MODELLING FLEXIBLE MANUFACTURING SYSTEMS - Modelling with Generalised Stochastic Petri Nets - page 192

Thus, a dead state could be reached when a type a part is in the segment in
front of machine M 1 wishing to enter it, and another part is being processed
by machine M 1 . This is a perfectly legal state according to our specification
of the system. A similar argument applies to the other deadlocks. This
problem can be solved by modifying the part movement control, introducing
a test that prevents a part from entering the transport segment of a machine
from which it requires processing if such machine is busy. This can be easily
implemented in our model by adding a test arc from the “machine-free”
place to the proper “enter segment” transition for machines M 1 and M 3 as
shown in Fig. 8.13. For machine M 2 , since every part entering its associated
transport segment needs its processing, it is enough not to give back the
“segment free” token when a part enters the machine.
Observe that we could have discovered this problem by means of reachability
analysis for any N ≥ 2; however, deadlock analysis helps in concentrating
on the subnet that causes the problem, moreover it allows to prove that a
dead state can be indeed reached working at a parametric level, i.e., without
instantiating a specific initial marking.

8.3.2 Performance analysis of the system with AGV trans-

port

In this section we present the performance analysis results for the FMS with
AGV transport.
We first study the throughput of the system as a function of the total num-
ber of parts circulating in it. To alleviate the state space growth problem,
we show how the model can be transformed obtaining two new models with
smaller state spaces, providing an upper and a lower bound on the through-
put, respectively. The analysis is performed forcing the model to match the
desired production mix: this is done by probabilistically choosing the type
of a part at the instant of its arrival. A second study is then performed
to determine how many pallets of each type are necessary to obtain the
required production mix.
The model used to compute the system throughput with forced production
mix is depicted in Fig. 8.14. Observe that this model has been obtained
from the model in Fig. 8.12 by merging the subnets representing the flow
of type a and type b parts into and out of the LU station to represent the
probabilistic choice of the type of a raw part entering the system.
The throughput of the system corresponds to the throughput of transition
mv 23−LU ; it can be computed from the steady-state probability of the mark-
ings, multiplying the firing rate of mv 23−LU by the probability of having at
least one token in place mv 23−LU .
Table 8.5 contains the complete specification of each transition rate/weight,
priority and ECS: five ECSs can be identified within this system. Three
of them can be considered “degenerate” ECSs as they comprise only one