Frank Kelly is Professor of the Mathematics of Systems in the University of Cambridge. He was elected a Fellow of the Royal Society in 1989, and a Foreign Member of the National Academy of Engineering in 2012. In 2013 he was awarded a CBE for services to mathematical sciences.

His main research interests are in random processes, networks and optimization. He is especially interested in applications to the design and control of networks and to the understanding of self-regulation in large-scale systems.

Frank Kelly has received several prizes for his work. In 1979 he won the Davidson Prize of the University of Cambridge. In 1989 he was awarded the Guy Medal in Silver of the Royal Statistical Society. He was awarded the 1991 Lanchester Prize of the Institute for Operations Research and the Management Sciences, and in 1997 the Naylor Prize of the London Mathematical Society. In 2005 he received the IEEE Koji Kobayashi Computers and Communications Award, in 2008 the John von Neumann Theory Prize of INFORMS, in 2009 the SIGMETRICS Achievement Award and the Gold Medal of the Association of European Operational Research Societies, in 2011 the Beale Medal of the Operational Research Society, in 2013 the INFORMS Saul Gass Expository Writing Award and in 2015 the Alexander Graham Bell Medal of the IEEE and the David Crighton Medal of the LMS and the IMA. He has been awarded Honorary Doctorates by Heriot-Watt University, Eindhoven University of Technology and Imperial College, London.

He served as Director of the Statistical Laboratory in the University of Cambridge from 1991 to 1993. He has served on the Scientific Board of HP's Basic Research Institute in Mathematical Sciences, the Scientific Council of EURANDOM, the Conseil Scientifique of France Telecom, and the Council of the Royal Society. He has chaired the Advisory Board of the Royal Institution/University of Cambridge Mathematics Enrichment Project, and the Management Committee of the Isaac Newton Institute for Mathematical Sciences.

He spent the academic year 2001-2 as a visiting professor at Stanford University. From 2003 to 2006 he served as Chief Scientific Adviser to the United Kingdom's Department for Transport. He was chair of the Council for the Mathematical Sciences from 2010 to 2013, a member of the RAND Europe Council of Advisors from 2008 to 2015, and Master of Christ's College from 2006 to 2016. He is currently chair of the Advisory Committee on Mathematics Education, and a trustee of the Isaac Newton Trust, the Applied Probability Trust, the Glenfield Trust, and the Alan Turing Institute.

Papers

• A Markov model of a limit order book: thresholds, recurrence, and trading strategies 
  Frank Kelly and Elena Yudovina
  Mathematics of Operations Research, to appear.
• Efficient advert assignment 
  Frank Kelly, Peter Key and Neil Walton
  Operations Research 64 (2016) 822-837. 
  An earlier version was presented at the 15th ACM Conference on Economics and Computation, 2014.
• Analytical Research Foundations for the Next-Generation Electric Grid 
  Committee Co-chairs: John Guckenheimer and Thomas Overbye
  National Academies of Sciences, Engineering, and Medicine, 2016.
• Critical behaviour in charging of electric vehicles 
  Rui Carvalho, Lubos Buzna, Richard Gibbens and Frank Kelly
  New J. Phys. 17 (2015) 095001
• Real time alpha-fairness based traffic engineering 
  Bill McCormick, Frank Kelly, Patrice Plante, Paul Gunning and Peter Ashwood-Smith 
  Proceedings of the ACM SIGCOMM 2014 Workshop on Hot Topics in Software Defined Networking, 199-200.
• Stochastic Networks 
  Frank Kelly and Elena Yudovina
  Cambridge University Press, 2014.
• Review of elements of methodology for HS2 business case, 2013.
• Mathematical sciences research - leading the way to UK economic growth,
  Deloitte Report, 2012. Short article: 
  Science in Parliament 70: 1 (2013), 11-12. 
  David Delpy and Frank Kelly 
• Statistical aspects of storage systems modelling in energy networks 
  A.I. Bejan, R.J. Gibbens and F. P. Kelly
  46th Annual Conference on Information Sciences and Systems (CISS), 2012.
