**Teaching:**

**Rumours, epidemics and
consensus on graphs : **Lecture notes Problem sheet

**Research Interests:**

I am
interested in the mathematical modelling of communication and computer
networks, and in decentralised algorithms for such networks. The mathematics
used in studying these problems comes from large deviations, random graphs,
queueing theory, information theory etc.

**Publications**

Note:
Copyright is held by the publishers unless indicated otherwise.

**Book**

Big Queues (with Neil O'Connell and Damon Wischik). Springer Lecture Notes in Mathematics, Volume 1838, 2004.

**Papers (by topic)**

**Computer viruses and worms**

A
random walk model for infection on graphs: spread of epidemics and rumours with
mobile agents (with M. Draief), *Discrete Event
Dynamical Systems, *2011.

How
to distribute antidote to control epidemics (with C. Borgs, J. Chayes and A. Saberi), *Random
Structures and Algorithms*, 2010.

Thresholds
for virus spread on networks (with M. Draief and
L. Massoulie), *Annals of Applied Probability*,
2008.

On the race of worms, alerts and patches
(with M. Vojnovic), *IEEE/ACM Trans. Networking*,
2008.

Efficient quarantining of scanning worms:
Optimal detection and co-ordination (with D. Gunawardena, P. Key, L. Massoulie and J. Scott), *Proc. IEEE Infocom*,
2006.

The effect of network topology on the spread of
epidemics (with L. Massoulie and D. Towsley), *Proc. IEEE Infocom*,
2005.

**Random graphs and stochastic processes on graphs**

Exponential
random graphs as models of overlay networks (with M. Draief
and L. Massoulie), *Journal of Applied Probability*,
2009.

On the connectivity and diameter of
small-world networks (with F. Xue), *Advances
in Applied Probability*, 2007*.*

Peer
counting and sampling in overlay networks based on random walks (with L. Massoulie, E. le Merrer and A.-M.
Kermarrec), *Distributed Computing*, 2007. An
earlier version appeared as* *Peer
counting and sampling in overlay networks: random walk methods in *Proc.
ACM Symp. Principles of Distributed Computing (PODC)*,
2006.

Efficient routing in Poisson small-world
networks (with M. Draief), *Journal of Applied
Probability,* 2006.

Failure resilience in balanced overlay
networks (with L. Massoulie) *Proc. 41st Annual
Allerton Conference on Communication, Control and Computing, *2003.

**Peer-to-peer systems and algorithms**

Efficient and adaptive epidemic-style protocols
for reliable and scalable multicast (with I. Gupta and A.-M. Kermarrec), *IEEE Trans. Parallel and Distributed Systems*,
2006.

A compact routing protocol for ad-hoc
networks (with M. Chen). Paper presented at *SpasWin**
2006.*

Network awareness and failure resilience in
self-organising overlay networks (with L. Massoulie
and A.-M. Kermarrec), *Proc. Symp.
Reliable Distributed Systems (SRDS)*, 2003.

Peer-to-peer membership management for
gossip-based protocols (with A.-M. Kermarrec and
L. Massoulie), *IEEE Trans. Computers*, 2003.

Probabilistic reliable dissemination in
large-scale systems (with A.-M. Kermarrec and L. Massoulie), *IEEE Trans. Parallel and Distributed Systems*,
2003.

Security for structured peer-to-peer overlay
networks (with M. Castro, P. Druschel, A. Rowstron and D. S. Wallach), in *Proc. Fifth Symposium on
Operating Systems Design and Implementation (OSDI)*, 2002.

HiScamp:
self-organizing hierarchical membership protocol (with A.-M. Kermarrec and L. Massoulie), in *Proc.
Tenth ACM SIGOPS European Workshop*, 2002.

SCAMP: Peer-to-peer lighweight
membership service for large-scale group communication (with A.-M. Kermarrec and L. Massoulie), in *Proc.
Third Intl. Workshop on Networked Group Communication (NGC)*, 2001.

**Communication networks**

Load Balancing and
Routing Games with Admission Prices (with T. Bodas
and D. Manjunath), in *Proc. IEEE CDC*, 2011 (to appear).

Load
balancing via random local search in closed and open systems (with S.
Lilienthal, D. Manjunath, A. Proutiere and F. Simatos), in *Proc. ACM Sigmetrics,
*2010. (Winner of the Best Paper award.)

