 extensively used to study communication networks such as modeling ATM links and the superposition of packetized voice and packet data stream. The use of MMPP in queuing theory has been well discussed and described in the literature. A useful reference for the MMPP is [FMH92]. There is also much discussion on various fitting procedures and the accuracy of MMPP models, for example [NSV99, Mei87]. MMPP is a doubly stochastic Poisson process where the intensities of the Poisson processes are defined by the states of an independent Markov chain. Figure 6.48 illustrates a two-state MMPP model. Thus, the Markov chain can be said to modulate the Poisson process, hence it is named Markov-modulated Poisson process. This modulation introduces correlations between successive interarrival times in the process. Equivalently, an MMPP process can be constructed by varying the arrival rate of a Poisson process according to an m- state irreducible continuous time Markov chain which is independent of the arrival process. Figure 6.48: Two State MMPP When the Markov chain is in state i, arrivals occur according to a Poisson process of arrival rate Ai. The MMPP is parameterized by the m-state continuous-time Markov chain with infinitesimal generator Q [OAS90] which is the generator matrix of the modulating chain, and the arrival rate matrix A which is the diagonal matrix of arrival rates in each state of that chain. They are defined by 6 Dimensioning for Single ATM-Based lub where ri -r = (6.44) 102..0 In the above definition, is the rate at which the modulated process transits from phase i to phase j. di is the arrival rate when the modulating chain is in phase i. For the m-state Markov chain, there are m Poisson arrival rates, i.e. A1, A2, A3, Am. A two-state MMPP denoted as MMPP(2) is described as a Markov chain with two states and two different intensities, sometimes referred to as Switched Poisson process (SPP). If the two intensities are equal the model becomes an ordinary Poisson process. The special case when one intensity is