Neil O'Connell

Estimating QoS Parameters For Atm Traffic Using Its Entropy (2007)

Sanov's theorem states that the sequence of empirical measures associated with a sequence of iid random variables satisfies the large deviation principle (LDP) in the weak topology with rate...

N.G. Duffield, J.T. Lewis, Neil O'Connell, Raymond Russell, F.Toomey

Introduction How will ATM carriers allocate the band-width required to guarantee the quality-of-service promised in their customer contracts? How can customers exploit to their advantage the tariff...

Queues, stores, and tableaux (2007)

A path-transformation for random walks and the Robinson-Schensted correspondence (2007)

Consider the single server queue with an infinite buffer and a FIFO discipline, either of type M/M/1 or Geom/Geom/1. Denote by A the arrival process and by s the services. Assume the stability...

Random matrices, non-colliding processes and queues (2007)

In [O'Connell and Yor (2002)] a path-transformation G was introduced with the property that, for X belonging to a certain class of random walks on the integer lattice, the transformed walk G(X) has...

On the free energy of a directed polymer in a Brownian environment (2006)

This is survey of some recent results connecting random matrices, non-colliding processes and queues.

Moriarty, John, O'Connell, Neil

We prove a formula conjectured in O'Connell and Yor (2001) for the free energy density of a directed polymer in a Brownian environment in 1+1 dimensions.

Queues, stores, and tableaux (2005)

Littelmann paths and Brownian paths (2005)

Consider the single-server queue with an infinite buffer and a first-in--first-out discipline, either of type M/M/1 or Geom/Geom/1. Denote by A the arrival process and by s the services. Assume the...

Biane, Philippe, Bougerol, Philippe, O'Connell, Neil

We study some path transformations related to Pitman's theorem [28, Th. 1.3] on Brownian motion and the three-dimensional Bessel process. We relate these to the Littelmann path model (see [22]) and...

Queues, stores, and tableaux (2005)

Queues, stores, and tableaux (2005)

Consider the single server queue with an infinite buffer and a FIFO discipline, either of type M/M/1 or Geom/Geom/1. Denote by A the arrival process and by s the services. Assume the stability...

Littelmann paths and brownian paths (2004)

Consider the single server queue with an infinite buffer and a FIFO discipline, either of type M/M/1 or Geom/Geom/1. Denote by A the arrival process and by s the services. Assume the stability...

Biane, Philippe, Bougerol, Philippe, O'Connell, Neil

We study some path transformations related to Littelmann path model and their applications to representation theory and Brownian motion in a Weyl chamber.

Invariant rate functions for discrete-time queues (2003)

Ganesh, Ayalvadi, O'Connell, Neil, Prabhakar, Balaji

We consider a discrete-time queue with general service distribution and characterize a class of arrival processes that possess a large deviation rate function that remains unchanged in passing...

Random matrices, non-colliding processes and queues (2002)

A path-transformation for random walks and the Robinson-Schensted correspondence (2002)

This is survey of some recent results connecting random matrices, non-colliding processes and queues.

Random matrices, non-colliding processes and queues (2002)

In [O'Connell and Yor (2002)] a path-transformation G was introduced with the property that, for X belonging to a certain class of random walks on the integer lattice, the transformed walk G(X) has...

Non-Colliding Random Walks, Tandem Queues, and Discrete Orthogonal Polynomial Ensembles (2001)

König, Wolfgang; BRIMS, Hewlett-Packard Laboratories; Koenig@math.tu-berlin.de, O'Connell, Neil; BRIMS, Hewlett-Packard Laboratories; Noc@hplb.hpl.hp.com, Roch, Sébastien; École Polytechnique; Sebastien.roch@polytechnique.org

We show that the function h(x)=prodi < j(xj-xi) is harmonic for any random walk in Rk with exchangeable increments, provided the required moments exist. For the subclass of random walks which can...

