Frank Kelly's papers
Google Scholar
citations
 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) 822837.
An earlier version was presented at the
15th ACM
Conference on Economics and Computation,
2014.
 Analytical
Research Foundations for the NextGeneration Electric Grid
Committee Cochairs: 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
alphafairness based traffic engineering
Bill McCormick, Frank Kelly, Patrice Plante, Paul Gunning and Peter
AshwoodSmith
Proceedings of the ACM SIGCOMM 2014 Workshop on Hot Topics
in Software Defined Networking, 199200.

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), 1112.
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 "NextGeneration Internet
Architectures and Protocols"
(Editors Byrav Ramamurthy,
George Rouskas and
Krishna Sivalingam),
Cambridge University Press, 2011. 257274.

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) 165194.

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) 17191780.
 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 BarrowGreen and Imre Leader, associate editors)
Princeton University Press, 2008. 862870.

Stability and fairness of explicit congestion control with
small buffers.
Frank Kelly, Gaurav Raina and Thomas Voice
Computer Communication Review 38:3 (2008) 5162.
 Networks:
modelling and control.
Editors Keith Briggs, Frank Kelly and Mike Smith.
Philosophical Transactions of the Royal Society A366 (2008) 18772092.
 Nonlinear
growth generates age changes in the moments of
the frequency distribution: the example of height in puberty.
T. J. Cole, M. CortinaBorja, J. Sandhu, F. P. Kelly and H. Pan.
Biostatistics 9 (2008) 159171.

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) 3638.

Road pricing.
Ingenia 29 (2006) 3440,
Proceedings of Conference on Statistics, Science and Public Policy
(A.M. Herzberg, editor).
Herstmonceux Castle, April 2008.

Traveltime maps  transforming our view of transport.
Chris Lightfoot and Frank Kelly
Asymptopia (2006) 12.

Data and innovation: the case for experimentation.
FST Journal, 19:2 (2006) 1415.

A contract and balancing mechanism for sharing
capacity in a communication network.
Edward Anderson, Frank Kelly and Richard Steinberg
Management Science 52 (2006) 3953.

Stability of endtoend algorithms for joint routing and
rate control.
Frank Kelly and Thomas Voice
Computer Communication Review 35:2 (2005) 512.

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) 391412.

Providing incentives in providerless networks.
Jon Crowcroft, Julian Chesterfield,Richard Gibbens, Frank Kelly and
Sven Östring
Ad Hoc Networks 2 (2004) 283289.

Modelling incentives for collaboration in mobile ad hoc networks.
Jon Crowcroft, Richard Gibbens, Frank Kelly and
Sven Östring
Performance Evaluation 57 (2004) 427439.

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) 13381352.

Fluid model for a network operating under a fair bandwidthsharing
policy.
F.P. Kelly and R. J. Williams
Annals of Applied Probability 14 (2004) 10551083.

Fairness and stability of endtoend congestion control.
European Journal of Control 9 (2003) 159176.
 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) 10161020.

Mathematical modelling of the Internet.
In "Mathematics Unlimited  2001 and Beyond"
(Editors B. Engquist and W. Schmid).
SpringerVerlag, Berlin, 2001. 685702.
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. 105116.

Fixedpoint models for the endtoend 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 selfmanaged Internet .
Philosophical Transactions of the
Royal Society A358 (2000) 23352348.

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) 21652182.

Distributed admission control.
F.P. Kelly, P.B. Key and S. Zachary
IEEE Journal on Selected Areas in Communications 18 (2000) 26172628.

A combinatorial
auction with multiple winners for universal service .
Frank Kelly and Richard Steinberg
Management Science 46 (2000) 586596.

A study of simple usagebased charging schemes for broadband
networks.
C. Courcoubetis, F.P. Kelly, V.A. Siris and R. Weber
Telecommunications Systems 15 (2000) 323343.

