Booklet of the conferenceThis is the booklet for print use.
Full abstracts with all authors can be found at:https://40yearsofrbm.wp.imt.fr/

Contents

About
Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Date and place . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Scientiﬁc committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Organizing committee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Invited speakers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sponsors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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4

Timetable
Monday, April 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tuesday, April 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Wednesday, April 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thursday, April 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Friday, April 28 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

5
6
7
8
9
10

List of Abstracts – Talks
Monday, April 24 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Tuesday, April 25 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Wednesday, April 26 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Thursday, April 27 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Friday, April 28 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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List of Participants

26

List of Posters

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Special issue of « Queueing Systems »29

Useful Information
Place . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Accommodation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Meals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Excursion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Poster session . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Wiﬁ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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Partner Institutions and Sponsors

313AboutDescription
The conference will bring together various researchers working on reﬂected stochastic processes
and their applications in other ﬁelds of mathematics. The conference will reﬂect the diversityof RBM topics: from the historical beginnings of the study of RBM to new developments andapplications.

Date and place
The conference take place in April 24-28, 2023 in Brittany in France, in the (small) city of Roscoﬀ,
where there is a beautiful CNRS conference center.

Scientiﬁc committee
Irina Kurkova

Jean-François Le Gall

Michel Mandjes

Ruth Williams

Organizing committee
Sandro Franceschi

Héléne Guerin

Kilian RaschelInvited speakers
Sebastian Andres
Onno Boxma
Xinyun Chen
Krzysztof Debicki
Mike Harrison
Sara Mazzonetto
Josh Reed

Rami Atar
Jose Blanchet
Maury Bramson
Amarjit Budhiraja
Zhen-Qing Chen
Cristina Costantini
Manon Defosseux
Philip Ernst
Ioannis Karatzas
David Lipshutz
Masakiyo Miyazawa Amber Puha
Martin Reiman
Gregory Schehr

Mireille Bousquet Mélou
Krzysztof Burdzy
Jim Dai
Mihai Gradinaru
Michel Mandjes
Kavita Ramanan
Ruth Williams

Sponsors
This meeting is funded by the Centre Henri Lebesgue, the ANR JCJC grant « RESYST » and the ERC
grant « Elliptic Combinatorics ».

4Timetable

The conference starts at 9 a.m. every day.
The conference can be followed online at the zoom link.
https://us02web.zoom.us/j/81950888340?pwd=djZTQzBXQ2FZQm1EaGhjR2xYTldYUT09

5

IS Invited Speaker RT Remote talk PD PhD or Postdoc.

Monday, April 24
9:00–9:20
9:20–9:30
Chairman
9:30–10:10

IS

10:10–10:50

IS

10:50–11:10
11:10–11:50

IS

11:50–12:30

IS

13:00
Chairman
15:00–15:40

IS

15:40–16:20

IS

12:20–16:40
16:40-17:20

IS

17:20-17:50

RT

19:30

6

Welcome coﬀee
Introduction of the organizers
Oﬀer Kella
Drift control of high-dimensional RBM:
Mike Harrison
A computational method based on
Stanford University
neural networks
A Skorohod problem for the heat
Rami Atarequation and particle systems withTechnion
selection
Coﬀee
Sebastian Andres
RBM meets RCM
University of Manchester
Krzysztof Burdzy
On the spine of Fleming-Viot process
University of Washington
Lunch
John Hasenbein
Invariant Measures of the Inﬁnite Atlas
Amarjit Budhiraja
Model: Domains of Attraction,
University of North Carolina
Extremality, and Equilibrium
at Chapel Hill
Fluctuations
Krzysztof Debicki
Extremes of reﬂected GaussianMathematical Institute,
processes
University of Wroclaw
Coﬀee
Harrison-Williams
RBM and Queueing Theory: An Early
Stanford University andHistory
University of California
Ruth Williams
Biochemical reaction networks andUniversity of California, San
reﬂecting diﬀusion processes
Diego
DinnerTuesday, April 25
Chairman
9:00–9:40

IS

9:40–10:20

IS

10:20–10:40
10:40–11:20

IS

11:20–12:00

IS

12:30
Chairman
15:00–15:40

IS

15:40–16:20

IS

12:20–16:40
16:40-17:10

RT

17:15-17:45

RT

17:50-18:20

RT

19:30

Guy Fayolle
Mireille Bousquet Mélou
On the stationary distribution of
CNRS, LaBRI, Université dereﬂected Brownian motion in a wedge
Bordeaux
Onno Boxma
Workload analysis of a two-queue ﬂuid
Eindhoven University ofpolling model
Technology
Coﬀee
Xinyun Chen
Asymptotic product-form stationary
Chinese University of Hongdistributions for reﬂected BrownianKong, Shenzhen
motions
Gregory Schehr
Universal order statistics for random
CNRS-Sorbonne Université
walks
Lunch
Frank Kelly
Jim Dai
Asymptotic steady-state independence
Cornell University andfor generalized Jackson networks in
CUHK-Shenzhen
multi-scale heavy traﬃc
Kavita Ramanan
Pathwise diﬀerentiability of reﬂected
Brown University
diﬀusionsCoﬀee
Asymptotic Control of Centralized
Jose Blanchet
Dynamic Matching Markets with
Stanford
General Utilities
Positive Recurrent Semimartingale
Maury Bramson
Reﬂecting Brownian Motion with
University of Minnesota
Divergent Fluid Paths
Martin Reiman
Parallel Server Systems under an
Columbia University
Extended Heavy Traﬃc Condition
Conference Dinner7

Wednesday, April 26
Chairmans
9:00–9:20

PD

9:20–9:40

PD

9:40–10:00

PD

10:00–10:20
10:20–10:40

PD

10:40–11:00

PD

11:00–11:20

PD

11:20–11:30
11:30–11:50

PD

11:50–12:10

PD

12:10–12:30

PD

13:00
14:30
18:30

19:30

8

Baris Ata and Aleks Mijatovic
Ben Estevez
Load Balancing in Parallel Queues andUniversity of North Carolina
Rank-based Diﬀusions
at Chapel Hill
Brownian motion with asymptotically
Miha Bresar
normal reﬂection in unbounded
University of Warwick
domains: from transience to stability
Andreas Nessmann
Asymptotics of Random Walks in theTechnische Universität Wien,
Quarter Plane
Université de Tours
Coﬀee
Benjamin Housley
Extended Lévy’s Theorem for a
University of Manchester
Two-Sided Reﬂection
Zhiqiang Zhang
Routing in a Queueing Loss Model
The University of Chicago
under Imperfect Classiﬁcations
Booth School of Business
Isao Sauzedde
CLT for reﬂecting Brownian motion in
University of Warwick
generalized parabolic domains
Coﬀee
Jin Guang
Uniform Moment Bounds for
The Chinese University ofGeneralized Jackson Networks in
Hong Kong, Shenzhen
Multi-scale Heavy TraﬃcRoyi Jacobovic
The moments of polynomial
University of Amsterdamfunctionals in Levy-driven queues
Charlie Hérent
An inverse Pitman’s theorem for a
Université Paris Cité /space-time brownian motion in a type
Université Gustave Eiﬀel
A11 Weyl chamber
Lunch
Excursion to Ile de Batz
Poster session at the Gulf Stream Hôtel
Miha Bresar, Khalifa Es-Sebaiy, Jules Flin,
Jin Guang, Maxence Petit, Zhiqiang Zhang
DinnerThursday, April 27
ChairmanPeter Lakner