Non-Colliding Random Walks, Tandem Queues, and Discrete Orthogonal Polynomial Ensembles (2001)

König, Wolfgang; BRIMS, Hewlett-Packard Laboratories; Koenig@math.tu-berlin.de, O'Connell, Neil; BRIMS, Hewlett-Packard Laboratories; Noc@hplb.hpl.hp.com, Roch, Sébastien; École Polytechnique; Sebastien.roch@polytechnique.org

We show that the function h(x)=prodi < j(xj-xi) is harmonic for any random walk in Rk with exchangeable increments, provided the required moments exist. For the subclass of random walks which can...

Eigenvalues of the Laguerre Process as Non-Colliding Squared Bessel Processes (2001)

König, Wolfgang; BRIMS, HP Labs; Koenig@math.tu-berlin.de, O'Connell, Neil; BRIMS, HP Labs; Neil.O.connell@ens.fr

Let A(t) be an n-times-p matrix with independent standard complex Brownian entries and set M(t)=A(t)*A(t). This is a process version of the Laguerre ensemble and as such we shall refer to it as the...

Eigenvalues of the Laguerre Process as Non-Colliding Squared Bessel Processes (2001)

König, Wolfgang; BRIMS, HP Labs; Koenig@math.tu-berlin.de, O'Connell, Neil; BRIMS, HP Labs; Neil.O.connell@ens.fr

Let A(t) be an n-times-p matrix with independent standard complex Brownian entries and set M(t)=A(t)*A(t). This is a process version of the Laguerre ensemble and as such we shall refer to it as the...

Pitman's 2M-X Theorem for Skip-Free Random Walks with Markovian Increments (2001)

Hambly, B. M.; University Of Oxford; Hambly@maths.ox.ac.uk, Martin, James B.; Cambridge University; Jbm11@cus.cam.ac.uk, O'Connell, Neil; BRIMS, HP Labs; Neil.O.connell@ens.fr

Let $(xi_k, kge 0)$ be a Markov chain on ${-1,+1}$ with $xi_0=1$ and transition probabilities $P(xi_{k+1}=1| xi_k=1)=a>b=P(xi_{k+1}=-1| xi_k=-1)$. Set $X_0=0$, $X_n=xi_1+cdots +xi_n$ and...

Pitman's 2M-X Theorem for Skip-Free Random Walks with Markovian Increments (2001)

Hambly, B. M.; University Of Oxford; Hambly@maths.ox.ac.uk, Martin, James B.; Cambridge University; Jbm11@cus.cam.ac.uk, O'Connell, Neil; BRIMS, HP Labs; Neil.O.connell@ens.fr

Let $(xi_k, kge 0)$ be a Markov chain on ${-1,+1}$ with $xi_0=1$ and transition probabilities $P(xi_{k+1}=1| xi_k=1)=a>b=P(xi_{k+1}=-1| xi_k=-1)$. Set $X_0=0$, $X_n=xi_1+cdots +xi_n$ and...

A Representation for Non-Colliding Random Walks (2001)

O'Connell, Neil; BRIMS, HP Labs; Neil.O.connell@ens.fr, Yor, Marc; Universite Pierre Et Marie Curie; Neil.O.connell@ens.fr

We define a sequence of mappings $Gamma_k:D_0(R_+)^kto D_0(R_+)^k$ and prove the following result: Let $N_1,ldots,N_n$ be the counting functions of independent Poisson processes on $R_+$ with...

A Representation for Non-Colliding Random Walks (2001)

O'Connell, Neil; BRIMS, HP Labs; Neil.O.connell@ens.fr, Yor, Marc; Universite Pierre Et Marie Curie; Neil.O.connell@ens.fr

We define a sequence of mappings $Gamma_k:D_0(R_+)^kto D_0(R_+)^k$ and prove the following result: Let $N_1,ldots,N_n$ be the counting functions of independent Poisson processes on $R_+$ with...

A large-deviation principle for Dirichlet posteriors (2000)

Ganesh, Ayalvadi J., O'connell, Neil

Let Xk be a sequence of independent and identically distributed random variables taking values in a compact metric space Ω, and consider the problem of estimating the law of X1 in a Bayesian...

Large deviations at equilibrium for a large star-shaped loss network (2000)

Graham, Carl, O'Connell, Neil

We consider a symmetric network composed of $N$ links, each with capacity $C$. Calls arrive according to a Poisson process, and each call concerns $L$ distinct links chosen uniformly at random. If...

