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November 11-12-13, 2015 Workshop on YEQT IX "Scaling limits in queueing networks"
SUMMARY
This will be the ninth edition of the Young European Queueing Theorists
(YEQT) workshop. The topic of this year’s workshop is about “Scaling limits
of queueing networks”. We have selected four topics in queueing theory
around which we intend to develop a clustered program: ORGANISERS *
* Scientific advisor: Onno Boxma (TU Eindhoven)
LIST OF SPEAKERSKEYNOTE:
TUTORIAL SPEAKERS
INVITED SPEAKERS
tentative WEDNESDAY NOVEMBER 11
THURSDAY NOVEMBER 12
FRIDAY NOVEMBER 13
ABSTRACTS
Gianmarco Bet Critical queues exhibiting the depletion-of-points effect Cédric Bourdais Reservation in vehicle-sharing systems We introduce a stochastic network as a simple homogeneous model for
vehicle sharing systems with reservation. Large systems are studied via the
mean field limit. This limit is a dynamical system solution of an ODE. We
prove that its equilibrium point is unique , characterized as a tandem of
two queues. This characterization allows to investigate the fleet size which
maximizes the average number of satisfied users (those who can find both a
car and a parking spot at the stations of their choice), when the system is
large and in stationary regime. The arguments are the probabilistic
interpretation of the limit, real analysis and combinatorics. Asaf Cohen A Multiclass Queueing Model in the Moderate-Deviation Heavy-Traffic Regime We consider a multiclass single-server queueing control problem in the
moderate-deviation heavy-traffic regime with a discounted risk-sensitive
cost. In the scaling limit, an optimal control problem associated with the
model is shown to be governed by a differential (deterministic) game that
can be explicitly solved and that admits an optimal stationary feedback
policy. We also present a stationary asymptotic optimal policy that
satisfies a state space collapse property. PRESENTATION (only available by email, please send request to koorn@eurandom.tue.nl) Sarah Eugene Stochastic Modelling of Polymerisation of Proteins To investigate intrinsic or extrinsic variability among amyloid formation
experiments, we propose and study a new stochastic model, which is able to
capture the main mechanisms of brillization while David Goldberg Beating the curse of dimensionality in inventory problems with lead
times Inventory models, which are core to the study of Operations Research and
Operations Management, share many features with queueing models and random
walks. Varun Gupta Designing load balancing and admission control policies: lessons from
NDS regime Harsha Honnappa Approximation Techniques for Transitory Stochastic Processes We start by considering a queueing system where a finite number of
customers apply for service, and service times are generally distributed and
service is first-come-first-served. We model the arrival epochs as
independent random variables drawn from a common ‘scattering’ distribution.
In prior work, showed that the diffusion approximation to the work load
process is a diffusion process reflected through what has come to be known
as the ‘directional derivative reflection map’. In general, it seems
impossible to compute the transient expectations associated with this
diffusion. Here, we first show that it is possible to obtain a much simpler
approximation under a first-order differentiability condition on the
distribution function. Second, once a diffusion approximation has been
found, we show how to compute approximations to the transient distribution
of the diffusion under two conditions: a) when the infinitesimal parameters
are slowly time-varying (or equivalently when steady state is a ‘reasonable’
approximation) we obtain an asymptotic expansion in terms of the point-wise
stationary approximation, and b) when the time interval of study [0,t] is so
small that steady state cannot be reached, we obtain Taylor series
expansions in terms of the initial transient of a regulated Brownian motion
with parameters ‘frozen’ to those at time zero. We conclude by discussing
the implications of these approximations on on optimal control of these
processes. Tom Kurtz Approaches to large system limits A variety of methods for proving large system limits will be illustrated
with models drawn form queueing and related contexts. Britt Mathijsen Workload shifting in critical many-server systems
To release pressure from systems during periods of overload, we introduce
the concept of Delayed Workload Shifting (DWS). Our basic model is an
M/M/s/n queue with the additional feature that customers meeting a full
system upon arrival are not admitted directly, but reattempt getting access
after a random amount of time. By scaling the number of servers s and the
threshold level n according to a two-fold QED regime, we show that the
system with DWS can be approximated in terms of the QED limits of the system
without DWS, but with corrected parameters that are obtained as solutions to
fixed point equations. DWS leads to substantial performance gains in the QED
regime. The DWS approximations serve as input for algorithms that achieve
predefined performance targets in both stationary and time-varying
