximum entropy, analytical and semi-empirical models of the mean number of hops, and statistical considerations to estimate the resource requirements as a function of the total traffic, number of nodes, grooming objectives, and constraints of interest. We find that the solution provided by a routing and grooming algorithm can be described by three key variables when the cost metric is the number of transponders. Two of these variables characterize the virtual topology of the routes over which the traffic is transported, and the third characterizes the efficacy of grooming the traffic into channels over the routes. Two minor variables capture the details of the number of routes and channels of the solution when the amount of traffic and number of nodes are small. The model is applied to analyze the dimensioning of optical ring and mesh networks transporting quasi-static, uniform, and random traffic with electronic grooming and optical bypass. The analytical results are compared to special cases considered by earlier analytical models and used to understand a broad range of results obtained by numerical optimization for several routing and grooming algorithms.