Phone calls. Say, an office worker gets 8*6 phone calls in an average shift of 8 hours, so one every 10 minutes on average. It doesn't matter how long ago the last call was, since the customers don't coordinate.

This real world example still doesn't perfectly match the theory. For example, if there was no call for a long time, it may indicate that it's some special day or the phone line is malfunctioning or whatever and it could mean that the next call is probably further in the future than the model would say.