environments. Similar algorithms can be designed for more advanced queueing
system, including systems with returning customers or tandem networks. Load Balancing in Heterogeneous Systems We consider the problem of load balancing in heterogeneous parallel processor sharing server systems, where the service rate achieved by a user at a server depends on both the user and the server. Such heterogeneity typically arises in wireless networks (e.g., servers may represent frequency bands, and the service rate of a user varies across bands). We investigate the performance of these systems under centralized and distributed control. In centralized systems, we focus on scenarios where the service rates of users at the various servers are unknown, and must be learnt in an online manner. The design of optimal load balancing strategies may then be casted as an instance of combinatorial bandits problems. We present fundamental performance limits for such problems, and propose algorithms approaching these limits. In distributed systems, users initially attach to an arbitrary server, and at random instants of time, may probe the load at a new server and migrate there to improve their service rate. We propose a natural distributed migration strategy, and analyze its convergence rate towards the Proportionally Fair allocation. We further establish its throughput optimality when users randomly arrive in the system and leave upon service completion. Kavita Ramanan Keynote: Stability of Stochastic Networks via Asymptotic Coupling An important question in stochastic networks is that of stability. A common approach that is used to prove uniqueness of stationary distributions is to establish positive Harris recurrence of the state process. We will describe situations when this approach does not work, or seems particular challenging and instead, illustrate via two examples how asymptotic (equivalent) couplings may provide a more convenient alternative. Scaling Limits of Randomized Load Balancing Networks We introduce a general framework of interacting
measure-valued representations for the study randomized load balancing
networks. For a particular example, we show how their scaling limits can be
used to provide insight into both the transient and steady state performance
measures of the network. Marty Reiman Asymptotically Optimal Control of (Some) Stochastic Service Systems
Many control problems that arise in stochastic service systems (including
both queueing and inventory systems) are extremely difficult to solve
exactly. This has given rise to a great deal of research effort involving
asymptotics, such as heavy traffic in the context of queueing systems, with
the goal of providing good controls. A standard criterion for goodness in
much of this work is asymptotic optimality. Philippe Robert On the dynamics of random neuronal networks We study the mean-field limit and stationary
distributions of a pulse-coupled network modeling the dynamics of a large
neuronal assemblies. Our model takes into account explicitly the intrinsic
randomness of firing times, contrasting with the classical
integrate-and-fire model. The ergodicity properties of the Markov process
associated to finite networks are investigated. We derive the limit in
distribution of the sample path of the state of a neuron of the network
when its size gets large. The invariant distributions of this limiting
stochastic process are analyzed as well as their stability properties. We
show that the system undergoes transitions as a function of the averaged
connectivity parameter, and can support trivial states (where the network
activity dies out, which is also the unique stationary state of finite
networks in some cases) and self-sustained activity when connectivity level
is sufficiently large, both being possibly stable. Mark Shifrin Asymptotically optimal policies for the multi-class finite queue We consider a multiclass G/G/1 queue where tasks of various classes are
served by single server with service sharing (scheduling) ability. Two
possible buffer configurations are addressed - the case where tasks of
different classes occupy dedicated buffers and the case where all tasks are
processed from a single shared buffer. There is task admission and server
scheduling control which aim to minimize the cost which consists of holding
and rejection components. We construct policies that are asymptotically
optimal in the heavy traffic limit. For both cases, the policies stem from
solution to Harrison-Taksar (HT) free boundary problem and are expressed by
a single free boundary point. The cµ priority rule is used by the policy in
the case of dedicated buffers, but in a way that is novel, and, in
particular, different than that used in Wen Sun The Time Scales For A Stochastic Network With Failures