9:O0–9:30

RT

9:30–10:10

IS

10:10–11:40
10:40–11:20

IS

11:20–12:00

IS

12:30
Chairman
15:00–15:40

IS

15:40–16:20

IS

12:20–16:40
16:40-17:20

IS

17:20-17:40

PD

17:40–17:50
17:50-18:10

PD

18:10-18:30

PD

19:30

Masakiyo Miyazawa
Tokyo University of Science
Cristina Costantini
Università di Chieti-Pescara

Palm problems arising in BAR approach
Obliquely reﬂecting diﬀusions incurved, nonsmooth domains

Coﬀee
Philip Ernst
On the diameter of the stopped spider
Imperial College London
processZhen-Qing Chen
Approximation of Liouville Brownian
University of Washington
motionLunch
François Chapon
Amber Puha
Diﬀusion Limits for Multiclass
California State University
Processor Sharing Queues
San Marcos
Sensitivity analysis of obliquelyDavid Lipshutz
reﬂected diﬀusions in convex
Flatiron Institutepolyhedral domains
Coﬀee
Mihai Gradinaru
Lévy driven non-linear Langevin type
IRMAR
equations
Jodi Dianetti
Multidimensional singular control andCenter for Mathematical
related Skorokhod problem: suﬃcient
Economics, Bielefeld
conditions for the characterization of
University
optimal controls
Coﬀee
Matsumoto-Yor and Dufresne type
Jonas Arista
theorems for a random walk on
Bielefeld University
positive deﬁnite matrices
Will FitzGerald
Reﬂected Brownian motions andUniversity of Manchester
random growth models
Dinner9

Friday, April 28
Chairman
9:00–9:40

IS

9:40–10:20

IS

10:20–10:40
10:40–11:20

IS

11:20–12:00

IS

12:15

10

Tomoyuki Ichiba
Lévy driven queues: the workload
Michel Mandjes
correlation function is positive,
Univ. of Amsterdam
decreasing and convex
Sara Mazzonetto
Parameter estimation for skew/sticky
Université de LorraineBM
Coﬀee
Josh Reed
RBM with Drift in a Wedge
NYU Stern
Ioannis Karatzas
Competing diﬀusive particle systems
Columbia University
and models of large equity markets
Lunch
End

List of Abstracts – Talks

Monday, April 24
Drift control of high-dimensional RBM: A computational method based on neuralnetworks
Mike Harrison Stanford University

IS

We consider a stochastic control problem whose state space is the d-dimensional non-negative orthant.
The controlled process Z evolves as a reﬂected Brownian motion whose covariance matrix is exogenously
speciﬁed, as are its directions of reﬂection from the orthant’s boundary surfaces. A controlling agent chooses
a drift vector at each time t based on the history of Z, and the cost rate at time t depends on both Z(t) andthe drift rate chosen. In our initial problem formulation, the objective is to minimize expected discounted
cost over an inﬁnite planning horizon, after which we treat the corresponding ergodic control problem.
Extending earlier work by Han et al. (Proceedings of the National Academy of Sciences, 2018, 8505-8510), we
develop and illustrate a simulation-based computational method that relies heavily on deep neural network
technology. Our method is accurate to within a fraction of one percent, and is computationally feasible indimensions up to at least d=20. (Based on joint work with Baris Ata and Nian Si.)A Skorohod problem for the heat equation and particle systems with selection
Rami Atar Technion

IS

Hydrodynamic limits of particle systems with selection are related to free boundary problems (FBP) associatedwith second order parabolic PDE. This relation has been established rigorously for some selection models
while it remains open for others, where the diﬃculty lies in questions of regularity of the free boundary. We
introduce a weak formulation of FBP in the form of a Skorohod problem for the PDE. It does not involvea free boundary at all, but at the same time reduces to a FBP provided the latter has a classical solution.
The weak formulation allows us to avoid regularity questions and characterize limits in terms of the PDE incases where classical solutions are expected to but not known to exist, as well as in cases where they are
not expected to exist.

11

RBM meets RCM
Sebastian Andres University of ManchesterIS

The random conductance model (RCM) is a well-established model for a random walk in random environment which has been object of intensive study in the last 15 years. Central questions of interest include
homogenisation results such as functional central limit theorems for the random walk or local limit theorems
for its heat kernel. In this talk we will review those results where one main focus will be on invarianceprinciples for RCMs on domains for which convergence towards reﬂected Brownian motion (RBM) has been
established by Chen, Croydon and Kumagai (A0P 2015). In the last part we will present a local limit theorem
for the killed Green function on strongly regular domains for ergodic conductances only satisfying a moment
condition. As an application we obtain scaling limits for inhomogenous discrete Gaussian free ﬁelds withrandom conductances. The last part is based on a joint work in progress with Martin Slowik (Mannheim)
and Anna-Lisa Sokol (Berlin).

On the spine of Fleming-Viot process
Krzysztof Burdzy University of Washington

IS

A Fleming-Viot process is a system of n particles driven by independent copies of a driving Markov process.
When one of the particles hits the boundary of the domain, it is killed, and some other particle branches.
There is only one inﬁnite path (spine) in the branching structure. Under some assumptions, when n goes toinﬁnity, the distribution of the spine converges to the distribution of the driving Markov process conditioned
to avoid the boundary of the domain forever. Based on joint articles with M. Bieniek, J. Englander, and T.
Tadic.

Invariant Measures of the Inﬁnite Atlas Model: Domains of Attraction, Extremality, and Equilibrium Fluctuations
Amarjit Budhiraja University of North Carolina at Chapel Hill

IS

The inﬁnite Atlas model describes a countable system of competing Brownian particles where the lowest
particle gets a unit upward drift and the rest evolve as standard Brownian motions. The stochastic processof gaps between the particles in this model is described by an inﬁnite dimensional Skorohod problem. This
Markov process does not have a unique stationary distribution and in fact there is a one parameter familyp(a),a>= 0 of product form mutually singular stationary distributions. We say that an initial distribution ofgaps is in the weak domain of attraction of the stationary measure p(a) if the time averaged laws of thestochastic process of the gaps, when initialized using that distribution, converge to p(a) weakly in the large
time limit. We provide general suﬃcient conditions on the initial gap distribution of the Atlas particles for it
to lie in the weak domain of attraction of p(a) for each a. Results on extremality and ergodicity of p(a) will
also be presented. Finally, we will introduce a SPDE that describes equilibrium ﬂuctuations associated withp(a). This is based on joint works with Sayan Banerjee and Peter Rudzis.

