Question

# When people call 9-1-1, the chance of not finding an available operator must be very, very

low, even though

the time that an operator spends on a call may be very, very long. The 9-1-1

office classifies calls as being of two types: informational (average time to answer of 1 minute) and

emergency (average time to answer of 15 minutes). About 20% of all calls are emergency. During

peak times calls arrive at a rate of 30 per hour.

The 9-1-1 office wants to employ enough operators so that no hold queue is necessary; in

fact, if all operators are busy then the call will automatically be transferred to a police station which

is outside the scope of our model.

Your objective is to develop a queueing model for this 9-1-1 office. In using queueing theory, it is

typical to have to simplify a real-world situation, so as to represent it as a single queue. Thus, first,

determine the average operator service rate for the 9-1-1 office system.

1. How many operators are needed to keep the probability that a call is transferred to the police

station under 2%?

2. With this number of operators, how many of them are busy on average?