MODELLING FLEXIBLE MANUFACTURING SYSTEMS - Modelling with Generalised Stochastic Petri Nets - page 180

Table 8.1: Input and output inventory in the cells of a Kanban system as a
function of the number of cards

Input buffer inventory Output buffer inventory

Cell 1 Card 2 Cards 3 Cards 1 Card 2 Cards 3 Cards

1 0.486 1.041 1.474 0.514 0.958 1.526

2 0.486 1.040 1.470 0.383 0.713 1.131

3 0.486 1.047 1.478 0.282 0.524 0.811

4 0.486 1.056 1.490 0.170 0.316 0.472

5 0.486 1.073 1.515 0.000 0.000 0.000

compute the average inventory of the input and output buffers of each cell
(average number of tokens in places IB i and OB i respectively). The results
are summarized in Table 8.1. Observe that while the input inventory is
fairly constant, the output inventory decreases as the cell position increases.

In a second set of experiments the system throughput was computed as a
function of the number of cards in the two cases of a fault free and a failure
prone system. The fault tolerance was studied on two models: the former
model represents a system in which all cells can fail, the latter represents a
system in which only one out of five cells can fail.
The GSPN model in Fig. 8.4 represents a failure prone cell. The only differ-
ence with respect to the model in Fig. 8.2 is the presence of the extra subnet
composed of two places OK i and FAILED i representing respectively the
condition “cell i is working” and “cell i is out of order”, and two transitions
failure i and repair i representing the occurrence of a failure and the com-
pletion of a repair, respectively. The inhibitor arc from place FAILED i to
transition inM i has the effect of interrupting the service upon the occurrence
of a failure.
The performance of the system is characterized by its throughput, which
can be computed as the throughput of transition exitCell 5 . In Fig. 8.5 the
performance of the system without failure is compared to that computed
when all cells can fail (the cells fail independently; the failure rate of each
cell is 0.02, while the repair rate is 0.4).
The results of Table 8.1 show that even in a perfectly balanced Kanban
system the cell performance is position-dependent. Hence, the influence of a
single failure on the system performance depends on the failed cell position.
This phenomenon was studied by comparing the throughput of a system in
which only the middle cell can fail, against that of a system in which only
the final cell can fail. The results are plotted in Fig. 8.6: observe that
a failure in the last cell has a less severe impact on the throughput, with