Flow lines with unlimited buffers: M/M/1-systems
Consider a flow-line system with M stations and unlimited buffer capacities.
Each station has a single server. The processing times of the jobs are independent
and identically distributed exponential random variables with mean b(m), m=1,2,...,M.
Jobs arrive at station 1 according to a Poisson process with rate lambda.
Under
these assumptions the performance criteria (flow time, queue length) can be
computed exactly through analysis of each station as a single-stage M/M/1 queueing
system.
Symbole:
| m |
index of stations
|
| b(m)
|
mean processing time at station m
|
| Q(m) |
queue length in front of station m |
| U(m)
|
utilization of station m |
|
W(m)
|
flow time at station m (waiting and processing)
|
Literature:
- Buzacott/Shanthikumar
(1993), Paragraph 5.4
|