• Reversibility and Stochastic Networks, 
  Cambridge University Press, 2011.
• An investigation of proportionally fair ramp metering 
  R.J. Gibbens and F. P. Kelly
  14th International IEEE Conference on Intelligent Transportation Systems, 2011.
• Explicit congestion control: charging, fairness and admission management. 
  Frank Kelly and Gaurav Raina
  In "Next-Generation Internet Architectures and Protocols"
  (Editors Byrav Ramamurthy, George Rouskas and Krishna Sivalingam), Cambridge University Press, 2011. 257-274.
• Heavy traffic on a controlled motorway 
  F. P. Kelly and R.J. Williams
  In "Probability and Mathematical Genetics: Papers in Honour of Sir John Kingman"
  (Editors N.H. Bingham and C.M. Goldie), Cambridge University Press, 2010.
• Resource pooling in congested networks: proportional fairness and product form. 
  F. P. Kelly, L. Massoulié and N. S. Walton 
  Queueing Systems 63 (2009) 165-194.
• State space collapse and diffusion approximation for a network operating under a fair bandwidth sharing policy. 
  W. Kang, F. P. Kelly, N. H. Lee and R. J. Williams.
  Annals of Applied Probability 19 (2009) 1719-1780.
• Hidden wealth: the contribution of science to service sector innovation. 
  (Chair of Working Group: David Rhind) 
  Royal Society, 2009.
• The mathematics of traffic in networks. 
  In "The Princeton Companion to Mathematics" 
  (Editor Timothy Gowers; June Barrow-Green and Imre Leader, associate editors) 
  Princeton University Press, 2008. 862-870.
• Stability and fairness of explicit congestion control with small buffers. 
  Frank Kelly, Gaurav Raina and Thomas Voice
  Computer Communication Review 38:3 (2008) 51-62.
• Networks: modelling and control. 
  Editors Keith Briggs, Frank Kelly and Mike Smith.
  Philosophical Transactions of the Royal Society A366 (2008) 1877-2092.
• Nonlinear growth generates age changes in the moments of the frequency distribution: the example of height in puberty. 
  T. J. Cole, M. Cortina-Borja, J. Sandhu, F. P. Kelly and H. Pan.
  Biostatistics 9 (2008) 159-171.
• Product form stationary distributions for diffusion approximations to a flow level model operating under a proportional fair sharing policy. 
  W. Kang, F. P. Kelly, N. H. Lee and R. J. Williams.
  Extended abstract for MAMA 07, 9th annual workshop on Mathematical performance Modeling and Analysis. 
  Performance Evaluation Review 36:2 (2007) 36-38.
• Road pricing.
  Ingenia 29 (2006) 34-40, 
  Proceedings of Conference on Statistics, Science and Public Policy (A.M. Herzberg, editor). Herstmonceux Castle, April 2008.
• Travel-time maps - transforming our view of transport.
  Chris Lightfoot and Frank Kelly
  Asymptopia (2006) 1-2.
• Data and innovation: the case for experimentation.
  FST Journal, 19:2 (2006) 14-15.
• A contract and balancing mechanism for sharing capacity in a communication network.
  Edward Anderson, Frank Kelly and Richard Steinberg
  Management Science 52 (2006) 39-53.
• Stability of end-to-end algorithms for joint routing and rate control. 
  Frank Kelly and Thomas Voice
  Computer Communication Review 35:2 (2005) 5-12.
• Fluid and Brownian approximations for an Internet congestion control model. 
  W. Kang, F. P. Kelly, N. H. Lee and R. J. Williams
  Proceedings of the 43rd IEEE Conference on Decision and Control (2004).
• Network dimensioning, service costing and pricing in a packet switched environment. 
  Gareth Davies, Michael Hardt and Frank Kelly
  Telecommunications Policy 28 (2004) 391-412.
• Providing incentives in providerless networks.
  Jon Crowcroft, Julian Chesterfield,Richard Gibbens, Frank Kelly and Sven Östring 
  Ad Hoc Networks 2 (2004) 283-289.
