7.3 Poisson demands with timedependent rate, revisited We have already
seen a procedure for simulating the generation of demands in an urban
service system according to a Poisson process with timedependent mean
rate (t)
That procedure
(Section 7.1.4) required two "passes" over the interval [0, 71: once to
determine the number of demands during [0, T] and a second time to
generate the time instants when these demands occur. In this problem you
will be asked to develop an alternative procedure which requires only a
single pass.
Refer once more to Figure 7.12. Define a function '(t)
such that
where _{0} is the maximum value of (t) in [0, T]. Suppose now that we used t_{i} = (n r_{i})/ _{0} to generate sample values of successive demand interarrival times, beginning at t = 0. This, of course, would lead to too many demands being generated in [0, T]. (The expected number of demands would be equal to _{0} · T.) How would you modify the foregoing procedure (by accepting or rejecting some demands) using (t) and '(t) to make it work correctly?
