Handout #3
|
Date: |
|
Queuing
Systems
Given a queuing system with one server.�
The queue can either be
empty or not empty.
The server can either be
busy or idle.
Upon
arrival:
|
|
|
Queue Status |
|
|
|
|
Not Empty |
Empty |
|
Server Status |
Busy |
Enter Queue |
Enter Queue |
|
Idle |
Impossible |
Enter Service |
|
Upon
service completion there are only two possibilities.� Either the server is busy and the queue is
not empty, or the server is idle and the queue is empty.
|
|
|
Queue Status |
|
|
|
|
Not Empty |
Empty |
|
Server Outcomes |
Busy |
Possible |
Impossible |
|
Idle |
Impossible |
Possible |
|
Interarrival and Clock Times
|
Customer |
Interarrival Time |
Arrival Time on Clock |
|
1 |
-- |
0 |
|
2 |
2 |
2 |
|
3 |
4 |
6 |
|
4 |
1 |
7 |
|
5 |
2 |
9 |
|
6 |
6 |
15 |
Service Times
|
Customer |
Service Time |
|
1 |
2 |
|
2 |
1 |
|
3 |
3 |
|
4 |
2 |
|
5 |
1 |
|
6 |
4 |
Simulation
Table Emphasizing Clock Times
|
Customer |
Arrival
Time (Clock) |
Time
Service Begins (Clock) |
Service
Time (Duration) |
Time
Service Ends (Clock) |
|
1 |
0 |
0 |
|
|
|
2 |
|
|
|
|
|
3 |
|
|
|
|
|
4 |
|
|
|
|
|
5 |
|
|
|
|
|
6 |
|
|
|
|