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Calculate the delay time from the arrival rate

Posted on 2014-03-06
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Last Modified: 2014-03-07
Hi

I have a queuing system. The arrival data comes in Poisson distribution with Lambda = 2.22 and the service has the Exponential distribution with Lambda = 2.38. The question is how can I calculate the time of delay in the queue before the server.
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Question by:amq10
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5 Comments
 
LVL 12

Expert Comment

by:tel2
ID: 39911162
Hi amq10,

Is this for homework, or what is this for?

Thanks.
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LVL 84

Assisted Solution

by:ozo
ozo earned 1000 total points
ID: 39911178
Wait times will approach infinity when the average service time is greater than the average arrival interval.
http://en.wikipedia.org/wiki/Kingman%27s_formula
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Author Comment

by:amq10
ID: 39912476
Hi Tel2,

It is not a homework. This is a part of my simulation model. I have done a first model with real data, but I face problem to calculate the delay when I changed the model.

The numbers that I gave in the question is an example to make it clear.

Thanks
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LVL 37

Accepted Solution

by:
TommySzalapski earned 1000 total points
ID: 39912548
ozo posted a link to Kingman's formula which will give you the average delay.
All you need to do is plug in your means and standard deviations.
Poisson
mean = lambda, stddev = sqrt(lambda)

Exponential
mean = 1/lambda, stddev = 1/lambda (yes, they are the same).
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Author Comment

by:amq10
ID: 39913145
Hi Tommy,
Many thanks for your explanation. indeed, it is useful and I did my calculation


Thank you
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