Optical Networks: A Practical Perspective - Part 49. This book describes a revolution within a revolution, the opening up of the capacity of the now-familiar optical fiber to carry more messages, handle a wider variety of transmission types, and provide improved reliabilities and ease of use. In many places where fiber has been installed simply as a better form of copper, even the gigabit capacities that result have not proved adequate to keep up with the demand. The inborn human voracity for more and more bandwidth, plus the growing realization that there are other flexibilities to be had by imaginative use of the fiber, have led people. | 450 WDM Network Design node i to node j otherwise btj 0. The solution to the lightpath topology design problem will specify which of the are 1 and which are 0. We assume that we can arbitrarily split the traffic between the same pair of nodes over different paths through the network. This is not a problem if the traffic is IP packets but if we were instead considering SONET circuits this is tantamount to assuming that the traffic between nodes consists of a large number of such circuits. This assumption is satisfied when we are designing a backbone network to support a large number of private leased lines such as Tls or T3s. Let the fraction of the traffic between s-d pair s d that is routed over link i j if it exists be ajd. Then AJj asidksd is the traffic in packets second between s-d pair 5 d that is routed over fink i j . The total traffic from all s-d pairs that is routed over link i j is thus Xy We define a parameter called the congestion as Amax max 7 Ay. Note that the AJ and thus the Ay and Amax are variables that we have to determine. Determining their values amounts to finding a routing algorithm. To understand why the congestion is an important parameter let us consider the case where the packet arrivals follow a Poisson process and the packet transmission times are exponentially distributed with mean time given by 1 g seconds. Making the standard assumption that the traffic offered to a link fightpath in the network is independent of the traffic offered to other links each link can be modeled as an M M 1 queue. The average queuing delay on link i j is then given by BG92 Section dij . M -ij The throughput can be defined as the minimum value of the offered load for which the delay on any link becomes infinite. This happens when Amax max j Ay 1. Thus our performance objective will be to minimize the congestion Xmax. We are now ready to state the problem formally as a mathematical program Objective function min Amax subject to Flow conservation .
