In the Erlang model, whats the relationship between the arrival process and the holding times? Are they both exponentials?
Let’s suppose that the arrivals are a Poisson process of rate λ, and that call holding times are Exponential and have mean 1/μ, i.e. have rate μ. That means that the time between two successive arrivals is an Exponential random variable of rate λ, and that the time between a call arriving and departing is Exponential of rate μ. Don’t get the two mixed up. Arrivals are a Poisson process. It doesn’t mean anything to say “arrivals are Exponential” (although it is perfectly proper to say “inter-arrival times are Exponential”). Note also that the number of arrivals that occur in an interval of length T has a Poisson distribution with parameter λT. There are two separate concepts here: a Poisson arrival process, and a Poisson distribution. If you’re as clever as Poisson, I’m sure you’ll get several different things named after you too.