• Modelling incentives for collaboration in mobile ad hoc networks.
  Jon Crowcroft, Richard Gibbens, Frank Kelly and Sven Östring 
  Performance Evaluation 57 (2004) 427-439.
• Fair Internet traffic integration: network flow models and analysis. 
  Intégration équitable du trafic dans l'Internet: modèles fluides de flots et leur analyse.
  Peter Key, Laurent Massoulié, Alan Bain and Frank Kelly
  Annales des Télécommunications 59 (2004) 1338-1352.
• Fluid model for a network operating under a fair bandwidth-sharing policy.
  F.P. Kelly and R. J. Williams
  Annals of Applied Probability 14 (2004) 1055-1083.
• Fairness and stability of end-to-end congestion control.
  European Journal of Control 9 (2003) 159-176.
• Rate control as a market equilibrium.
  F. P. Kelly and V. V. Vazirani
  Unpublished manuscript (2002).
• On packet marking at priority queues.
  R.J. Gibbens and F.P. Kelly
  IEEE Transactions on Automatic Control 47 (2002) 1016-1020.
• Mathematical modelling of the Internet.
  In "Mathematics Unlimited - 2001 and Beyond" (Editors B. Engquist and W. Schmid). Springer-Verlag, Berlin, 2001. 685-702. An earlier version appeared in "ICIAM 99: Proceedings of the Fourth International Congress on Industrial and Applied Mathematics" (editors J.M. Ball and J.C.R. Hunt). Oxford University Press, 2000. 105-116.
• Fixed-point models for the end-to-end performance analysis of IP networks.
  R.J. Gibbens, S.K. Sargood, C. Van Eijl, F.P. Kelly, H. Azmoodeh, R.N. Macfadyen, N.W. Macfadyen 
  13th ITC Specialist Seminar: IP Traffic Measurement, Modeling and Management, Sept 2000, Monterey, California
• Models for a self-managed Internet .
  Philosophical Transactions of the Royal Society A358 (2000) 2335-2348.
• An approach to service level agreements for IP networks with differentiated services.
  R.J. Gibbens, S.K. Sargood, F.P. Kelly, H. Azmoodeh, R. Macfadyen, N. Macfadyen 
  Philosophical Transactions of the Royal Society A358 (2000) 2165-2182.
• Distributed admission control.
  F.P. Kelly, P.B. Key and S. Zachary
  IEEE Journal on Selected Areas in Communications 18 (2000) 2617-2628.
• A combinatorial auction with multiple winners for universal service .
  Frank Kelly and Richard Steinberg 
  Management Science 46 (2000) 586-596.
• A study of simple usage-based charging schemes for broadband networks.
  C. Courcoubetis, F.P. Kelly, V.A. Siris and R. Weber 
  Telecommunications Systems 15 (2000) 323-343.
• Measurement-based usage charges in communication networks.
  Costas Courcoubetis, Frank Kelly and Richard Weber 
  Operations Research 48 (2000) 535-548.
• Distributed connection acceptance control for a connectionless network.
  R.J. Gibbens and F.P. Kelly 
  In "Teletraffic Engineering in a Competitive World" (Editors P. Key and D. Smith), ITC16. Elsevier, Amsterdam, 1999. 941-952.
• Resource pricing and the evolution of congestion control .
  R.J. Gibbens and F.P. Kelly 
  Automatica 35 (1999) 1969-1985.
• Rate control in communication networks: shadow prices, proportional fairness and stability.
  Frank Kelly, Aman Maulloo and David Tan 
  Journal of the Operational Research Society 49 (1998) 237-252.
• An intelligent agent for optimizing QoS-for-money in priced ABR connections .
  C. Courcoubetis, G.D. Stamoulis, C. Manolakis and F.P. Kelly 
  In Proc. of International Conference on Telecommunications (ICT), 1998.
• Measurement-based connection admission control
  R. J. Gibbens and F. P. Kelly 
  In "Teletraffic Contributions for the Information Age" (Editors V. Ramaswami and P.E. Wirth), ITC15. Elsevier, Amsterdam, 1997. 879-888.
