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Features: Faculty Insights


An algorithm developed by Frank Kelly, Professor of the Mathematics of Systems in the Department of Pure Mathematics and Mathematical Statistics, underpins improvements in mobile phone and internet performance worldwide. The practical outcome of his pioneering research can be found in over 1.3 billion iPhones, and is now a standard feature of 5G.

All traffic on the internet (downloads, videos, etc.) is broken down into, and transferred as, packets. These packets contain information about the source and the destination. Transmission Control Protocol (TCP) is the main system of rules for transferring these packets across the internet.

In the late 1990s, Frank Kelly developed a conceptual mathematical framework which elegantly described packet-switched networks, such as the internet. His foundational theory demonstrated that TCP effectively solves a very large-scale resource allocation problem, and that it is both stable and fair.

Kelly’s further mathematical research in the early 2000s helped show the generality and range of applicability of the conceptual framework in an era of rapidly growing communications capacity. It explained why the internet worked as well as it did, providing confidence in its reliability and robustness under rapid growth, and rendering re-design unnecessary. This work has been extremely influential in the networking community, and provided the foundation of future internet research.

Round trips, routing and congestion control

With increased demands on the internet, in 2005 Kelly developed a novel algorithm to route traffic via multiple paths. He constructed a fluid-flow (differential equation) model describing which path (route) should be used, and how much traffic (rate control) should be sent. This novel multipath extension to TCP, the main system of rules for transferring data across the internet, increases reliability and performance without compromising stability.

TCP is an acknowledgement-based system; once a packet arrives safely, an acknowledgement is sent to the sender. The time that elapses between the sending of a packet and receipt of acknowledgment is known as the Round-Trip Time (RTT).  Initially, it appeared to be very hard to stabilise a system sending traffic over multiple paths with RTTs potentially differing by several orders of magnitude.

However, Kelly had two major insights. Firstly, Kelly realised that the local stability of the network can be seen as decentralised, so you only need to know about congestion on the route you are looking at. This makes it simpler, and less demanding, when looking at RTTs of different orders of magnitude.

Secondly, in the conceptual Open Systems Interconnection (OSI) model of the internet, there are seven defined 'layers', each of which is responsible for a different protocol. TCP operates at the transport layer. Kelly’s key contribution was to show that routing choice and congestion control are part of the same problem, and therefore routing allocation should be integrated with flow control at the transport (i.e the same) layer.

Faster data transfer and improved resilience

Subsequently, an international group of computer science researchers, involving a former PhD student of Kelly’s, Damon Wischik, translated Kelly’s pioneering work on routing traffic via multiple paths into a practical implementation: Multipath TCP (MPTCP). Due to Kelly’s key insight that routing and rate control should take place at the same layer, without requiring modification of any of the layers above or below, MPTCP is a direct 'drop-in' replacement for TCP rather than a major re-design of the Internet.

MPTCP has had extensive reach and significant impact. It provides quicker responses, faster data transfer, and improved resilience to traffic surges and link failures than TCP. It therefore greatly improves the user experience of demanding Internet applications such as video streaming and speech recognition - for example, Apple Siri. Siri (like other apps such as Maps and Apple Music) uses MPTCP to switch seamlessly between Wi-Fi and cellular networks, even when users are moving, to significantly improve performance. To date, MPTCP has been deployed in over 1.38 billion Apple iPhones worldwide, representing sales of over $951 billion.

Smartphones are not MPTCP’s only application. MPTCP has also increased internet speed in 6 countries and was recently adopted as a standard feature of 5G developments. In 2015, a spin-off company from the development partners in MPTCP launched an  innovative technology, Hybrid Access Networks. These networks use MPTCP to combine xDSL (wired) and LTE (wireless), providing higher bandwidth - faster Internet - services in rural areas, where xDSL performance is poor. To date, the networks have been introduced in six countries, including the Netherlands and Finland.

In 2020, with increased demand for mobile broadband, the 3GPP 3rd Generation Partnership Project, uniting seven standards organisations from Asia, Europe, and North America, made MPTCP a standard feature for 5G.

Frank Kelly’s research demonstrates the impact of mathematics on the daily lives of millions of people worldwide - maths at our fingertips.

This article introduces one of the examples of the Faculty's high impact research that was submitted as part of the Research Excellence Framework (REF) 2021, a major UK exercise to assess the quality of research at UK universities.