Consider a small barber shop with three masters, which is described in terms of a birth...

 

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Consider a small barber shop with three masters, which is described in terms of a birth and death process, X = {X(t): t>0}, having instant rates {k= 9:0 3 and k = = 0 when k> 3. 1. Derive the stationary (limiting) distribution for a number, X(t) of customers at time t. 2. Find the queue length, L 3. Determine the proportion of time when X(t) = 0. Equivalently, find the stationary probability of the event (X(t) = 0). Consider a small barber shop with three masters, which is described in terms of a birth and death process, X = {X(t): t>0}, having instant rates {k= 9:0 3 and k = = 0 when k> 3. 1. Derive the stationary (limiting) distribution for a number, X(t) of customers at time t. 2. Find the queue length, L 3. Determine the proportion of time when X(t) = 0. Equivalently, find the stationary probability of the event (X(t) = 0).