**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.