• Charging schemes for multiservice networks 
  David Songhurst and Frank Kelly 
  In "Teletraffic Contributions for the Information Age" (Editors V. Ramaswami and P.E. Wirth), ITC15. Elsevier, Amsterdam, 1997. 781-790. An earlier version appeared in the IEE Colloquium on Charging for ATM (1996).
• Tariffing in the new IP/ATM environment .
  Dawson Walker, Frank Kelly and Jonathan Solomon
  Telecommunications Policy 21 (1997) 283-295.
• Charging and rate control for elastic traffic .
  European Transactions on Telecommunications, volume 8 (1997) pages 33-37.
• Charging and accounting for bursty connections 
  In "Internet Economics" (Editors Lee W. McKnight and Joseph P. Bailey) MIT Press, 1997. 253-278.
• Braess' paradox in a loss network . 
  N.G Bean, F.P. Kelly, and P.G. Taylor
  Journal of Applied Probability 34 (1997) 155-9.
• Notes on effective bandwidths . 
  In "Stochastic Networks: Theory and Applications" (Editors F.P. Kelly, S. Zachary and I.B. Ziedins) Royal Statistical Society Lecture Notes Series, 4. Oxford University Press, 1996. 141-168.
• Modelling communication networks, present and future .
  Philosophical Transactions of the Royal Society A354 (1996) 437-463.
• Network programming methods for loss networks. 
  R.J. Gibbens and F.P. Kelly
  IEEE Journal on Selected Areas in Communications, 13 (1995), 1189-1198.
• A decision-theoretic approach to call admission control in ATM networks . 
  R.J. Gibbens, F.P. Kelly, and P.B. Key
  IEEE Journal on Selected Areas in Communications, 13 (1995), 1102-1114.
• Dynamic Alternative Routing . 
  R.J. Gibbens, F.P. Kelly, and P.B. Key
  In "Routing in Communication Networks" (Editor Martha Steenstrup ) Prentice Hall, Englewood Cliffs, 1995. 13-47.
• Dynamic routing in stochastic networks. 
  In "Stochastic Networks" (Editors F.P. Kelly and R.J. Williams ) The IMA Volumes in Mathematics and its Applications, 71. Springer-Verlag, New York, 1995. 169-186.
• Mathematical models of multiservice networks . 
  In "Complex Stochastic Systems and Engineering" (Editor D.M. Titterington ) Oxford University Press 1995, 221-234.
• Computational complexity of loss networks.
  Graham Louth, Michael Mitzenmacher and Frank Kelly 
  Theoretical Computer Science 125 (1994) 45-59.
• Bounds on the performance of dynamic routing for highly connected networks.
  Mathematics of Operations Research 19 (1994) 1-20.
• On tariffs, policing and admission control for multiservice networks .
  Operations Research Letters 15 (1994) 1-9.
• Dimensioning playout buffers from an ATM network.
  F.P. Kelly and P.B. Key
  Eleventh UK Teletraffic Symposium, Cambridge. 
  Performance Engineering in Telecommunications Networks (1994) 16A/1 - 16A/9.
• Dynamic routing in multiparented networks.
  R.J. Gibbens, F.P. Kelly, and S.R.E. Turner
  IEEE/ACM Transactions on Networking 1 (1993) 261-270.
• Dynamic routing in open queueing networks: Brownian models, cut constraints and resource pooling .
  F.P. Kelly and C.N. Laws
  Queueing Systems 13 (1993) 47-86.
• Network routing . 
  Philosophical Transactions of the Royal Society A337 (1991) 343-367.
• Loss networks . 
  Annals of Applied Probability, 1 (1991), 319-378.
• Effective bandwidths at multi-class queues. 
  Queueing Systems 9 (1991) 5-16.
• Coalitions in the international network. 
  R.J. Gibbens, F.P. Kelly, G.A. Cope and M.J. Whitehead
  In "Teletraffic and Datatraffic" (Editors A. Jensen and V.B. Iversen), ITC13. Elsevier, Amsterdam, 1991. 93-98.
