During tax season the IRS hires seasonal workers to help answer the questions of taxpayers who call a special toll-free number for information. Suppose that calls to this line occur at an average rate of 60 calls per hour and follow a Poisson distribution. An IRS worker can handle an average of 5 calls per hour with service times, exponentially distributes. Assume that there are 10 IRS workers and when they are all busy, the phone system can keep 5 additional callers on hold. IRS TOLL-FREE
QUEUE 1 : M / M / C / K
Q U E U E S T A T I S T I C S (time units = hrs)
Number of identical servers . . . . . . . . . 10
Mean arrival rate . . . . . . . . . . . . . . 60.0000
Mean service rate per server . . . . . . . . 5.0000
Waiting room capacity . . . . . . . . . . . . 5
Mean server utilization (%) . . . . . . . . . 95.6087
Expected number of customers in queue . . . . 2.4506
Expected number of customers in system . . . 12.0114
Probability that a customer must wait . . . . 0.8111
Probability of service denial . . . . . . . . 0.2033
IRS TOLL-FREE
QUEUE 1 : M / M / C / K
PROBABILITY DISTRIBUTION OF NUMBER IN SYSTEM
Number Prob 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
+
UNDER 0.0059|+ |
5 0.0099|+ |
6 0.0199|*- |
7 0.0340|**- |
8 0.0511|***--- |
9 0.0681|***+ |
10 0.0817|+ |
11 0.0980| |
12 0.1176| |
13 0.1412|+ |
14 0.1694|+ |
15 0.2032|+|
+
Using the computer output above respond to the following questions:
1. What percentage of the time is an IRS worker busy?
2. What percentage of callers gets a busy signal when they place their calls?
3. What is the average number of callers waiting for a turn to talk to the IRS workers?
4. What is the probability that a customer must wait?
5. What is the probability that a customer gets immediate attention and does not have to wait?
6. The arrival rate of calls is 60 calls per hour. If the office is open 8 hours a day, what is the expected number of customers denied service per day?

7. The average revenue per customer is $120. Estimate lost revenue per day due to service denial.