i, i + 1], without any impact on the behaviour of the GKCS.
The steady state performance measures of particular interest in a GKCS are the following: the average work in process and the average number of finished parts for each stage, the proportion of back-ordered demands, the average number of back-ordered demands and the average waiting time of a back-ordered demand.
The queueing network of a GKCS can be viewed as a multi-class closed queueing network by considering each type of kanbans as one class of customers.
Example 1 is a single-stage GKCS and Example 2 is a 3-stage GKCS.
We will give more information about the production capacity of the considered single-stage GKCS in the next section.
Consider a GKCS composed of three identical stages in tandem.
Consider now the case of the non-saturated GKCS with back-ordered demands.
In this section, we presented an analytical method for evaluating the performance of a GKCS.
In this section we consider a GKCS consisting of only one stage.
Therefore, a saturated single-stage GKCS can be modelled as a closed queueing network consisting of the m stations of the manufacturing process and having a population of K customers.
The production capacity of a single-stage GKCS is a function of the number of kanbans K, but is independent of the target inventory level S.
In the case of exponential distributions, the queueing network modelling the saturated single-stage GKCS has a product form solution.