 zero is called Interrupted Poisson Process (IPP). 6.4.3.2 MMPP(2)/D/1 In the above section 6.4.1.2, two system models on the AAL2 packet level are presented for different traffic scenarios. For case (a), there is only one service type, either RT or NRT traffic. According to its system model, with MMPP as the arrival process model, the resultant queuing model is MMPP/D/1 where the service process is deterministic. Thus the AAL2 delay or the lub transport delay can be derived from the calculation of the queuing delay of MMPP/D/1 model. The 2-state case has received attention as a simple tractable process which can closely approximate much more complicated processes and predict queuing delays very accurately. Therefore in this thesis, a two-state MMPP (denoted as MMPP(2)) is suggested for modeling the arrival traffic. The following presents the analytical approach for calculating the waiting time distribution for the MMPP(2)/D/1 system. It is given that the MMPP(2)/D/1 with the infinitesimal generator Q of the underlying Markov chain and with the arrival rate matrix A: (6.45) Let T be the steady-state vector of Q, and e be the unitary column vector. Assuming the unit service time, the traffic intensity is then given by p=Ae. Lucantoni presented the Laplace transform of the virtual waiting time distribution (CDF) for the MMPP/G/1 queue in [Luc91]: 6.4 Dimensioning for Transport Network Performance F(s)= s(1-p)g[sI+Q-A(1-H(s)]'e (6.46) Here H(s) is the Laplace transform of the service time distribution. For the MMPP/D/1 system, due to the deterministic service time distribution with the unit service time, the Laplace transform of the service time distribution H(s) = e-s. So from the equation (6.46), the complementary cumulative distribution function (CCDF) of the virtual waiting time of the MMPP/D/1 can be derived. Let W(x) = Pr(W>x) be the complementary cumulative distribution function of the virtual waiting time W. The Laplace transform of W(x) is given in equation (6.47): (6.47) Where g = (g1, 1-g1) is the steady-