Environmental Engineering Reference
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lengths can be used here as well:
( 1
u j )( 1
+
v k + 1 )u j < 0
(nonurgent tote)
s j
=
0 (urgent tote)
where v k + 1 is the aggregated urgency value for the next decision point along the
route, which is requested in a communication act (FIPA request-ref ) to the divert
agent. The formula secures that urgent totes will group along the shortest route
(as v k + 1 is close to 1), whereas nonurgent totes are punished along the detour.
If there are no queues on the routes the v k + 1 is 0, and the scale factor has no
effect.
The mergers in the middle lane simply give higher priority to input lanes with
more urgent totes. The ratio between the aggregated urgency factors of the input
lanes becomes the ratio for merging totes from the input lanes.
( 1
u j )( 1
v k + 1 )u j
11.6.3 Saturation Management
Another important strategy is trying to avoid queues by minimizing the load on
the system in critical areas. Consider slow-starting queues of cars at an intersec-
tion when the light turns green. Acceleration ramps and reaction times relative to
drivers ahead accumulate to long delays in traffic queues, even though, in theory,
all drivers should be able to accelerate synchronously (no reaction time).
The same problem arises in the BHS, where reaction times correspond to the
delay of the element head reporting clear. 4 These matters result in the char-
acteristics of the work in progress against capacity curve (WIPAC), which is
further described in Kragh (1990), who states that the capacity of a system goes
down dramatically if the load on the system exceeds a certain threshold value,
as indicated in the Figure 3.22.
Saturationmanagement
Normalcontrol
Work in-Progress/Load on System
Figure 3.22
Theoretical WIPAC
4 In the mechanical setup of the BHS, a tote can only be forwarded from one conveyor element to
the next element if that element is clear. A synchronized row of totes can then pass at full speed,
from one element to another. In queue situations, acceleration ramps delays each element.
 
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