MANU1420 Inter-Arrival Time Distribution Assignment Sample

Manufacturing Systems Modelling Project 

Abstract on Inter-Arrival Time Distribution

The present paper discusses aspects about a store where customers enter at an interval dt that follows up an EXP ( 45 ) distribution and they have a speed following an UNIF ( 0.2 , 0.5 ) distribution.

Methodology & Content

1. Finding the number of customers that enter the store

From 7am to 5pm there are 10 hours = 600 minutes .

As E [ EXP ( 45 ) ] = 45 and VAR ( EXP ( 45 ) ) = 45 => the medium time of entering the store = 45 .

So , 600 / 45 = 13 is the number of visitors entering the store .

2. Finding the medium – average time of entering the store

Following up with the EXP ( 45 ) distribution => the medium time is equal to 45 , as in the above comments is stated .

3. There are 7 routes with probabilities or risks to enter the store by these customers.

- p = CDF ( x2 ) – CDF ( x1 ) = ( x2-x1 ) *PDF ( a ) => p = dx * PDF ( a ) => p = PDF ( EXP ( 45 ) ) * 45 = 45 2

- x2 - x1 = IQR = inter quantile range .

Risk or probability. Definition

where f : R => R is the probability distribution having positive values and integrable on the real axis to 1 and p,Q are the probability and associated quantile.

Conclusion on Inter-Arrival Time Distribution

To sum up, there are 13 visitors or customers in medium that enter into the store at every 45 minutes interval in medium and the risks for taking a route is following up the distribution from the point 3 in Methodology & Content.

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