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Summary of commands and operations for determining simulation times

Posted on July 28, 2021 by Abigail Stason

ARRIVE {TIME = CUNIFORM(15.6, 19.9)};
Time = low value + randomnumber*(highnumber – lownumber)
For ARRIVE{TIME = CUNIFORM(15.6,19.9)}; with a random number = 0.234:
Interarrival time = 15.6 + (19.9 – 15.6)*0.234 = 16.6062 seconds (or whatever time units are being used.)

ARRIVE{TIME = 0 MAX NORMAL(15.6, 2.34)};
Time = mean + Zrand*sigma
For ARRIVE{TIME = 0 MAX NORMAL(15.6, 2.34)}; with random number = 0.281:
Interarrival time = MEAN + Ztable value for the random number * SIGMA
Get Z0.281 = -0.58, so the Interarrival Time = 15.6 – 0.58*2.34 = 14.2428 seconds
If the random number was greater than 0.5, then the Z table value will be positive, telling you that you must go to the right of the mean.

ARRIVE { TIME = EXPD(0.2) };
Time = interarrival time = -Ln(1 – Random Number)/Lambda
Lambda = 5 trucks per minute (measured in field as total trucks/total time)
For ARRIVE{TIME = EXPD(0.2)}; (i.e. lambda = 5 cars/minute), with a random number = 0.393469:
Interarrival time = -Ln(1-0.393469)/5 = 0.10000 seconds

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