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

Given the tonnage, 0, to be carried on the waterway and the ton-
_
nage, C, of an optimal or average tow, one can determine the number
of trips required to achieve 0, viz.,
P(t)
X = 0/E, (4.23)
where X is the number of trips per time period. A trip is defined as
any point-to-point movement. While X is the number of trips required
to produce a waterway tonnage of 0, there may not be a one-to-one re-
lationship between X and the number of trips by tows operating on the
waterway because of the possibility of trips involving empty tows.
This consideration may be accounted for by adjusting k by the factor
(1 + p), where p represents the percentage of unproductive trips (i.e.,
with unlcadedbargee) which requires an empty barge backhaul. Let ?.*
be the adjusted trip rate:
where 0 p 1. .
X* = (1 + p)X, (4.24)
It is assumed that the possibility of a tow's being at any given
point on the waterway is independent of the time since the last tow
was there. This implies a Poisson distribution for the arrival of
taws; that is, the probability that n arrivals occur within an inter-
val of time of duration t is given by ' .
-
(X*O ne -\*t
n!
(4.25)
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