Selected Examples

Markov-modulated Poisson Arrivals

A Markov-modulated Poisson Process (MMPP) is a Poisson process that has its parameter controlled by a Markov process. These arrival processes are typical in communications modeling where time-varying arrival rates capture some of the important correlations between inter-arrival times. This example has a Markov-modulated Poisson process that serves to control the arrival process to a single-queue, single-server queueing model.

Figure 9.12: Markov-Modulated Poisson Arrivals

Figure 9.12 shows one way to model an MMPP. The process labeled "Markov-modulated Poisson Process" samples from an MMPP distribution and sets the value of the parameter lambda, the mean inter-arrival time for an exponential random variable in the Sampler labeled "MMPP Arrivals.". In the upper process, lambda is given the values 10, .1, and 1 based on the state of a Markov chain. The state is changed in the Modifier components labeled "state." Each has a conditional component driven by an observation of a uniform random variable. So, for a given state, the state is changed to the next state and the value of lambda is chosen for the MMPP Arrivals Sampler. The selected lambda is set in the MMPP Arrivals Sampler, and the process is delayed for an exponential amount of time whose parameter is state dependent. The transaction then goes to a switch that routes based on the state for the next state change.

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