Telephone calls arrive at a department store catalog ordering center with two operators. If both operators are busy, the calls are automatically put on hold and queued on a first-come first-served basis to be serviced by the next available operator. However, there is a limit to the queue space. A maximum of 5 calls can be put on hold and queued. The time spent by each operator in taking the order is exponentially distributed with a mean service time of 6 minutes. The calls have exponentially distributed interarrival times and occur at a mean rate of 15 per hour. The first four questions below are for hand calculation with the rate diagram.

1) Construct the rate diagram for this system;

2) What is the expected number of calls on hold waiting for service?

3) How much time should an arriving call expect to spend in the system (waiting for and receiving service)?

4) What fraction of time are both operators busy?

Suppose the queue space is infinite. Construct an ARENA model for the problem and then use the process analyzer to determine the maximum mean arrival rate the two servers can handle (i.e. the queue will not continue to grow over time). Keep the mean arrival rate as an integer. Show the screenshot of the result from the process analyzer. (Hint: You may want to use VARIABLE to specify the interarrival time in CREATE).