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Calculate the delay time from the arrival rate

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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amq10
Asked:
amq10
2 Solutions
 
tel2Commented:
Hi amq10,

Is this for homework, or what is this for?

Thanks.
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ozoCommented:
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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amq10Author Commented:
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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TommySzalapskiCommented:
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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amq10Author Commented:
Hi Tommy,
Many thanks for your explanation. indeed, it is useful and I did my calculation


Thank you
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