Question: 2 3 (30 pts) Customers arrive at a queueing system according to a Poisson process with a mean arrival rate of 2 customers per minute.

2 3 (30 pts) Customers arrive at a queueing

2 3 (30 pts) Customers arrive at a queueing system according to a Poisson process with a mean arrival rate of 2 customers per minute. The service time has an exponential distribution with a mean of 1 minute. An unlimited number of servers are available as needed so customers never wait for service to begin. (a) Construct the rate diagram for this queueing system. (b) Write down the first three balance equations for the birth-and-death process. (c) Find the expected waiting time of a customer in the queue Wq. (d) Find the expected waiting time of a customer in the system W. (e) Find the expected number of customers L in the system

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