The Erlang model with non-poisson call arrivals

The Erlang formula is known to be insensitive to the holding time distribution beyond the mean. While calls are generally assumed to arrive as a Poisson process, we prove that it is in fact sufficient that users generate sessions according to a Poisson process, each session being composed of a random, finite number of calls and idle periods. A key role is played by the retrial behavior in case of call blocking. We illustrate the results by a number of examples. Categories and Subject Descriptors G.3 [Probability and statistics]: Queueing theory General Terms Performance Keywords Erlang formula, loss networks, insensitivity

• Type: Conference
• Year: 2006
• Where: SIGMETRICS
• Authors: Thomas Bonald
• Keywords: Erlang Formula, Holding Time Distribution, Poisson Process, SIGMETRICS 2006