You never have a fraction of a call. Ideally one call does not "cause" additional calls (but in practice it does, as people go away to think about things and call back again.) These two facts together would tend to suggest Poisson.
However, Poisson requires that the incident probability is constant. That is not the case for call centers, which definitely get busier at various times. The peak times vary with the industry and the time-zone range served by the call center (and with the customer concentration in each of those time zones.) Therefor, you cannot model as Poisson.
What you might be able to do is divide the times up into segments, and model each segment as Poisson with a different probability.
There are other modelling techniques for analyzing cyclic trends; see http://www.mathworks.com/help/ident/time-series-model-identification.html
