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Performance evaluation of an FMS (static allocation approach)

A Flexible Manufacturing System (FMS) is modeled as a closed queueing network (CQN). The number N of pallets is so large, that the bottleneck station has a utilization of 100%. Following the determination of the bottleneck station the performance criteria of the other stations are derived. The result can be considered as the asymptotic behavior of the FMS for large numbers of pallets.
The last station (M) is the transportation station (central server). Its relative arrival frequency is always 1.0 (non-editable). Be sure that the relative arrival frequencies of the remaining stations (1 to M-1) sum up to 1.


m index of stations
e index of the bottleneck station
b(m) mean processing time of a typical workpiece at station m
p(m) relative arrival frequency of a workpiece at station m
S(m) number of servers (machines, vehicles, etc.) at station m
X(m) throughput of station m
U(m) utilization of station m


  • unlimited (very large) number of pallets
  • universal pallets


- Tempelmeier/Kuhn (1993), Chapter 3

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