Queueing theory and the M/M/1/∞/∞ model are discussed. An example queue has arrivals of 10, 25, 5, 15, 20 customers separated by service times of 35, 20, 60, 15, 134 units. The queue length over time is plotted, reaching a maximum of 5 customers. Waiting times between arrivals are given as random variables with values for 5 arrivals totaling 20 time units. The average queue length is calculated as the total time customers spend waiting divided by the time period.

1. simulation
Teacher: behravan
behravan
1

2. (Queueing theory)
behravan
2

3. A/B/c/N/K
A
B
G
D
M
B A
c
N
K
M/M/1/∞/ ∞
behravan
3

4. -
A1=10, A2=25, A3=5, A4=15, A5=20
S1=35, S2=20,S3=60,S4=15,S5=134
L(t)
t
L(t)
1
S1=35
10
S1=15
45
behravan
55
70
75
t
4

5. T=75
L(t)
t
L(t)
T3
T2
T1
T1
T0
T2
T1
T1
T0
behravan
t
5

6. T0=3,T1=12,T2=4,T3=1
behravan
6

7. T
W1,W2,…,WN
[0,T]
[0,T]
N
N=5,W1=2,W2=5,W3=5,W4=7,W5=4
w
behravan
7

8. L=λw
N=5
behravan
T=20
8

9. behravan
9