Measurementbased usage charges in communication networks.
Costas Courcoubetis, Frank Kelly and Richard Weber
Operations Research 48 (2000) 535548.

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. 941952.

Resource pricing and the
evolution of congestion control .
R.J. Gibbens and F.P. Kelly
Automatica 35 (1999) 19691985.
 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) 237252.

An intelligent agent for optimizing QoSformoney
in priced ABR connections .
C. Courcoubetis, G.D. Stamoulis, C. Manolakis
and F.P. Kelly
In Proc. of International Conference on Telecommunications (ICT), 1998.

Measurementbased 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. 879888.

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. 781790.
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) 283295.
 Charging and
rate control for elastic traffic .
European Transactions on Telecommunications, volume 8 (1997) pages 3337.

Charging and accounting for bursty connections
In "Internet Economics" (Editors Lee W. McKnight and Joseph P. Bailey)
MIT Press, 1997. 253278.

Braess' paradox in a loss network
.
N.G Bean, F.P. Kelly, and P.G. Taylor
Journal of Applied Probability 34 (1997) 1559.
 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. 141168.
 Modelling communication networks,
present and future .
Philosophical Transactions of the
Royal Society A354 (1996) 437463.

Network programming methods for loss networks.
R.J. Gibbens and F.P. Kelly
IEEE Journal on Selected Areas in Communications, 13 (1995), 11891198.

A decisiontheoretic 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), 11021114.
 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. 1347.

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.
SpringerVerlag, New York, 1995. 169186.

Mathematical models of multiservice networks .
In "Complex Stochastic Systems and Engineering" (Editor D.M.
Titterington ) Oxford University Press 1995, 221234.

Computational complexity of loss networks.
Graham Louth, Michael Mitzenmacher and Frank Kelly
Theoretical Computer Science 125 (1994) 4559.

Bounds on the performance of dynamic routing
for highly connected networks.
Mathematics of Operations Research 19 (1994) 120.

On tariffs, policing and admission control for multiservice networks
.
Operations Research Letters 15 (1994) 19.

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) 261270.

Dynamic routing in open queueing networks: Brownian models,
cut constraints and resource pooling .
F.P. Kelly and C.N. Laws
Queueing Systems 13 (1993) 4786.

Network routing .
Philosophical Transactions of the
Royal Society A337 (1991) 343367.

Loss networks .
Annals of Applied Probability, 1 (1991), 319378.

Effective bandwidths at multiclass queues.
Queueing Systems 9 (1991) 516.

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. 9398.

Routing and capacity allocation in networks with
trunk reservation.
Mathematics of Operations Research 15 (1990) 771793.

A paradox of congestion in a queuing network.
J.E. Cohen and F.P. Kelly
Journal of Applied Probability 27 (1990) 730734.

Asymptotic stationarity of queues in series
and the heavy traffic approximation .
W. Szczotka and F.P. Kelly
Annals of Probability 18 (1990) 12321248.
 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, 113127.

Dynamic routing in fully connected networks.
R.J. Gibbens and F.P. Kelly
IMA Journal of Mathematical Control and Information 7 (1990) 7711.
 On
critically loaded loss networks.
P.J. Hunt and F.P. Kelly
Advances in Applied Probability 21 (1989), 831841.

Limit theorems for loss networks with diverse routing.
I.B. Ziedins and F.P. Kelly
Advances in Applied Probability 21 (1989), 804830.

On a class of approximations for closed queueing networks.
Queueing Systems 4 (1989) 6976.

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.
10191025.

Fixed point models of loss networks.
Journal of the Australian Mathematical Society B31 (1989) 204218.

Routing in circuitswitched networks: optimization,
shadow prices and decentralization .
Advances in Applied Probability 20 (1988), 112144.

The optimization of queueing and loss networks.
In
"Queueing Theory and its Applications" (Editors O.J. Boxma and R. Syski),
1988, 375392. CWI Monographs 7,
NorthHolland, Amsterdam.

