Q2 Z2,(Q2) Z2(Q2) - Institute for Water Resources - U.S. Army

t¼ - ;e carried on thc waterway will bo reflected in the arrival rate
of tows and thereby in the locking time involved. Changes in tow size
will be reflected in the arrival rate also. Finally, changes in lock
sizes will be reflected in the service rate,
Note on Capacity of a Waterway and Optimal Tolls. The model of
locking employed above might be used to determine the capacity of a
waterway and to measure the congestion which ensues from having an
additional tow on the waterway.
As noted above, locking consists of the operations of (1) wait-
ing for permission to approach the lock, (2) approaching the lock and
maneuvering into the chamber, (3) filling or emptying the lock, (4)
multiple locking if necessary, and (5) leaving the lock and maneuver-
ing out into the channel. Operations (1) and (3) will be independent
of the number of barges in the tow, but the other operations will be
directly related to the number of barges. One might show this rela-
tionship, T L (Nb), as in Figure 4.4 where TL is the total service time
(assuming a constant amount of time is spent in queue) and N b is the
number of barges in the tow. Note that there are sharp discontinuities
when double or triple locking is necessary, for part of the tow must
be tied off, the lock must go through one cycle empty, the rest of
the tow must be pulled into or out of the lock from the shore, and
the tow must be reassembled.
One measure of the capacity of a waterway would be the maximum
feasible number of barges that could be locked through in a given
period of time. This idea was explored earlier by Bottoms. 26 Since
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