Heterogeneous sources model for DSL access multiplexers

We study a Digital Subscriber Line Access Multiplexer (DSLAM) that multiplexes streaming Packetized Telephony (PT) and/or Video-on-Demand (VoD) traffic. To this end, the distribution of the amount of work in a discrete-time single-server queueing model with heterogeneous sources and general packet lengths is calculated. Obtaining actual data concerning the distribution of this quantity is notoriously hard. We outline how the tail distribution can be extracted from the steady-state probability generating function (pgf) through a multiple-pole series expansion. Introduction: We study the behavior of a DSLAM [1] supporting a large number of subscribers with streaming audio and/or video applications, where different PT and VoD devices can have different codec bit rates. To this end, we first analyze a discrete-time queueing model where (each application of) each subscriber is modeled as a traffic source that generates packets with generally distibuted lengths and according to a 2-state discrete-time Markov modulated Bernoulli process (MMBP) [2]. The analysis of such a system often is a difficult task, due to the fact that the sources are heterogeneous (PT and VoD sources with different codec rates for instance generate packets at a different rate and/or of different length), and because of the