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

This probability distribution corresponds to completely random arriv-
als. The mean of the distribution is '4* and is identified with the
':k discussed above. In queuing theory Equation (4.25) is called an
arrival distribution and is an important input to a model capable of
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predicting waiting time.
Suppose a lock exists through which all tows must pass in order
to complete a trip. The number of tows that are handled by the lock
in a given period of time is called the service rate of the lock. .
Several operations are included in the "service" of a tow through a
lock: (1) preparation of the lock, (2) rearrangement of the tow for
locking, (3) entrance of tow, (4) locking, (5) rearrangement of tows
for departure, and (6) departure of tow. Since . each of these opera-
tions is likely to be stochastic in its duration, it is plausible to .
treat the service rate of the lock as a, random variable. Specifically,
it is assumed that the service rate has a Poisson distribution whose
mean, the average service rate, is denoted by p. Such a distribution'
implies that the probability of prolongation of service is independent
of how long ago the service began. Many service operations exhibit
a Poisson distribution, e.g., telephone conversations, grocery check-
out facilities, various repair operations, etc. 21 In addition, use
of a Poisson service rate coupled with a Poisson arrival rate permits
the resulting queuing model to be relatively simple. Furthermore, it
will be possible to judge the quality of the'resulting model to see
if undue error is caused by these assumptions.
It seems -likely that p, the average service rate, can be closely
approximated for a proposed lock by experience with locks already in ,
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