A study of teletraffic problems in multicast networks

Abstract

This dissertation studies teletraffic engineering of dynamic multicast connections. The traditional models in teletraffic engineering do not handle multicast connections properly, since in a dynamic multicast tree, users may join and leave the connection freely, and thus the multicast tree evolves in time.

A model called multicast loss system is used to calculate blocking probabilities in a single link and in tree-type networks. In a single link case, the problem is a generalised Engset problem, and a method for calculating call blocking probabilities for users is presented. Application of the reduced load approximation for multicast connections is studied. Blocking probabilities in a cellular system are studied by means of simulation.

The analysis is mainly concentrated on tree type networks, where convolution-truncation algorithms and simulation methods for solving the blocking probabilities exactly are derived. Both single layer and hierarchically coded streams are treated. The presented algorithms reduce significantly the computational complexity of the problem, compared to direct calculation from the system state space. An approximative method is given for background traffic.

The simulation method presented is an application of the Inverse Convolution Monte-Carlo method, and it gives a considerable variance reduction, and thus allows simulation with smaller sample sizes than with traditional simulation methods.

Signalling load for dynamic multicast connections in a node depends on the shape of the tree as well as the location of the node in the tree. This dissertation presents a method for calculating the portion of signalling load that is caused by call establishments and tear-downs.