I would like to make a phone call at the average arrival rate of λ = 300 [call / minute] per minute in the Poisson distribution of the telephone exchange and save it on the list.

I don't know even if I look at the site. Give me advice. Thank you.


1 Answer 1


As simple calculation, you can do something like this to simulate a sequence of calls. The list returned gives the times of calls.

With[{callRate = 300, nCalls = 10}, 
  Accumulate @ RandomVariate[PoissonDistribution[callRate], nCalls]]

{318, 634, 920, 1222, 1517, 1801, 2097, 2428, 2717, 3021}

Note: I only use SeedRandom[1] to get reproducible results, so that others can check my work.

However, you are likely to want to make many such lists, so I recommend converting the calculation to a function. Like so:

    callRate_?NumberQ /; callRate > 0/callRate,
    nCalls_Integer /; nCalls > 0] := 
  Accumulate @ RandomVariate[PoissonDistribution[callRate], nCalls]


eedRandom[1]; calls[300, 10]


{318, 634, 920, 1222, 1517, 1801, 2097, 2428, 2717, 3021}

  • $\begingroup$ thank you very much for advice! $\endgroup$ Feb 14, 2019 at 7:41

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