The data below shows results for two different queuing systems,
Queue 1 and Queue 2. The times and rates use hours for the time
dimensions.
Quantity

Queue 1

Queue 2

Arrival Rate

5

5

Service Rate

3

3

Type

M/M/2

M/M/2/5

Mean Time in System

1.901

0.511

Mean Time in Queue

0.758

0.178

Mean Time in Service

0.333

0.333

Throughput Rate

5

4.424

P(0)

0.901

0.143

P(1)

0.152

0.239

P(2)

0.126

0.199

P(3)

0.105

0.166

P(4)

0.088

0.138

P(5)

0.073

0.115

a. What is the probability that a customer must wait in the
queue for each of the two systems?
b. What is the probability that an arriving customer will balk
for each system?
c. What is the expected number of customers in each system?
d. Comment on the general reasons for the differences or similarities
observed in the answers above.
