Analyzing a degenerate buffer with general inter-arrival and service times in discrete time

We present the queueing analysis of a degenerate buffer having access to a single server. This system cannot realize any given delay, but only values that are an integer multiple of a basic unit called the granularity. This leads typically to longer sojourn times, and higher loss probability. We apply a probability generating function approach to analyze a model with independent and identically distributed inter-arrival times and burst sizes, that allows to capture correlation in the arrival process. For infinite buffer sizes we derive an expression for the maximum tolerable arrival intensity. Further, we present a heuristic for the loss rate in a finite buffer. We assess the accuracy thereof by means of a numerical comparison, and find it to be very reliable.

• Type: Journal
• Year: 2007
• Where: QUESTA
• Authors: Wouter Rogiest, Koenraad Laevens, Joris Walraevens, Herwig Bruneel
• Keywords: Degenerate Buffer, Longer Sojourn Times, Probability Generating Function, QUESTA 2007