The table below gives data on accepted and rejected gaps of vehicles on the minor road of an unsignalized intersection. If the arrival of major road vehicles can be described by the Poisson distribution, and the peak hour volume is 1100 veh/hr, determine the expected number of accepted gaps that will be available for minor road vehicles during the peak hour.
What will be an ideal response?
First, determine critical gap, tc, using the algebraic method. Determine the change
in number of accepted and rejected gaps for the gap lengths given, shown in the
following table.
The critical gap occurs in the range exhibiting the smallest difference
between change in number of gap accepted and change in number of gaps
rejected; in this case, this is between 2.5 and 3.5 seconds.
Using Equation 6.56, determine the value of the critical gap.
tc = t1 + [?t(r – m)] / [(n – p) + (r – m)]
tc= 2.5 + 1(52 – 18) / [(35 – 30) + (52 – 18)]
tc= 3.37 s
Then, using Equation 6.61, determine the expected number of available gaps
during the peak hour.
V= 1100 veh.
T = 3600 sec.
? = 1100/3600 = 0.306
Freq (h ? t) = (V – 1)(e–?t) = (1,100 – 1)(e–(0.306(3.37))) = 392 gaps
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