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Asynchronous flow line: three stations with finite buffers
We consider a three-stage flow line with
finite buffer storage space. The servive times at each station are exponentially
distributed with means 1/my1, 1/my2 and 1/my3, respectively. Station 1 is never
starved. The buffer size of station 2 and three is finite (maximum size is 5).
The system is modelled as a continuous-time markov chain. First the steady-state
balance equations are build up, as described in Buzacott/Shathikumar (1993),
Chapter 5.4. Then the system is solved.
The system state is described with the tupel (x,y), where
| x |
number of workpieces that have finished processing
at station 1 but have not left station 2 (in process at station 2, waiting
in the buffer in front of station 2 or waiting on the machining table of
the blocked station 1) |
| y |
number of workpieces that have finished processing
at station 2 but have not left station 3 (in process at station 3, waiting
in the buffer in front of station 3 or waiting on the machining table of
the blocked station 2) |
Symbole:
| my1 |
mean processing rate (1/mean processing time) at
station 1 |
| my2 |
mean processing rate (1/mean processing time) at
station 2 |
| my3 |
mean processing rate (1/mean processing time) at
station 3 |
| u(i,j) |
transition rate between states i and j |
| X |
throughput of the system |
| RS |
right-hand side of the system of balance equations |
Literature:
- Buzacott/Shanthikumar (1993), Chapter 5.4
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