The number of packets transmitted by collision
detect random access schemes.
F.P. Kelly and I.M. MacPhee
Annals of Probability 15 (1987) 15571568.

Onedimensional circuitswitched networks .
Annals of Probability 15 (1987) 11661179.

Instability in a communication network.
In
"Open Problems in Communication and Computation" (Editors Thomas M. Cover,
B. Gopinath),
1987, 6369. Springer, New York.

Blocking probabilities in large circuitswitched networks.
Advances in Applied Probability 18 (1986) 473505.

On autorepeat facilities and telephone network performance.
Journal of the Royal Statistical Society (Series B)
48 (1986) 123132.

Stochastic models of computer communication systems.
Journal of the Royal Statistical Society (Series B) 47 (1985) 379395,
with Discussion 415428.

Some probabilistic aspects of network flow.
In "Computer Communications" (Editor B. Gopinath), Proceedings of Symposia
in Applied Mathematics, 31, 1985, 1544. American Mathematical Society.

Segregating the input to a series of buffers.
Mathematics of Operations Research, 10 (1985) 3343.
 An asymptotic
analysis of blocking.
In Modelling and
Performance Evaluation Methodology,
Lecture Notes in Control and
Information Sciences 60. Springer, 1984, 320.
 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) 128133.

Sojourn times in closed queueing networks.
F.P. Kelly and P.K. Pollett
Advances in Applied Probability, 15 (1983) 638656.

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, 111121.
NorthHolland, 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) 117139.
 Invariant
measures and the qmatrix.
In "Probability, Statistics and Analysis: Papers in Honour of Professor
David Kendall"
(Editors J.F.C. Kingman and G.E.H. Reuter), 1983, 143160.
London Mathematical Society
Lecture Notes Series 79, Cambridge University Press.

The throughput of a series of buffers.
Advances in Applied Probability 14 (1982) 633653.

Markovian functions of a Markov chain.
Sankhya 44 (1982) 372379.

A remark on search and sequencing problems.
Mathematics of Operations Research, 7 (1982) 154157.

On optimal search with unknown detection probabilities.
Journal of Mathematical Analysis and Applications
88 (1982) 422432.
 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) 5595.

Networks of quasireversible nodes.
In "Applied ProbabilityComputer Science: the Interface" Volume 1,
(Editors R.L. Disney and T.J. Ott), Birkhauser, Boston, 1982. 329.

Multiarmed bandits with discount factor near one: the Bernoulli
case.
Annals of Statistics 9 (1981) 9871001.

How a group reaches agreement: a stochastic model.
Mathematical Social Sciences, 2 (1981), 18.

The asymptotic behaviour of an invasion process.
Journal of Applied Probability, 14 (1977) 584590.

Regional taxonomy using trend surface coefficients.
(or here)
A.D. Cliff and F.P. Kelly
Environment and Planning A9 (1977) 945955.

Markov point processes.
B.D. Ripley and F.P. Kelly
J. London Math. Soc. 15 (1977) 188192.
 Exact
results for the Moran neutral allele model.
Advances in Applied Probability, 9 (1977) 197201.

The departure process from a queueing system.
Mathematical Proceedings of the Cambridge Philosophical Society,
80 (1976) 283285.

A note on Strauss's model for clustering.
F.P. Kelly and B.D. Ripley
Biometrika, 63 (1976), 357360.

Stochastic models with electrical analogues.
Mathematical Proceedings of the Cambridge Philosophical Society,
80 (1976) 145151.

Networks of queues.
Advances in Applied Probability, 8 (1976) 416432.

On stochastic population models in genetics.
Journal of Applied Probability, 13 (1976) 127131.

Markov processes and Markov random fields.
Bulletin of the International Statistical Institute, 46
(1976) 397404.

Networks of queues with customers of different types.
Journal of Applied Probability, 12 (1975) 542554.
Frank Kelly
Statistical Laboratory
University of Cambridge