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?