Mirco Tribastone Fluid limits for formal models of software performance Formal languages for the specification and analysis of software performance models are attractive because they can express several real-world communication and coordination paradigms such as fork/join synchronization, asynchronous interaction, and layered service behavior. Being often based on continuous-time Markov chains, unfortunately they are prone to the infamous problem of state-space explosion, which severely hinders their practical applicability to large-scale systems. This talk will discuss the key ideas on automatically deriving (and proving the convergence of) fluid limits for such languages, with applications to the approximation of layered queuing networks based on ordinary differential equations (ODEs). We will also present ongoing work on taming the complexity of certain models where even the ODE limits are not compact enough for tractable numerical analysis. Hannah Van den Bossche Public vs. personal transportation: a rational choice based on queueing theory One’s choice between public and personal transport for the daily commute
depends on various factors including convenience, comfort, monetary cost and
travel times. Abstracting convenience, comfort and monetary cost in a single
fixed cost, we focus on the tradeoff between travel times and this cost,
assuming fixed travel times for public transport. Such a tradeoff obviously
depends on the decisions of other commuters, as travel times for personal
transport depend on traffic density. This dependency is very well captured
by the so-called fundamental diagram of traffic flow. The diagram relates
traffic flux (and therefore also the travel times) to traffic density, an
increased density leading to increased travel times. Amadine Véber Resource sharing with logarithmic weights We shall consider a communication network in which J
clients share a server. If client j has x jobs waiting, it receives a
fraction of the capacity of the server which is proportional to ln(1+x). In
contrast with the case of a linear allocation of resources (i.e.,
proportional to x), when the total number of jobs tends to infinity several
timescales interact in a fine way to shape the asymptotic behaviour of the
system. Dongyuan Zhan Compensation and Staffing to Trade Off Speed and Quality in Large Service Systems Most common
queueing models used for service system design assume the servers work at
fixed (possibly heterogeneous) rates. However, real-life service systems are
staffed by people, and people may change their service speed in response to
their compensation incentives. The delicacy is that the resulting employee
service rate affects the staffing, but also the staffing affects the
resulting employee service rate. Our objective in this paper is to find a
joint compensation and staffing policy that induces optimal service system
performance.
PRACTICAL INFORMATION● VenueEurandom, Mathematics and Computer Science Dept, TU Eindhoven, De Groene Loper 5, 5612 AZ EINDHOVEN, The Netherlands
Eurandom is located on the campus of
Eindhoven University of
Technology, in the
Metaforum building
(4th floor) (about
the building). The university is
located at 10 minutes walking distance from Eindhoven main railway station (take
the exit north side and walk towards the tall building on the right with the
sign TU/e).
● RegistrationCLOSED !! Unfortunately we can not except anymore registrations. We are at maximum capacity. We will ask all speakers if we can put their presentations online after the event, so if you could not be there in person, you can at least read all the material.
● Accommodation / FundingHotel will be booked for all invited speakers. Please give your arrival and departure date on the registration form. Other participants have to make their own arrangements. For hotels around the university, please see: Hotels (please note: prices listed are "best available"). More hotel options can be found on the webpages of the Tourist Information Eindhoven, Postbus 7, 5600 AA Eindhoven.
● TravelFor those arriving by plane, there is a convenient direct train connection between Amsterdam Schiphol airport and Eindhoven. This trip will take about one and a half hour. For more detailed information, please consult the NS travel information pages or see Eurandom web page location. Many low cost carriers also fly to Eindhoven Airport. There is a bus connection to the Eindhoven central railway station from the airport. (Bus route number 401) For details on departure times consult http://www.9292ov.nl The University can be reached easily by car from the highways leading to Eindhoven (for details, see our route descriptions or consult our map with highway connections.
● Conference facilities : Conference room, Metaforum Building MF11&12The meeting-room is equipped with a data projector, an overhead projector, a projection screen and a blackboard. Please note that speakers and participants making an oral presentation are kindly requested to bring their own laptop or their presentation on a memory stick.
● Conference SecretariatUpon arrival, participants should register with the workshop officer, and collect their name badges. The workshop officer will be present for the duration of the conference, taking care of the administrative aspects and the day-to-day running of the conference: registration, issuing certificates and receipts, etc.
● CancellationShould you need to cancel your participation, please contact Patty Koorn, the Workshop Officer.
● ContactMrs. Patty Koorn, Workshop Officer, Eurandom/TU Eindhoven, koorn@eurandom.tue.nl SPONSORSThe organisers acknowledge the financial support/sponsorship of:
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