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3 Create Entities Using Intergeneration Times

3-6

f x

( ) =

< <

Maximum Minimum

Minimum Maximum

0 Otherwise

The exponential distribution with mean 1/λ has probability density function

f x

x x

l l

( )

exp

( )

≥

The probability density function does not predict the actual intergeneration time between

a particular entity and the next entity. By integrating the probability density function

for the distribution you select, you can determine the probability that the block generates

the next entity in a range of durations after the previous entity.

Interpreting Probability Density Function

Suppose you set Distribution to Exponential and set Mean to 0.5. A mean of 0.5 in

the exponential distribution corresponds to

= =

0 5

During the simulation, suppose the block has just generated an entity. The probability

that the block generates the next entity during the next 0.3 seconds is the probability

that the intergeneration time is in the range from 0 to 0.3. You can compute this

probability by integrating the probability density function over that range:

f x dx

x dx

[ . ]

( )

exp( )

0 0 3

2 2

0 3

£ £

= -

intergeneration time

ÚÚ

= - -

= - - +

exp( )

exp( . )

0 6 1

0 45

0 3

1 2 ... 67 68 69 70 71 72 73 74 75 76 77 ... 113 114

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