Unrealistic to use poission when modeling calls to switchboard?

[shrek]

Isn't is unrealistic to use a poission distribution when modeling calls to a switchboard within, say, an 1 hour time interval?

One of the assumptions of the poisson model is that the process must be stationary. The probability of an occurrence must be the same over the entire time period.

This assumption is clearly violated in many situations. For example, a 24 hour customer service switchboard serving a particular time zone will clearly have more calls between 7-8pm, when most people are home from work, than say 4-5am, when most people are sleeping.

Agree?

[TheEcologist]

Isn't is unrealistic to use a poission distribution when modeling calls to a switchboard within, say, an 1 hour time interval?

One of the assumptions of the poisson model is that the process must be stationary. The probability of an occurrence must be the same over the entire time period.

This assumption is clearly violated in many situations. For example, a 24 hour customer service switchboard serving a particular time zone will clearly have more calls between 7-8pm, when most people are home from work, than say 4-5am, when most people are sleeping.

Agree?

I’m sure I’ve seen this problem before, which textbook do you guys use?

If you only use a single univariate model, I would say you are correct.

Maybe a bivariate model including time, or a series of poisson model for each respective period would be better.

[shrek]

It's not from any particular textbook. It's a common example cited in textbooks and online if you search for "poisson" and "switchboard."

Are statisticians simply using poisson to approximate the number of calls, while fully aware that an assumption of the poisson process is being violated? Or am I not understanding something?