• Routing and capacity allocation in networks with trunk reservation.
  Mathematics of Operations Research 15 (1990) 771-793.
• A paradox of congestion in a queuing network. 
  J.E. Cohen and F.P. Kelly
  Journal of Applied Probability 27 (1990) 730-734.
• Asymptotic stationarity of queues in series and the heavy traffic approximation . 
  W. Szczotka and F.P. Kelly
  Annals of Probability 18 (1990) 1232-1248.
• Bistability in communication networks. 
  R.J. Gibbens, P.J. Hunt, and F.P. Kelly
  In "Disorder in Physical Systems: a Volume in Honour of John M. Hammersley" (Editors Geoffrey Grimmett and Dominic Welsh), Oxford University Press, 1990, 113-127.
• Dynamic routing in fully connected networks.
  R.J. Gibbens and F.P. Kelly 
  IMA Journal of Mathematical Control and Information 7 (1990) 77-11.
• On critically loaded loss networks. 
  P.J. Hunt and F.P. Kelly
  Advances in Applied Probability 21 (1989), 831-841.
• Limit theorems for loss networks with diverse routing. 
  I.B. Ziedins and F.P. Kelly
  Advances in Applied Probability 21 (1989), 804-830.
• On a class of approximations for closed queueing networks. 
  Queueing Systems 4 (1989) 69-76.
• Dynamic Alternative Routing - modelling and behaviour. 
  R.J. Gibbens, F.P. Kelly, and P.B. Key
  In "Teletraffic Science" (Editor M. Bonatti), ITC12. Elsevier, Amsterdam, 1989. 1019-1025.
• Fixed point models of loss networks. 
  Journal of the Australian Mathematical Society B31 (1989) 204-218.
• Routing in circuit-switched networks: optimization, shadow prices and decentralization . 
  Advances in Applied Probability 20 (1988), 112-144.
• The optimization of queueing and loss networks. 
  In "Queueing Theory and its Applications" (Editors O.J. Boxma and R. Syski), 1988, 375-392. CWI Monographs 7, North-Holland, Amsterdam.
• The number of packets transmitted by collision detect random access schemes. 
  F.P. Kelly and I.M. MacPhee
  Annals of Probability 15 (1987) 1557-1568.
• One-dimensional circuit-switched networks . 
  Annals of Probability 15 (1987) 1166-1179.
• Instability in a communication network. 
  In "Open Problems in Communication and Computation" (Editors Thomas M. Cover, B. Gopinath), 1987, 63-69. Springer, New York.
• Blocking probabilities in large circuit-switched networks. 
  Advances in Applied Probability 18 (1986) 473-505.
• On auto-repeat facilities and telephone network performance. 
  Journal of the Royal Statistical Society (Series B) 48 (1986) 123-132.
• Stochastic models of computer communication systems. 
  Journal of the Royal Statistical Society (Series B) 47 (1985) 379-395, with Discussion 415-428.
• Some probabilistic aspects of network flow. 
  In "Computer Communications" (Editor B. Gopinath), Proceedings of Symposia in Applied Mathematics, 31, 1985, 15-44. American Mathematical Society.
• Segregating the input to a series of buffers. 
  Mathematics of Operations Research, 10 (1985) 33-43.
• An asymptotic analysis of blocking. 
  In Modelling and Performance Evaluation Methodology, 
  Lecture Notes in Control and Information Sciences 60. Springer, 1984, 3-20.
• The product form for sojourn time distributions in cyclic exponential queues. 
  O. J. Boxma, F. P. Kelly and A. G. Konheim 
  Journal of the ACM 31 (1984) 128-133.
• Sojourn times in closed queueing networks. 
  F.P. Kelly and P.K. Pollett 
  Advances in Applied Probability, 15 (1983) 638-656.
• The dependence of sojourn times in closed queueing networks. 
  In "Mathematical Computer Performance and Reliability" (Editors G. Iazeolla, P.J. Courtois and A. Hordijk), 1984, 111-121. North-Holland, Amsterdam.
