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Flow lines with unlimited buffers: GI/GI/1-systems
An asynchronous flow line with unlimited buffer capacities and general processing
times is modelled as a series of single-stage GI/GI/1 queueing systems. The
performance criteria (flow time, queue length) are sequentially computed, starting
with the first station.
Symbols:
| m |
index of stations
|
| CV2a(1)
|
squared coefficient of variation of the interarrival time
at station 1 |
| b(m) |
mean processing time at station m |
| CV2b(m) |
squared coefficient of variation of the processing time at station m |
| CV2(a) |
squared coefficient of variation of the interarrival time at station
m |
| CV2(d) |
squared coefficient of variation of the interdeparture time at station
m |
| L(m) |
mean number of workpieces (customers) at station m |
| L |
mean number of workpieces in the flow line |
| W(m) |
mean flow time at station m |
| W |
mean flow time through the system |
| E{x} |
expected value of xx (for x = L(m), L, W(m), W) |
Assumptions:
- general distributed interarrival times at station 1
- general distributed processing times at all stations
- single-server stations
- unlimited buffers
- the mean arrival rat at station 1 must be lower than the smallest
processing rate of any station
Literatur:
- Buzacott/Shanthikumar (1993), Paragraph 5.4.2
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