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Four cashiers are on duty in a bank where customers may be assumed to arrive independently...

Four cashiers are on duty in a bank where customers may be assumed to arrive independently and at random, at an average rate of 60 per hour. If a cashier is free, then an arriving customer receives immediate attention; otherwise a central queue is formed. The service time for each cashier may be assumed to be exponentially distributed with mean 2 minutes. The traffic intensity  is .

Assume that the queue is in equilibrium

What is the probability that at any time all the cashiers are idle?
What proportion of customers receive immediate service?
What proportion of customers arrive to find that all the cashiers are busy and one person is waiting to be served?
Math   Statistics-And-Probability   
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