12Extremes of reﬂected Gaussian processes
Krzysztof Debicki Mathematical Institute, University of Wroclaw

IS

We derive exact asymptotics of the tail distribution of extreme-type functionals of reﬂected (at 0) Gaussian
processes with stationary increments. Then, we turn to the multidimensional case for which we analyse
asymptotic properties of the probability of hitting the upper orthant.

RBM and Queueing Theory: An Early History
Mike Harrison1 Ruth Williams2 1 Stanford University 2 University of California

IS

In this talk we will recap the development of RBM as a limit of, or approximation for, conventional discreteﬂow queueing models. Emphasis will be on the speakers’ personal experiences and personal involvement inthe ﬁeld between 1960 and 2000.

Biochemical reaction networks and reﬂecting diﬀusion processes
Ruth Williams University of California, San Diego

RT

In 2019, Leite and Williams proposed certain reﬂected diﬀusion processes as approximations to continuous
time Markov chain models frequently used to model biochemical reaction networks. These diﬀusions live inthe positive orthant of a d-dimensional space and are conﬁned there by a smoothly varying oblique reﬂection
ﬁeld on the boundary. Leite and Williams showed that, under mild conditions, these diﬀusions can beobtained as weak limits of certain jump-diﬀusion extensions of the traditional Langevin approximations, andtherefore called these constrained Langevin approximations. In this talk, we will review this approximationand describe some progress on proving error estimates for strong versions of this approximation and also
describe some remaining open problems. Part of this work is joint with Felipe Campos.

13

Tuesday, April 25
On the stationary distribution of reﬂected Brownian motion in a wedge
Mireille Bousquet Mélou CNRS, LaBRI, Université de BordeauxIS

We consider the classical problem of determining the stationary distribution of the semimartingale reﬂected
Brownian motion (SRBM) in a two-dimensional wedge. We focus on the algebraic and diﬀerential natureof the Laplace transform of this stationary distribution. We derive necessary and suﬃcient conditions
for this Laplace transform to be a rational, algebraic, diﬀerentially ﬁnite or more generally diﬀerentiallyalgebraic function (meaning that it satisﬁes a polynomial diﬀerential equation). These conditions are simple
explicit linear dependencies between the angles of the model. We thus recover in particular the Dieker andMoriarty conditions for rationality. In the D-algebraic case, we obtain moreover simple, explicit integral-free
expression in terms of a hypergeometric function. To prove these results, we start from a functional equationthat the Laplace transform satisﬁes, to which we apply a variety of tools ranging from combinatorics to
Galois theory.
This is a joint work with Andrew Elvey Price, Sandro Franceschi, Charlotte Hardouin and Kilian Raschel.

Workload analysis of a two-queue ﬂuid polling model
Onno Boxma Eindhoven University of Technology

IS

We analyze a two-queue random time-limited Markov modulated polling model. Fluid arrives at the twoqueues as two independent ﬂows with deterministic rates. A single server serves both queues at constant
speeds, alternatingly spending an exponentially distributed amount of time in each queue and experiencing
no switchover time. We derive a functional equation for the Laplace-Stieltjes transform of the stationary
joint ﬂuid content (workload) distribution, that leads to a Riemann-Hilbert boundary value problem (BVP).
After taking a heavy-traﬃc limit, and restricting ourselves to the symmetric case, the boundary value problem
simpliﬁes and can be solved explicitly. Next, allowing for more general (Levy) input processes and serverswitching policies, we investigate the transient process-limit of the joint workload in heavy traﬃc, exploiting
the RBM theory. Again solving a BVP, we determine the stationary distribution of the limiting process. We
show that, in the symmetric case, this distribution coincides with our earlier BVP solution, implying that inthis case the two limits (stationarity and heavy traﬃc) commute.
Joint work with Stella Kapodistria, Oﬀer Kella and Mayank Saxena.

Asymptotic product-form stationary distributions for reﬂected Brownian motions
Xinyun Chen Chinese University of Hong Kong, ShenzhenIS

We prove that a sequence of multi-scaled stationary distributions of reﬂected Brownian motions (RBMs)
has a product-form limit. Each component in the limit is an exponential distribution. The multi-scalingcorresponds to the « multi-scale heavy traﬃc » recently advanced in Dai, Glynn and Xu (2023) for generalized
Jackson networks. The proof utilizes the basic adjoint relationship (BAR) ﬁrst introduced in Harrison andWilliams (1987) that characterizes the stationary distribution of an RBM. This is a joint work with Jin Guangat CUHK-Shenzhen, Jim Dai at Cornell, and Peter Glynn at Stanford.

14

Universal order statistics for random walks
Gregory Schehr CNRS-Sorbonne UniversitéIS

I will study the statistics of the gaps ∆k,n between the k th and (k + 1)th maximum of the set of positions{x1 , . . . , xn } of a random walk after n steps, starting from the origin. I will discuss the case of continuous
jump distributions f (η), with a corresponding Lévy index 0 < µ ≤ 2. I will show that one can obtain an exact
analytical expression for the probability distribution Pk,n (∆) valid for any k and n, and jump distributionf (η), which is amenable to an asymptotic large n analysis. In this limit, one ﬁnds that the gap distribution
becomes stationary, i.e., limn→∞ Pk,n (∆) = Pk (∆). Furthermore, for µ > 1, I will show that in the limit of
k → ∞ the stationary distribution exhibits a universal scaling form Pk (∆) ∼ k 1−1/µ Pµ (k 1−1/µ ∆) which
depends only on the Lévy index µ, but not on the details of the jump distribution. This limiting scaling
function Pµ (x) can be computed explicitly in terms of Mittag-Leﬄer functions.

Asymptotic steady-state independence for generalized Jackson networks in multiscale heavy traﬃc
Jim Dai Cornell University and CUHK-ShenzhenIS

We prove that under a multi-scale heavy traﬃc condition, the stationary distribution of the scaled queue
length process in any generalized Jackson network has a product-form limit. Each component in the productform has an exponential distribution, corresponding to the Brownian approximation of a single station queue.
Each “single station” can be constructed precisely and its parameters have a good intuitive interpretation. The
proof employs a basic adjoint relationship (BAR)-approach that has been advanced recently by Braverman,
Dai, and Miyazawa (2017, 2023). This is a joint work with Peter Glynn at Stanford and Yaosheng Xu at
Amazon.

