Production and Operations Management Consulting.
Asynchronous flow line: Two stations with a finite buffer
An asynchronous flow line comprising two processing stations and a buffer. Processing times follow exponential distributions with means 1/my1 and 1/my2. Interarrival times at station 1 are exponential-distributed with mean 1/lam. Alternatively, it may be assumed, that station 1 is never starved (infinite arrival rate). The buffer size is limited (sizes between 0 and 2 are possible). Station 2 is never blocked. Production blocking (blocking-after-service) is assumed. Workpieces finding station 1 busy (or blocked) are rejected.
The flow line is modelled as a continuous time markov chain.
The state of the system is described with the tupel (x,y), where x=state of station 1 and y=state of station 2.
Possible states of station 1:
|2||busy and one workpiece in buffer|
|3||busy and twoworkpieces in buffer|
After the balance equations have been built up, the system is solved. The probabilities of the states are analysed to find the throughput of the system and the mean work-in-process.
|lam||arrival rate at station 1|
|my1||processing rate (1/mean processing time) at station 1|
|my2||processing rate (1/mean processing time) at station 2|
|L||work-in-process at a station|
|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|
(1993), p. 55-56
- Viswanadham/Narahari (1992), p. 423-425