Consider a single-server queue to which customers arrive according to a Poisson process with parameter ...

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Consider a single-server queue to which customers arrive according to a Poisson process with parameter λ = 0.04/min and where the service times of all customers are fixed at 10 min. When there are three units in line, the system becomes saturated and all additional arrivals are turned away. The instants of departure give rise to an imbedded Markov chain with states 0, 1, 2, and 3. Find the one-step transition matrix of this chain and the resultant stationary distribution. Then compare this answer with the result you would have gotten without truncation. Consider a single-server queue to which customers arrive according to a Poisson process with parameter λ = 0.04/min and where the service times of all customers are fixed at 10 min. When there are three units in line, the system becomes saturated and all additional arrivals are turned away. The instants of departure give rise to an imbedded Markov chain with states 0, 1, 2, and 3. Find the one-step transition matrix of this chain and the resultant stationary distribution. Then compare this answer with the result you would have gotten without truncation.

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The onestep transition matrix of the imbedded Markov chain is given by P 096 004 0 0 096 ... View the full answer