Pathwise diﬀerentiability of reﬂected diﬀusions
Kavita Ramanan Brown UniversityISDiﬀerentiability of ﬂows and sensitivity analysis are classical topics in dynamical systems. In the stochastic
context, stochastic ﬂows have been well studied by Kunita and others. However, the analysis of theseproperties for constrained or reﬂected processes, which arise in a variety of applications, is challenging due
to the discontinuous dynamics at the boundary of the domain, and is further complicated when the boundary
is non-smooth. We show that the study of both diﬀerentiability of ﬂows and sensitivities of constrained
processes in convex polyhedral domains can be largely reduced to the study of directional derivatives ofan associated map, called the Skorokhod map, and we introduce an axiomatic framework to characterizethese directional derivatives. In addition, we establish pathwise diﬀerentiability of a large class of reﬂected
diﬀusions in convex polyhedral domains and show that they can be described in terms of certain constrained
stochastic diﬀerential equations with time-varying domains and directions of reﬂection. This is based on
joint works with David Lipshutz.

15

Asymptotic Control of Centralized Dynamic Matching Markets with General Utilities
Jose Blanchet Stanford

RT

We consider a matching market where buyers and sellers arrive according to Poisson processes. Participants
abandon at a constant rate — independent of the arrivals. The utility for matching a given buyer with a seller
is a general random variable. The utilities are i.i.d. and independent of arrivals and abandonment. We study
this market in heavy-traﬃc and analyze two families of policies: a) the population threshold policy, matching
an arriving agent to its best available mate only if the number of mates in the system is above a threshold, andb) the utility threshold policy, matching an arriving agent to its best available mate only if the corresponding
utility is above a threshold. We obtain a Skorokhod problem which we use to characterize optimal (utility
maximization) population threshold policies depending on the domain of attraction corresponding to theutilities. Analogous characterizations for optimal utility-based threshold policies are also discussed. This talkis based on joint work with Martin I. Reiman, Virag Shah, Lawrence M. Wein, Linjia Wu.

Positive Recurrent Semimartingale Reﬂecting Brownian Motion with Divergent
Fluid Paths
Maury Bramson University of Minnesota

RT

Fluid paths correspond to the paths of a semimartingale reﬂecting Brownian motion (SRBM), but with therandomness removed. Their behavior is therefore often easier to analyze than that of the corresponding
SRBM. In Dupuis and Williams (1994), it was showed that, in any dimension d, if every ﬂuid path is attracted
to the origin, then the corresponding SRBM must be positive recurrent.
It remained unknown whether the converse direction always holds. In d=2, the proof that the converse
holds is relatively straightforward, but the proof in d=3 is more complex. A similar approach in d=4 alreadybecomes unmanageable because of the many possible cases that need to be analyzed.
In Bramson (2011), examples were given, in d>5, with divergent ﬂuid paths whose corresponding SRBM
are positive recurrent. In these examples, the covariance matrix for the SRBM is the identity matrix I. The
existence of examples in d=4 and d=5 was left open. Heyda has recently produced examples in d=4 and d=5
with divergent ﬂuid paths whose corresponding SRBM are positive recurrent. For the examples in d=5, thecovariance matrix is I; for the examples in d=4, a diﬀerent covariance matrix is needed.
In this talk, we will summarize the above results in d>5, and how related techniques can be applied in d=4
and d=5.

16

Parallel Server Systems under an Extended Heavy Traﬃc Condition
Martin Reiman Columbia University

RT

Parallel server systems (PSS) are queueing control problems with a relatively simple structure. There are
I classes of customers and K servers, and the service rate depends on the class-server pair. The controls
involve both deciding which server serves each customer, as well as the order in which they are served.
The objective is to minimize the expected inﬁnite horizon total discounted cost, where the cost rate is alinear function of the queue length vector. A linear program (LP) known as the static allocation problem wasintroduced in order to deﬁne heavy traﬃc for these systems. Previous work on PSS made the key assumptionthat the static allocation LP has a unique solution. We relax this assumption, introducing the extended heavy
traﬃc condition, which allows multiple solutions. The existence of multiple solutions to the LP introducescomplications in the treatment of this problem. In particular, there is now freedom to choose among the LP
solutions, which determine the ﬂuid scale allocation of eﬀort by the servers. This non-deterministic ﬂuid
limit leads to technical problems along with a more complicated limiting workload control problem (WCP).
Under the additional assumption of complete resource pooling, we provide an asymptotic lower bound on
the achievable cost in terms of the solution of the WCP. In addition, for the simple special case of I=K=2,
where the WCP is solvable, we translate the optimal control into a control policy for the original PSS andprove that it is asymptotically optimal. (Based on joint work with Rami Atar and Eyal Castiel.)

Wednesday, April 26
Load Balancing in Parallel Queues and Rank-based Diﬀusions
Ben Estevez University of North Carolina at Chapel HillPD

We analyze heavy traﬃc limits and stationary distributions of rank-based routing policies where incoming
jobs are routed to servers with probability depending on their ranked queue-lengths. The limiting reﬂected
diﬀusions are connected to the gaps between particles in rank-based diﬀusions like the Atlas model. We
discuss in particular the special case where a small fraction of the incoming jobs is channeled to theshortest queue and the rest are uniformly routed, which we call the marginal join-the-shortest-queue (MJSQ)
policy, and compare this to well-known load balancing schemes. This policy signiﬁcantly reduces overhead
communication costs compared to the asymptotically optimal join-the-shortest-queue policy, but we haveshown that it nevertheless achieves comparable performance. Even when the whole system is unstable, wehave shown that the gap between the maximum and minimum queue length under MJSQ is tight, exhibiting
a novel form of load balancing. The stationary distributions of the limiting diﬀusion processes (for the generalrank-based routing policies) are identiﬁed as product laws of Exponential random variables. The associatedstatistics of the pre-limiting process have been shown to converge to those of the limiting diﬀusion as theheavy traﬃc parameter goes to inﬁnity.
Joint work with Sayan Banerjee and Amarjit Budhiraja.