A law of large numbers for random hierarchical sequences, BRIMS (2000)

B. M. Hambly, Neil O'connell

We generate a hierarchical sequence of random variables from a map taking k copies of a Banach space to itself. With a simple assumption on the map and an integrability condition for the initial...

Renormalization of Hierarchical Sequences (2000)

Hambly And Neil, B. M. Hambly, Neil O'connell

We generate a hierarchical sequence of random variables from a map taking k copies of a Banach space to itself. With a simple assumption on the map and an integrability condition for the initial...

On the Characteristic Polynomial of a Random Unitary Matrix (2000)

C. P. Hughes, J.P. Keating, Neil O'connell

We present a range of fluctuation and large deviations results for the logarithm of the characteristic polynomial Z of a random N \Theta N unitary matrix, as N ! 1. First we show that ln Z= ln N ,...

Random Matrix Theory and the Derivative of the Riemann Zeta Function (2000)

C. P. Hughes, J. P. Keating, Neil O'connell

Random matrix theory (RMT) is used to model the asymptotics of the discrete moments of the derivative of the Riemann zeta function, i(s), evaluated at the complex zeros 2 + ifl n , using the methods...

Sample path large deviations in finer topologies (1999)

Peter Eichelsbacher, Neil O'connell

Abstract. In this paper we present sufficient conditions for sample path large deviation principles to be extended to finer topologies. We consider extensions of the uniform topology by Orlicz...

A large deviation principle for Dirichlet posteriors (1999)

A. J. Ganesh, Neil O'connell

Let X k be a sequence of independent and identically distributed random variables taking values in a compact metric space\Omega\Gamma and consider the problem of estimating the law of X 1 in a...

An inverse of Sanov's theorem (1999)

Ayalvadi Ganesh, Neil O'Connell

Let X k be a sequence of iid random variables taking values in a finite set, and consider the problem of estimating the law of X 1 in a Bayesian framework. We prove that the sequence of posterior...

Large deviations for queue lengths at a multi-buffered resource (1998)

The linear geodesic property is not generally preserved by a FIFO queue (1998)

In this paper we obtain the large deviation principle for scaled queue lengths at a multi-buffered resource, and simplify the corresponding variational problem in the case where the inputs are...

Ganesh, A. J., O'Connell, Neil

If a FIFO queue is fed by several input streams that jointly satisfy a sample path large deviation principle (LDP) with "linear geodesics," then the cumulative departures (up to a large time) also...

The Linear Geodesic Property is Not Generally Preserved By a Fifo Queue (1996)

A. J. Ganesh, Neil O'connell, Accepted Ann

If a FIFO queue is fed by several input streams that jointly satisfy a sample path large deviation principle (LDP) with `linear geodesics', then the cumulative departures (upto a large time)...

Queue Lengths and Departures at Single-Server Resources (1996)

Large Deviations for Queue Lengths at a Multi-Buffered Resource (1995)

In this paper I will review and illustrate some large deviation results for queues with interacting traffic, both for shared buffer and shared capacity models. These results are examples of a general...

Large Deviations in Queueing Networks (1995)

We solve a variational problem that arises in consideration of the large deviation properties of queue lengths at a multi-buffered resource.

Predicting Quality of Service for Traffic with Long-Range Fluctuations (1995)

In this paper we describe how the joint large deviation properties of traffic streams are altered when the traffic passes through a shared buffer according to a FCFS service policy with stochastic...

N.G. Duffield, J.T. Lewis, Neil O'Connell, Raymond Russell, Fergal Toomey

We present the tail asymptotics in a queue serviced at constant rate and whose input process has long-range dependence, for example, fractional Brownian Motion (fBM) with Hurst parameter H ? 1=2....

Entropy Of ATM Traffic Streams: A Tool For Estimating QoS Parameters (1995)

N.G. Duffield, J.T. Lewis, Neil O'Connell, Raymond Russell, Fergal Toomey

this paper, we are concerned with the components of cell-loss and cell-delay which are attributable to a single buffer of finite size. The QoS parameters we are concerned with are:

Branching and Inference in Population Genetics (1994)