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The calculations in a location-discrete model can be reduced considerably by prolonging the segments because this will reduce the number of events. But this abstraction will also make the representation less accurate. The representation accuracy of location-discrete models of steady conveyors for piece goods therefore has to be evaluated in a direct comparison with the event-discrete simluation in order to verify its suitability for practical use.This study is based on the model of the irreducible transport hubs [Gro schallau84] (fig. 1) which differentiates between the three elements track, switch and junction in order to simulate the conveyor elements.
Fig. 1: Variables at a junction and effect of the strategy on the flow rate
Owing to the location-discrete modelling the time set-off for the given conveying speed is only small at tracks and switches compared to continuous event-discretely modelled conveying processes. At junctions, however, the predetermined handling strategies may lead to a variation of lead and waiting times for piece goods (transport objects) before the elements. This can have a decisive influence on the distribution of these time shares within a more complexe model consisting of many hubs. The central aspect of this study therefore is the junction element.
The model consists of a junction with two input tracks where goods sequences with randomly distributed intermediate arrival times are dispatched and which are handled by the junction element according to the strategy. For each transport object the time when it enters and leaves the model and thus the lead and waiting times can be determined individually (fig. 2).
Fig. 2: Comparison of a continuous and a location-discrete model
The simulated container conveyor system holds containers of equal length. For the location- discrete model the segment length is set to the length of one container.
The input sequences at the paths E1 and E2 are set as continuous, randomly distributed inputtimes with an average intermediate arrival time λm between two objects. For the location-discrete model the input times have been converted into integral values on the time basis T. Each of the generated input sequences is simulated according to four strategies (fig. 1) for both cases. The result are the total lead time TLT as well as the sum of the path-related waiting times WT1 and WT2.
Results
The x-coordinate in figure 3 shows the accumulated distribution of the relative deviations between the location-discrete and the continuous simulation of these three variables. In the location-discrete simulation the chance that two containers arrive at the junction simultaneously sinks in line with a sinking intermediate arrival time. Stochastic and batch-wise handling can only be carried out at random. For this reason the output sequences of both simulations may differ by pairs. The bit error rate as indicator for containers which have been confused at the junction by pairs indicates the frequency of these confusions during a predetermined input sequence.
Fig. 3: Relative deviations and bit errors of TLT and WT in the location-discrete simulation (kum.)