17

Brownian motion with asymptotically normal reﬂection in unbounded domains:from transience to stability
Miha Bresar University of Warwick

PD

We quantify the asymptotic behaviour of multidimensional driﬂtess diﬀusions in domains unbounded
in a single direction, with asymptotically normal reﬂections from the boundary. We identify the critical
growth/contraction rates of the domain that separate stabil- ity, null recurrence and transience. In thestable case we prove existence and uniqueness of the invariant distribution and establish the polynomial
rate of decay of its tail. We also establish matching polynomial upper and lower bounds on the rate ofconvergence to stationarity in total variation. All exponents are explicit in the model parameters that
determine the asymptotics of the growth rate of the domain, the interior covariance, and the reﬂection
vector ﬁeld. Proofs are probabilistic, and use upper and lower tail bounds for additive functionals up to
return times to compact sets, for which we develop novel sub/supermartingale criteria, applic- able togeneral continuous semimartingales. Narrowing domains fall outside of the standard literature, in part
because boundary local time can accumulate arbitrarily rapidly. Establishing Feller continuity (essential
for characterizing stability) thus requires an extension of the usual approach. Our recurrence/transienceclassiﬁcation extends previous work on strictly normal reﬂections, and expands the range of phenomena
observed across all dimensions. For all recurrent cases, we provide quantitative information through upperand lower bounds on tails of return times to compact sets.
(Based on joint work with Aleks Mijatovic and Andrew Wade)

Asymptotics of Random Walks in the Quarter Plane
Andreas Nessmann Technische Universität Wien, Université de ToursPD

The main question posed in this presentation will be about the behaviour of the number of lattice paths
starting from a ﬁxed point and ending at (possibly another) ﬁxed point, where we let the number of steps
go to inﬁnity. As the scaling limit of a random walk is a Brownian motion, it is not all that surprising thatthese asymptotics closely resemble those of the equivalent continuous problem; something that has beenshown for the ﬁrst order terms in 2011 by Denisov and Wachtel. In this presentation it will be shown that forﬁnite, orbit-summable models a generalisation of their result holds, which allows us to write an asymptotic
expansion as a series of polyharmonic functions with polynomial weights.

Extended Lévy’s Theorem for a Two-Sided Reﬂection
Benjamin Housley University of ManchesterPD

We aim to set forth an extension of the result found in paper [2], which ﬁnds an explicit realisation of areﬂecting Brownian motion with drift −µ , started at x , reﬂecting above zero, and its local time at zero. In
this paper we ﬁnd a corresponding realisation for a reﬂecting Brownian motion with drift −µ, started at x,
reﬂected both above zero and below one, along with a corresponding expression in terms of associatedlocal times, namely as the diﬀerence between the local time at zero and the local time at one.

18

Routing in a Queueing Loss Model under Imperfect Classiﬁcations
Zhiqiang Zhang The University of Chicago Booth School of BusinessPD

Motivated by reducing the recidivism (reoﬀense) rate in criminal justice we study a multiclass loss model(multiclass G/M/s/s+M) to help determine admission decisions to incarceration diversion programs thathave limited capacities, which serves as an alternative to incarceration and could lower the likelihood ofrecidivism but cannot prevent reoﬀense while in the program. Service time in the model corresponds totime in the diversion program, and reneging corresponds to an oﬀense being committed while in service. A(potentially imperfect) classiﬁcation algorithm predicts which individuals may beneﬁt the most from theprograms and which individuals have the most risk to recidivate. The admission decisions aim to minimize
the long-run average total cost, which consists of recidivism cost, diversion program cost, and incarceration
cost. The major trade-oﬀ is to whether admit the current arriving individual or reserve the spot for upcoming
individuals who could potentially beneﬁt more. We ﬁrst formulate a ﬂuid control problem and show thatthe solution to that ﬂuid control problem motivates using a simple prioritization scheme to determine
admission decisions, assuming either no prediction error or existence of a stochastic ordering property.
Next, moving to diﬀusion control, under a heavy-traﬃc regime, we approximate the system state (program
population for diﬀerent classes) by a multi-dimensional reﬂected Brownian motion in a rectangle with lower
left-hand corner at the origin, and dimension equal to the number of classes. For a single class setting,the one-dimensional diﬀusion problem can be analytically solved. However, for the multiclass setting, themultidimensional diﬀusion control problem is analytically very challenging, and we are investigating potential
decomposition heuristics leveraging the priority schedule from the ﬂuid control to solve approximately.

CLT for reﬂecting Brownian motion in generalized parabolic domains
Isao Sauzedde University of WarwickPD

We consider an obliquely reﬂected Brownian motion in a 1+d dimensional domain given by the points (x, y)such that |y|d is smaller than a function which asymptotically grows as a (possibly negative) power of x.
Depending on that power and on the reﬂection ﬁeld, the resulting process has a diﬀerent behaviour at theﬁrst order: the x component can either explode in ﬁnite time, or be diﬀusive, or diverge toward inﬁnity as
any power of t greater than a half. In this last intermediate case, we will explain this ﬁrst order behaviour aswell as the central limit theorem that comes after.
This talk is based on a joint work with A. Mijatović and A. Wade.

Uniform Moment Bounds for Generalized Jackson Networks in Multi-scale Heavy
Traﬃc
Jin Guang The Chinese University of Hong Kong, Shenzhen

PD

We establish uniform moment bounds for steady-state queue lengths of generalized Jackson networks (GJN)
in multi-scale heavy traﬃc as recently proposed by Dai et al. [2022]. Uniform moment bounds lay thefoundation for further analysis of the limit stationary distribution. Our result can be used to verify the crucial
moment state space collapse (SCC) assumption in Dai et al. [2022] to establish a product-form limit of GJN in
the multi-scale heavy traﬃc regime. Our proof utilizes a novel basic adjoint relationship (BAR) approach tocharacterize the stationary distribution directly.

19

The moments of polynomial functionals in Levy-driven queues
Royi Jacobovic University of Amsterdam

PD

Consider the problem of computing the moments of the area beneath the workload process of a stable
M/G/1 queue during a busy period. This problem was introduced by Iglehart (1971) who solved the ﬁrst
moment. Later, Cohen (1978) solved the second moment and there are no existing results about higher
moments. In this work, we solve this long-standing problem in the setup of a Levy-driven queue. Speciﬁcally,
the main result of the current work is a new recursive formulae which yield all moments (including jointones) of polynomial functionals of the workload process. This is a joint work with Peter Glynn and Michel
Mandjes.

An inverse Pitman’s theorem for a space-time brownian motion in a type A11
Weyl chamberCharlie Hérent Université Paris Cité / Université Gustave EiﬀelPD

We present an inverse Pitman’s theorem for a space-time Brownian motion conditioned in Doob’s sense
to remain in an aﬃne Weyl chamber. Our theorem provides a way to recover an unconditioned spacetime
Brownian motion from a conditioned one applying a sequence of path transformations.

