There are a number of interesting mathematical properties exhibited by Poisson processes. Primarily, superposition of independent Poisson processes results in a new Poisson process whose rate is the sum of the rates of the independent Poisson processes. Further, the independent increment property renders a Poisson process memoryless. Poisson processes are common in traffic applications scenarios that consist of a large number of independent traffic streams. The reason behind the usage stems from Palm's Theorem which states that under suitable conditions, such large number of independent multiplexed streams approach a Poisson process as the number of processes grows, but the individual rates decrease in order to keep the aggregate rate constant. Traffic aggregation need not always result in a Poisson process. The two primary assumptions that the Poisson model makes are: 1. The number of sources is infinite 2. The traffic arrival pattern is random. In the compound Poisson model, the base Poisson model is extended to deliver batches of packets at once. The inter-batch arrival times are exponentially distributed, while the batch size is geometric Mathematically, this model has two parameters, λ, the arrival rate, and ρ in (0,1), the batch parameter. Thus, the mean number of packets in a batch is 1/ ρ, while the mean inter-batch arrival time is 1/ λ. Mean packet arrivals over time period t are tλ/ ρ. The compound Poisson model shares some of the analytical benefits of the pure Poisson model: the model is still memoryless, aggregation of streams is still (compound) Poisson, and the steady-state equation is still reasonably simple to calculate, although varying batch parameters for differing flows would complicate the derivation. Markov models attempt to model the activities of a traffic source on a network, by a finite number of states. The accuracy of the model increases linearly with the number of states used in the model. However, the complexity of the model also increases proportionally with increasing number of states. An important aspect of the Markov model - the Markov Property, states that the next (future) state depends only on the current state. In other words, the probability of the next state, denoted by some random variable Xn+1, depends only on the current state, indicated by Xn, and not on any other state Xi, where i This model was principally designed to recognize that address locality applies to routing decisions; that is, packets that arrive near each other in time are frequently going to the same destination.