A service facility according to a poisson process

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Customers arrive at a service facility according to a Poisson process with rate λ. The (only) server is able to serve up to two customers at a time. However, an arbitrary customer is not served immediately if the server is busy upon his arrival. The service time has an exponential distribution with parameter when the service is provided to icustomer(s) at a time, for i = 1,2. Moreover, we suppose that the service times are independent random variables and that there can be at most two customers waiting at any time. We define the states

(a) Write the balance equations of the system. Do not solve them.

(b) Calculate, in terms of the limiting probabilities, the probability that

(i) the server is serving two customers at a time, given that he is busy,

(ii) an arriving customer who enters the system will not be served alone.

Reference no: EM131130578

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