Thursday, April 27
Palm problems arising in BAR approach
Masakiyo Miyazawa Tokyo University of ScienceRT

We consider a Markov process with time homogeneous transitions which is jointly stationary with multiple
point processes. Assuming that these point processes have ﬁnite intensities, we deﬁne Palm distributions
concerning them. Motivated by a BAR (Basic adjoint relationship) approach, which extensively uses the Palm
distributions, we are interested in two problems; (a) when this stationary Markov process inherits the same
Markov structure under the Palm distributions, and (b) how the state changes at counting instants of thepoint processes can be handled to derive stationary equations when there are simultaneous counts andeach of them inﬂuences the state changes. We call (a) and (b) Palm problems.
For (a), we show that, if the Markov process is strong Markov, then it is again a strong Markov process under
the Palm distribution, and its transition operator is unchanged. However, the jump transition of the Markov
process at a counting instant of each point process may require the predictability of those instants. For (b),we make it clear under what framework it can be well handled. We also discuss how those results can beapplied in deriving BAR’s for queueing networks.

20

Obliquely reﬂecting diﬀusions in curved, nonsmooth domains
Cristina Costantini Università di Chieti-PescaraIS

Obliquely reﬂecting diﬀusions in curved, nonsmooth domains, arise, for instance, in diﬀusion approximationof certain stochastic networks (switched networks, networks operating under resource sharing). In a
polyhedral domain with constant direction of reﬂection on each face, Dai and Williams (1996) ﬁnd very
general conditions on the directions of reﬂection under which reﬂecting Brownian motion can be constructed
and uniquely characterized. These conditions are necessary for simple polyhedrons. For a curved, nonsmoothdomain and varying direction of reﬂection, there were several important results in the 1980s and 1990s, but
all of them under conditions restrictive in some respect. In this talk, after brieﬂy reviewing the main resultsin the literature, I will discuss a series of recent joint papers with T.G. Kurtz (published and unpublished)that present a new construction of semimartingale reﬂecting diﬀusions and new uniqueness results in some
types of domains. In particular, we obtain existence and uniqueness in a 2-dimensional piecewise smoothdomain, under very general, geometric, easily veriﬁable conditions. In fact our conditions are optimal in
the sense that they reduce to those of Dai and Williams (1996) in the case of a polyhedron with constantdirection of reﬂection on each face. Moreover our conditions allow for cusps in the boundary of the domain.
The construction part of our work is based on constrained martingale problems, while the uniquenesspart is based on a new reverse ergodic theorem for killed, inhomogeneous Markov chains that, in a sense,
generalizes the Krein-Rutman theorem used in Kwon and Williams (1991).

On the diameter of the stopped spider process
Philip Ernst Imperial College LondonIS

We consider the « Brownian spider » (Walsh Brownian motion), which is constructed as a set of half-lines, or“ribs,” meeting at a common point O. A Brownian motion on a spider starting at zero may be constructedfrom a standard reﬂecting Brownian motion by assigning an integer uniformly and independently to eachexcursion which is then transferred to an excursion on rib.
In the early 2000s, Lester Dubins posed the following problem: how can one design a stopping time tomaximize the coverage of Brownian motion on the spider for a given expected time? Dubins et al. (2009)
provided a solution to the optimal strategy for n=1,2 ribs, and Ernst (2016) gave an alternative solution tothat presented by Dubins et al. (2009). However, neither Dubins et al. (2009) nor Ernst (2016) succeeded inproviding a solution to the general question.
Over the past few years, we studied an alternative version of Dubins’ question in which the coverage or sizeof the spider process is measured diﬀerently. Instead of measuring the spider as the sum of the lengths of its
ribs, we consider the ‘true’ diameter, that is, the sum of the two longest ribs. The resulting optimal stopping
problem can, rather surprisingly, be completely solved. This work (to appear, Mathematics of Operations
Research, 2023) is joint with E. Bednarz and A. Osekowski.
The solution to the original formulation of the Dubins’ problem remains open.

21

Approximation of Liouville Brownian motion
Zhen-Qing Chen University of Washington

IS

Liouville Brownian motion was introduced as a canonical diﬀusion process under Liouville quantum gravity.
It is constructed as a time change of 2-dimensional Brownian motion by the continuous additive functional
associated with a Liouville measure, through a regularizing approximation procedure of the Gaussian freeﬁeld. In this talk, we are concerned with the question whether one can construct Liouville Brownian motion
directly from the Liouville measure. We will present a discrete approximation scheme that in fact works forany time-changed Brownian motion by a Revuz measure that has full support. Based on joint work with
Yang Yu.

Diﬀusion Limits for Multiclass Processor Sharing Queues
Amber Puha California State University San Marcos

IS

Consider a single server queue that serves a ﬁnite number heterogeneous job types according to theprocessor sharing service discipline. Measure valued processes that keep track of the residual service timesof all jobs in the system at any given time are a natural descriptor of the system state. Under appropriate
asymptotic assumptions, including standard heavy traﬃc assumptions, we show that (suitably rescaled)measure valued processes corresponding to a sequence of such queues converge in distribution to certain
measure valued diﬀusion processes. An important contribution of this work is to devise a new methodology
for establishing state-space collapse via the use of a certain relative entropy functional.

Sensitivity analysis of obliquely reﬂected diﬀusions in convex polyhedral domains
David Lipshutz Flatiron InstituteIS

Sensitivity analysis of an obliquely reﬂected diﬀusion in a convex polyhedral domain with respect to its
deﬁning parameters (initial condition, drift coeﬃcient, diﬀusion coeﬃcient and directions of reﬂection) is ofinterest from both theoretical and applied perspectives. In this talk, we characterize pathwise derivativesof such reﬂected diﬀusions in terms of solutions to a linear constrained stochastic diﬀerential equation
whose coeﬃcients, domain and directions of reﬂection depend on the state of the reﬂected diﬀusion.
We demonstrate how pathwise derivatives are useful in Monte Carlo methods to estimate sensitivities ofa reﬂected diﬀusion, and also in characterizing sensitivities of the stationary distribution of a reﬂection
Brownian motion. This work is joint with Kavita Ramanan.

Lévy driven non-linear Langevin type equations
Mihai Gradinaru IRMARIS

We will study a one-dimensional kinetic stochastic model driven by a stable Lévy process, and having a
non-linear time-inhomogeneous drift. More precisely, a process (V, X) is considered, where X is the
position of a particle having velocity V the solution of a stochastic diﬀerential equation with a drift of theform t−β F (V ) and driven by a stable process. The behaviour of the process (V, X) will be described fortwo diﬀerent situations : when the noise is small, or in large time but with ﬁxed noise.

22

Multidimensional singular control and related Skorokhod problem: suﬃcientconditions for the characterization of optimal controls
Jodi Dianetti Center for Mathematical Economics, Bielefeld University

PD

We characterize the optimal control for a class of singular stochastic control problems as the unique solution
to a related Skorokhod reﬂection problem. The optimization problems concern the minimization of adiscounted cost over an inﬁnite time-horizon through a process of bounded variation aﬀecting an Itôdiﬀusion. The setting is multidimensional, the drift of the state equation and the costs are convex, thevolatility matrix can be constant or linear in the state. Our result applies to a relevant class of linear-quadraticmodels and it allows to construct the optimal control in degenerate and non degenerate settings consideredin the literature.