Performance
analysis of contention based medium access control protocols (with G.
Sharma and P. Key),* IEEE Trans. Info. Theory*, 2009. This is an extended
version, with full proofs, of an* *earlier paper*
*with the same title in *Proc. IEEE Infocom*,
2006.

Large deviations of the interference in a wireless
communication model (with G. L. Torrisi), *IEEE
Trans. Info. Theory*, 2008.

Dynamic
decentralized multi-channel MAC protocols (with H. Seferoglu,
A. Lakshmikantha and P. Key), in *Proc. Information
Theory & Applications Workshop*, 2008.

Congestion pricing and non-cooperative
games in communication networks (with K. Laevens
and R. Steinberg), *Operations Research*, 2007.

Modeling the impact of
buffering on 802.11 (with K. Duffy), *IEEE Communication Letters*,
2007.

Congestion notification and probing mechanisms
for endpoint admission control (with P. Key, D. Polis and R. Srikant), *IEEE/ACM Trans. Networking*, 2006.

Resource allocation with persistent and transient
flows (with S. Deb and P. Key). *IEEE/ACM Trans. Networking*, 2005.

Feedback and bandwidth sharing in networks
(with P. Key and L. Massoulie), *Proc. 39th Annual
Allerton Conference on Communication, Control and Computing, *2001.

Congestion pricing and user adaptation (with K. Laevens and R. Steinberg), *Proc. IEEE Infocom,* 2001.

**Bayes' asymptotics**

Bayesian inference for Markov chains
(with P. Eichelsbacher), *Journal of Applied
Probability*, 2002.

Moderate deviations for Bayes posteriors (with
P. Eichelsbacher), *Scandinavian Journal of
Statistics*, 2002.

A large deviation principle for Dirichlet
posteriors (with N. O'Connell). *Bernoulli*, 2000.

An inverse of Sanov's theorem (with N.
O'Connell). *Statistics & Probability Letters*, 1999.

Bayesian network management (with P. J. Green, N.
O'Connell and S. M. Pitts), *Queueing Systems*, 1998.

**Queueing theory**

A class of risk processes with reserve-dependent
premium rate: sample path large deviations and importance sampling (with C.
Macci and G. L. Torrisi), *Queueing
Systems,* 2007.

A class of risk processes with delayed
claims: ruin probability estimates under heavy-tailed conditions (with G.
L. Torrisi), *Journal of Applied Probability,*
2006.

The calculus of Hurstiness (with D. J. Wischik), 2005.

Sample
path large deviations principles for Poisson shot noise processes, and
applications (with C. Macci and G. L. Torrisi), *Electronic Journal of Probability,* 2005.

Invariant rate functions for discrete time
queues (with N. O'Connell and B. Prabhakar), *Annals of Applied
Probability, *2003.

A large deviation principle with queueing applications
(with N. O'Connell), *Stochastics and Stochastic Reports*, 2002.

The linear geodesic property is not generally
preserved by a FIFO queue (with N. O'Connell), *Annals of Applied
Probability*, 1998.

Large deviations of the sojourn time for queues in
series *Annals of Operations Research*, 1998.

Bias correction in effective bandwidth estimation, *Performance Evaluation*,
1996.

Stationary tail probabilities in exponential server tandems with renewal
arrivals (with V. Anantharam), *Queueing Systems*,
1996.

Optimal buffer allocation in tandems of last-come-first-served queues (with
V. Anantharam), *Queueing Systems*, 1995.

Optimal buffer allocation in Jackson networks: Correctness within a constant
of a rule of thumb (with V. Anantharam), *IEEE
Trans. Info. Theory*, 1994.

**Probability**

Large and moderate deviations for matching and
empirical discrepancies (with N. O'Connell), *Markov Processes and
Related Fields,* 2007.

Information loss in riffle shuffling (with D.
Stark and N. O'Connell). *Combinatorics, Probability and Computing, *2002.

Poissonian behaviour of Ising Spin Systems in an External Field (with B. Hambly, N. O'Connell, D. Stark and P. Upton), *Journal of
Statistical Physics*, 2000.

**Miscellaneous**

Spontaneous
emergence of multiple drug resistance in tuberculosis before and during therapy
(with C. Colijn, T. Cohen and M. Murray), *PLoS** ONE*, 2011.

A
Ca2+-based computational model for NMDA receptor-dependent synaptic plasticity
at individual post-synaptic spines in the hippocampus (with O. Rackham, K. Tsaneva-Atanasova and J. Mellor), *Frontiers in Synaptic
Neuroscience*, 2010.