The data below shows results for two different queueing 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.
|