Matsumoto-Yor and Dufresne type theorems for a random walk on positivedeﬁnite matrices
Jonas Arista Bielefeld University

PD

We establish analogues of the geometric Pitman 2M − X theorem of Matsumoto and Yor and of the classicalDufresne identity, for a multiplicative random walk on positive deﬁnite matrices with Beta type II distributed
increments. The Dufresne type identity provides another example of a stochastic matrix recursion that
admits an explicit solution.

Reﬂected Brownian motions and random growth models
Will FitzGerald University of ManchesterPD

I will discuss an identity between the invariant measure of a reﬂected system of Brownian motions anda vector of point-to-line last passage percolation times. By time reversal, this describes the distributionof the maximum over all time of the largest eigenvalue in Dyson Brownian motion with negative drifts. A
positive temperature version relates the point-to-line partition functions of two directed polymers in an
inverse-gamma and Brownian environment, and generalises Dufresne’s identity.

23

Friday, April 28
Lévy driven queues: the workload correlation function is positive, decreasing
and convex
Michel Mandjes Univ. of Amsterdam

IS

In this talk I will consider Lévy-driven queues, i.e., reﬂected Lévy processes, generalising the class of reﬂected
Brownian motions, with a focus on structural properties of the workload correlation function. After having
introduced the objects studied, I’ll proceed by stating the conjecture that has been around for quite a while,
namely that the workload correlation is a positive, decreasing and convex function of time. As a historicaccount, I’ll brieﬂy discuss the seminal contribution by Ott on the special case of the M/G/1 queue, basedon exploiting properties of complete monotone functions. The same methodology has been used in theextension (by Es-Saghouani and me) to queues with spectrally positive Lévy input, whereas later (in a paper
by Glynn and me) the spectrally negative case was dealt with. For a long time, there was little hope to provethe conjecture for general Lévy input (and, for that matter, for reﬂected random walks in discrete-time).
In a recent paper (that I wrote with Berkelmans and Cichocka), we provide an elementary proof, only
relying on basic properties of Lévy processes and their reﬂected version. Importantly, the argumentation
extends to double reﬂection, and also covers reﬂected random walks. Time permitting, I also discuss various
ramiﬁcations due to Kella and me, and I comment on the question whether the structural properties carryover to the Markov modulated case.

Parameter estimation for skew/sticky BM
Sara Mazzonetto Université de LorraineIS

In this talk we consider some one-dimensional diﬀusions whose behavior is perturbed by a barrier-point.
The perturbation nature of partial-reﬂection (skew BM) or sticky is encoded by a parameter. Our goal is to
discuss parameter estimation from high-frequency observations of a trajectory. In particular, in the case of
skew BM we discuss the main properties of the Maximum Likelihood Estimator (MLE) such as asymptotic
mixed normality with a non standard rate of 1/4 and the behavior for all possible values of the parameter.
Moreover, thanks to a recent asymptotic inverse function theorem, we give an inﬁnite series expansionof the MLE. This talk is partially based on a joint works with A. Anagnostakis (LJK Grenoble) and A. Lejay(IECL/Inria Nancy)

24

RBM with Drift in a Wedge
Josh Reed NYU SternIS

We study reﬂecting Brownian motion with drift constrained to a wedge in the plane. Our ﬁrst set of results
provide necessary and suﬃcient conditions for existence and uniqueness of a solution to the corresponding
submartingale problem with drift. Next, we study a version of the problem with absorption at the vertex of
the wedge. In this case, we provide a condition for existence and uniqueness of a solution to the problem
and some results on the probability of the vertex being reached. We also prove that in the case of 1 <alpha < 2, RBM in a wedge is a Dirichlet process. Speciﬁcally, its unique Doob-Meyer type decompositionis given by Z=X+Y, where X is a two-dimensional Brownian motion and Y is a continuous process of zeroenergy. Furthermore, we show that for p > alpha , the strong p-variation of the sample paths of Y is ﬁnite oncompact intervals, and, for 0 < p <= alpha, the strong p-variation of Y is inﬁnite on [0,T] whenever Z has been
started from the origin. We also show that on excursion intervals of Z away from the origin, (Z,Y) satisﬁes thestandard Skorokhod problem for X. However, on the entire time horizon (Z,Y) does not satisfy the standard
Skorokhod problem for X, but nevertheless we show that it satisﬁes the extended Skorkohod problem.

Competing diﬀusive particle systems and models of large equity markets
Ioannis Karatzas Columbia UniversityIS

We introduce and study stable multidimensional diﬀusions interacting through their ranks. These interactions
give rise to invariant measures which are in broad agreement with stability properties observed in large
equity markets over long time-periods. The models we present assign growth rates and variances that
depend on both the name (identity) and the rank (according to capitalization) of each individual asset. Suchmodels are able realistically to capture certain critical features of the observed stability in capital distribution
over the past century, all the while being simple enough to allow for rather detailed analytical study.
The methodologies used in this study touch upon the question of triple points for systems of competing
diﬀusive particles; in particular, some choices of parameters may permit triple (or higher-order) collisions tooccur. We show, however, that such multiple collisions have no eﬀect on any of the stability properties of
the resulting system. This is accomplished through a detailed analysis of collision local times.
The models have connections with the analysis of Queueing Networks in heavy traﬃc, with multi-dimensional
Diﬀusions reﬂected on the faces of the positive orthant, and with competing particle systems in Statistical
Mechanics (e.g., Sherrington- Kirkpatrick model for spin-glasses). Their hydrodynamic-limit behavior isgoverned by generalized porous medium equations with convection, and the ﬂuctuations around these limits
by appropriate linear stochastic partial diﬀerential equations of parabolic type with additive noise. Whereas,
limits of a diﬀerent kind display phase transitions and are governed by Poisson-Dirichlet distributions. We
survey progress on some of these fronts, and suggest open problems for further study.