• Nuclear position in the cells of the mouse early embryo. 
  W.J.D. Reeve and F.P. Kelly 
  Journal of Embryology and Experimental Morphology 75 (1983) 117-139.
• Invariant measures and the q-matrix. 
  In "Probability, Statistics and Analysis: Papers in Honour of Professor David Kendall" (Editors J.F.C. Kingman and G.E.H. Reuter), 1983, 143-160. 
  London Mathematical Society Lecture Notes Series 79, Cambridge University Press.
• The throughput of a series of buffers. 
  Advances in Applied Probability 14 (1982) 633-653.
• Markovian functions of a Markov chain. 
  Sankhya 44 (1982) 372-379.
• A remark on search and sequencing problems. 
  Mathematics of Operations Research, 7 (1982) 154-157.
• On optimal search with unknown detection probabilities. 
  Journal of Mathematical Analysis and Applications 88 (1982) 422-432.
• Eigenvalue inequalities for products of matrix exponentials. 
  J.E. Cohen, S. Friedland, T. Kato and F.P. Kelly 
  Linear Algebra and its Applications 45 (1982) 55-95.
• Networks of quasi-reversible nodes. 
  In "Applied Probability-Computer Science: the Interface" Volume 1, 
  (Editors R.L. Disney and T.J. Ott), Birkhauser, Boston, 1982. 3-29.
• Multi-armed bandits with discount factor near one: the Bernoulli case. 
  Annals of Statistics 9 (1981) 987-1001.
• How a group reaches agreement: a stochastic model. 
  Mathematical Social Sciences, 2 (1981), 1-8.
• The asymptotic behaviour of an invasion process. 
  Journal of Applied Probability, 14 (1977) 584-590.
• Regional taxonomy using trend surface coefficients. 
  (or here)
  A.D. Cliff and F.P. Kelly
  Environment and Planning A9 (1977) 945-955.
• Markov point processes. 
  B.D. Ripley and F.P. Kelly
  J. London Math. Soc. 15 (1977) 188-192.
• Exact results for the Moran neutral allele model. 
  Advances in Applied Probability, 9 (1977) 197-201.
• The departure process from a queueing system. 
  Mathematical Proceedings of the Cambridge Philosophical Society, 80 (1976) 283-285.
• A note on Strauss's model for clustering. 
  F.P. Kelly and B.D. Ripley
  Biometrika, 63 (1976), 357-360.
• Stochastic models with electrical analogues. 
  Mathematical Proceedings of the Cambridge Philosophical Society, 80 (1976) 145-151.
• Networks of queues. 
  Advances in Applied Probability, 8 (1976) 416-432.
• On stochastic population models in genetics. 
  Journal of Applied Probability, 13 (1976) 127-131.
• Markov processes and Markov random fields. 
  Bulletin of the International Statistical Institute, 46 (1976) 397-404.
• Networks of queues with customers of different types. 
  Journal of Applied Probability, 12 (1975) 542-554.

Books

• Stochastic Networks 
  Frank Kelly and Elena Yudovina
  Cambridge University Press, 2014.
• Reversibility and Stochastic Networks 
  Wiley, Chichester, 1979, reprinted 1987, 1994. Cambridge University Press, 2011.
• Probability, Statistics and Optimization, A Tribute to Peter Whittle 
  Wiley Series in Probability and Mathematical Statistics 
  Editor: F.P. Kelly 
  Wiley, Chichester, 1994
• Stochastic Networks 
  IMA Volumes in Mathematics and its Applications, Volume 71 
  Editors: F.P. Kelly and R.J. Williams
  Springer-Verlag, New York 1995
• Mathematical Models in Finance 
  Editors: S.D. Howison, F.P. Kelly and P. Wilmott
  Chapman and Hall, 1995
• Stochastic Networks: Theory and Applications 
  Royal Statistical Society Lecture Notes Series, 4. 
  Editors: F.P. Kelly, S. Zachary and I.B. Ziedins
  Oxford University Press, 1996