July 17, 2024

The Fields Institute
Industrial Mathematics Seminar Series

Thursday, February 11, 1999
5:00 - 7:30 p.m.
Room 230, The Fields Institute


5:00 - 6:00 p.m.
"Virtual Networks and Programmable Network Nodes"
Alberto Leon-Garcia, Department of Electrial and Computer Engineering, University of Toronto

6:30 - 7:30 p.m.
"Cell Loss Probablities Using the Oldest-Cell-First Discipline
David R. McDonald, Department of Mathematics and Statistics, University of Ottawa


"Virtual Networks and Programmable Network Nodes"
Alberto Leon-Garcia, Department of Electrical and Computer Engineering, University of Toronto

Future packet-switching networks are expected to be versatile in the provisioning of multi-service, multi-domain, and multi-discipline environments. The concept of multi-service or integrated services networking has already been proposed in ATM and Integrated Services Internet. The concept of multi-domain or multiple administrative domain has also been implemented, in a limited sense, as in Virtual Private Network or Virtual Local Area Network. The demands for multiple disciplines such as organizational policies and operational functionality in a single network have been increased accordingly to provide a rich environment for customized control of the network. All such requirements for future networks impose additional challenges to the already-difficult problems of network control and management, including for example, packet classification and scheduling, admission and access controls, and bandwidth management.

In this talk we will discuss our ongoing work on the virtual network concept and its use to simplify the tasks of network control and management. Network control and management tasks can be separated into smaller and simpler sets that are organized in a hierarchical manner. Each such set is exercised on a virtual network of a similarly-organized hierarchy of virtual networks. In this manner, virtual networks enable customization of network control and management mechanisms. With proper allocation of network resources, a virtual network can effectively provide the (virtual) environment of a programmable network. We will also give an overview on current work on the development of a programmable network node.

"Cell Less Probabilities Using the Oldest-Cell-First Discipline"
David R. McDonald, Department of Mathematics and Statistics, University of Ottawa

Consider an ATM multiplexer where M input links contend for time slots on one output link which transmits C cells per second. Each input link has its own queue of size B cells. The traffic is delay sensitive so B is small (e.g. B = 20). We assume that each of the M input links carries Constant Bit Rate traffic from large number of independent Virtual Connections which are subject to jitter. The fluctuations of the aggregate traffic arriving at queue i, i = 1,...M, is modeled by a Poisson process. The Quality of Service of one connection is determined in part by the queueing delay across the multiplexer and the Cell Loss Ratio (CLR) or proportion of cells from this connection lost because the buffer is full.

The Oldest-Cell-First (OCF) discipline is a good compromise between competing protocols like round-robin queueing or serving the longest queue. The OCF discipline minimizes the total cell delay among all cells arriving at the contending queues. Moreover, the CLR is similar to that obtained by serving the longest queue. We develop Quality of Service formulae for this protocol that can be calculated on-line for Connection Admission Control. These formulae follow from a simple new expression for the exact asymptotics of a M|D|1 queue.


Alberto Leon-Garcia received the B.S., M.S., and Ph.D. degrees in electrical engineering from the University of Southern California, in 1973, 1974, and 1976 respectively. He is a Full Professor in the Department of Electrical and Computer Engineering of the University of Toronto and he currently holds the Nortel Institute Chair in Network Architecture and Services. In 1999 he became an IEEE member for 'For contributions to multiplexing and switching of integrated services traffic'.

He teaches undergraduate and graduate courses in communication networks, and conducts research in resources management of broadband networks and service end systems, switch and router design, Internet performance, and wireless packet access networks. He is currently leading a team that is developing a programmable network node that can be used for the rapid prototyping of packet network protocols. He is also Director of the Master of Engineering in Telecommunications program.

David McDonald is a Professor at University of Ottawa and has been a Senior Industrial Fellow at Nortel (Bell Northern Research), a Visiting Professor in Industrial and Systems Engineering at Georgia Tech and a consultant with Newbridge Networks. He was educated at the University of Toronto, King's College London and the University of Montreal. His two doctoral students and 5 M.Sc. students have all found work in high technology industries, except for one who is a mathematics professor.

Dr. McDonald's research interests range broadly in Applied Probability. He has 37 papers in print and several more submitted. The basis of today's lecture is the article: Huang, C-C. and McDonald, D. (1998), VCC cell loss probabilities using the oldest-cell-first discipline. He hopes the talk will show an interesting interplay between common sense and some cute mathematical ideas.


The Industrial Mathematics Seminar is offered to any interested participant -- no reservation is necessary.