25

List of Participants

AndresAristaAssiotisAta
Atar
Blanchet
Bousquet-Mélou
Boxma
BramsonBresarBudhiraja
BurdzyChaponChaumont
Chen
Chen
Costantini
Dai
DebickiDefosseux
Dianetti
Ernst
Es-Sebaiy
Estevez
FayolleFerrari
FitzGerald
FlinFranceschi
Gradinaru
Guang
GuérinHarrison
Hasenbein
HérentHousley
IchibaIgnatiouk-Robert
Jacobovic
Karatzas
Kella

26

Sebastian
Jonas
Theo
Baris
Rami
Jose
Mireille
Onno
Maury
Miha
AmarjitKrzysztof
FrancoisLoïcXinyunZhen-Qing
Cristina
Jim
Krzysztof
Manon
Jodi
PhilipKhalifa
Benjamin
Guy
GiorgioWill
Jules
SandroMihai
Jin
HélèneJ. Michael
John
Charlie
BenjaminTomoyuki
Irina
Royi
IoannisOﬀer

University of Manchester
Bielefeld University
University of Edinburgh
University of Chicago
Technion
Stanford
CNRS, LaBRI, Université de Bordeaux
Eindhoven University of Technology
University of Minnesota
University of Warwick
University of North Carolina at Chapel Hill
University of Washington
Institut de Mathématiques de Toulouse
Université d’Angers
Chinese University of Hong Kong, Shenzhen
University of Washington
Università di Chieti-Pescara
Cornell University and CUHK-Shenzhen
Mathematical Institute, University of Wroclaw
Université Paris Cité
Center for Mathematical Economics, Bielefeld University
Imperial College London
Kuwait University
University of North Carolina at Chapel Hill
Inria (Paris Saclay)
Universität Bielefeld
University of Manchester
Université de Lorraine
Télécom SudParis
IRMAR
The Chinese University of Hong Kong, Shenzhen
Université du Québec à Montréal
Stanford University
University of Texas at Austin, USA
Université Paris Cité (MAP5) / Univ Gustave Eiﬀel (LIGM)
University of Manchester
University of California Santa Barbara
Université de Cergy-Pontoise
University of Amsterdam
Columbia University
The Hebrew University of Jerusalem

KellyKourkova
Krell
LaknerLipshutz
Mandjes
Mazzonetto
Mijatovic
Miyazawa
NessmannNguyenO’Connell
Petit
Puha
RamananRaschelReed
Sarantsev
Sauzedde
SchehrSi
WachtelWalshWilliams
Zhang

Frank
Irina
Nathalie
Peter
David
MichelSara
Aleksandar
Masakiyo
AndreasThi Trang
Neil
Maxence
Amber
KavitaKilianJosh
AndreyIsao
Gregory
Nian
VitaliHarrietRuth
Zhiqiang

University of Cambridge
Sorbonne Universite
université Rennes 1
New York University
Flatiron InstituteUniv. of Amsterdam
Université de Lorraine
University of Warwick
Tokyo University of Science
Technische Universität Wien, Université de Tours
Laboratoire de Mathématiques Bretagne Atlantique, UBS
University College Dublin
Sorbonne Université / ENS Rennes
California State University San Marcos
Brown University
CNRS, Université d’Angers
NYU Stern
University of Nevada, Reno
University of Warwick
CNRS-Sorbonne Université
The University of Chicago, Booth School of Business
Universität Bielefeld
Université d’Angers
University of California, San Diego
The University of Chicago Booth School of Business

27

List of Posters

Brownian motion with asymptotically normal reﬂection in unbounded domains:from transience to stability
Miha Bresar, University of Warwick

Wasserstein bounds in the CLT of the MLE for the drift coeﬃcient of a stochastic
partial diﬀerential equation
Khalifa Es-Sebaiy, Kuwait University

Absorption probability of a reﬂected Brownian in a cone and Tutte invariants
Jules Flin, Université de Lorraine - Télécom Sud Paris

Uniform Moment Bounds for Generalized Jackson Networks in Multi-scale Heavy
Traﬃc
Jin Guang, The Chinese University of Hong Kong, Shenzhen

Asymptotics of Green’s functions of reﬂected Brownian in a quadrant
Maxence Petit, Sorbonne Université - ENS Rennes

Routing in a Queueing Loss Model under Imperfect Classiﬁcations
Zhiqiang Zhang, The University of Chicago Booth School of Business28

Special issue of « Queueing Systems »Queueing Systems: Theory and Applications is seeking submissions to a forthcoming Special Issue
on Reﬂected Brownian Motion. Reﬂected Brownian Motion (RBM) forms an important researchdomain in probability, with strong links within queueing theory. A famous example is Heavy Traﬃc
Limits theorems for Queueing Networks which determine convergences of queues towards RBM.
This Special Issue aims to publish articles on reﬂected stochastic processes and their applicationsin other ﬁelds of mathematics.
This special issue has been motivated by the conference and it covers all themes included in theconference. Thus in the same spirit of the conference, it intends to reﬂect the diversity of RBM
topics: from the historical beginnings of the study of RBM to new developments and applications.
The call for articles is open to all (not only to conference participants).
We identify a few key topics (the following list is non-exhaustive!):
RBM and queuing systems/risk models ; RBM and boundary value problems / complex analysis /asymptotic techniques ; RBM in higher dimension ; Pathwise properties of RBM ; RBM as an exactly
solvable model (exponential stationary distributions, etc.) ; Stochastic processes related to RBM(reﬂected diﬀusions in polyhedral domains, etc.) ; The history of RBM.
The submission deadline is September 30, 2023.
The call for papers and the submissions process may be found here:
https://www.springer.com/journal/11134/updates/23636094
If you are interested in submitting your work to this special issue, please let us know. The threeorganizers of the conference Sandro Franceschi, Héléne Guerin, Kilian Raschel, together withMichel Mandjes member of the scientiﬁc committee of the conference as well as editor-in-chief of«Queueing Systems», will be acting as the guest editors. Please don’t hesitate to ask us, if you haveany questions regarding this special issue!

29

Useful Information

Place
The conference will take place in April 24-28, 2023 in Brittany in France, in the (small) city of Roscoﬀ,
where there is a beautiful CNRS conference center. Talks will be held at the conference center
Place Georges Teissier.

Accommodation
You will be accommodated in three diﬀerent hotels: Hotel Gulf Stream, Hotel de France and Hoteld’Angleterre. Hotel de France and Hotel d’Angleterre are very close to the conference center, Hotel
Gulf Stream is at a 15-minute walk.

Meals
Accommodation and meals will be taken at Hôtel Le Gulf Stream from the Sunday evening until
Friday noon (except the meal on Sunday evening). Dinner is at 7:30 p.m every day. The conference
dinner will be held on Tuesday.

Excursion
An excursion to Ile de Batz is planned Wednesday, April 26. The walk on the Ile de Batz is generally
very popular with lecturers (10 mn sea crossing). The boat leaves at 14:30 and the departure is at
Quai Neuf ("Les Vedettes de l’Ile de Batz" compagny).

Poster session
The poster session will be held on Wednesday before the dinner at Gulf Stream Hotel at 18:30.

Wiﬁ
Wi-Fi will be available during the conference. Instruction connection will be given.

30

Partner Institutions and Sponsors

This meeting take place CNRS conference center Station biologique de Roscoﬀ and is funded by
the Centre Henri Lebesgue, the ANR JCJC grant « RESYST » and the ERC grant « Elliptic Combinatorics ».

31

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SERVICE ACCUEIL ET CENTRE DE CONFÉRENCES