Organisers: Michel Mandjes (UvA, CWI, EURANDOM) & Ivo Adan (TU/e, UvA, EURANDOM)

2010: April 14 - September 17 - December 10

2009: October 7 - December 16

December 10, 2010

The next STAR seminar on Stochastic Networks will take place on Friday 10 December 2010 (HG 6.96).
This seminar aims to offer a day-full program of activities, such as invited talks, an open problem session, a reading seminar, and room for discussion and collaboration.
 
Programme:

September 17, 2010

The morning talks (10-13 hrs) will be in Room P2.27 of the P building (former math building);
the afternoon talks in Room A3.06 (14-16 hrs) of the A building. There will be a lunch at the mensa between 13 and 14 hrs.

10:30-11:10 Maartje Zonderland (LUMC/UT): Design of Appointment Systems for Outpatient Clinics with Scheduled and Unscheduled Arrivals

11:10-11:30 coffee break

11:30-12:15 Paulien Koeleman (CC Zorgadviseurs/VU): Optimal outpatient appointment scheduling

12:15-13:00 Melania Calinescu (CBS/VU): Forecasting and Capacity Planning for Ambulance Services

13:00-14:00 lunch

14:00-14:40 Annemieke van Dongen (VUmc): Completion times at the VUmc Emergency Department

14:40-15:20 Benjamin Kemper (IBIS-UvA): Process improvement in healthcare: A model for overall resource efficiency

15:20-16:00 Sandjai Bhulai (VU): Optimal personnel planning and admission scheduling in rehabilitation facilities

Route description

April 14, 2010 (Yellow room)

9.30-10.00 Coffee and tea

10.00-10.30 Ohad Perry (CWI, Amsterdam)

Heavy-Traffic Limits Via an Averaging Principle; Convergence and Stability Analysis

Abstract

We consider a parallel-server system with two customer classes and two server pools operating under a Fixed-Queue-Ratio with Thresholds (FQR-T) routing rule. In this talk I will outline the proof of convergence to the fluid limit, which builds on a heavy-traffic averaging principle and a resulting state-space collapse. I will then discuss properties of the fluid limit, such as stability and interchange of limits. Building on the fluid, convergence to diffusion limits are also established.

10.30-11.00 Bahar Kaynar (VU, Amsterdam)

Finite-state Markov Chains obey Benford's Law

Abstract
A sequence of real numbers (x_n) is Benford if the significands, i.e. the fraction parts in the floating-point representation of (x_n) are distributed logarithmically.

Similarly, a discrete-time irreducible and aperiodic finite-state Markov chain with probability transition matrix P and limiting matrix P^* is Benford if every component of both sequences of matrices (P^n - P^*) and (P^{n+1}-P^n) is Benford or eventually zero. Using recent tools that established Benford behavior both for Newton's method and for finite-dimensional linear maps, via the classical theories of uniform distribution modulo 1 and Perron-Frobenius, this talk shows the derivation of a simple sufficient condition (``nonresonant'') guaranteeing that P, or the Markov chain associated with it, is Benford.

This result in turn is used to show that almost all Markov chains are Benford, in the sense that if the transition probabilities are chosen independently and continuously, then the resulting Markov chain is Benford with probability one.

Concrete examples illustrate the various cases that arise, and the theory is complemented with several simulations and potential applications.

11.00-11.15 Break

11.15-12.15 Reading seminar

Speaker: Werner Scheinhardt (Universiteit Twente, Enschede)

He will discuss a topic in road traffic, admission control on motorways by ramp metering:

        - Heavy traffic on a controlled motorway
          By F.P. Kelly and R.J. Williams (pdf on http://arxiv.org/abs/1002.4591)

        - An investigation of proportionally fair ramp metering
          By R.J. Gibbens and F.P. Kelly

12.15-13.45 Lunch break

13.45-14.45 Problem Session

Onno Boxma (EURANDOM, TU/e) on "Semi-open problems for open and closed queuing systems"
Peter van de Ven (EURANDOM, TU/e) on "Stability of random-access networks"

14.45-15.00 Break

15.00-16.00 Doug Down (McMaster University, Canada)

Control of a single server with abandonments

We consider a single server with two types of arrivals, where customers may abandon while waiting. In a system with no abandonments, a c-mu rule is known to be optimal. We discuss the applicability of the c-mu rule in this setting as well as novel difficulties the analysis of such a model presents.

There will also be a reading seminar (in which a set of important papers from the literature is reviewed).

December 16, 2009

Place: University of Amsterdam, Nwe. Achtergracht 166, 1018 WV Amsterdam, zaal B 2.40:

Time: 10.00 - 16.00 h.

10.00-10.30 Bernardo D'Auria (Universidad Carlos III de Madrid, Spain)"Brownian queues with modulated buffer"

Abstract
In this talk we analyze a two-sided regulated Brownian motion, generally known as Brownian queue, whose reflecting barriers depend on an independent random environment. The environment is an irreducible finite state space Markov chain and depending on its state we assume that
the Brownian Motion's parameters change together with the level value of the upper reflecting barrier. What makes this model interesting and different form the classical ones is the intrinsic presence of discontinuities in its dynamics due to the abrupt changes of the barrier level that imply impulsive losses in the buffer content of the queue. For this model we study the stationary distribution, and in the special case of a
two-state environment we analyze in more detail the time duration from a fixed instant up to the next discontinuity ofthe process.

Joint work with Offer Kella.

10.30-11.00 Remco Germs (Rijksuniversiteit Groningen) "Analysis of Finite Buffer State Dependent Bulk Queues"

Abstract
In this talk we discuss the analysis of a finite buffer bulk queue wherein the arrival and service rates and the arrival and service batch sizes may depend on the number of customers in the queue. Using semi-regenerative analysis we develop a numerically stable method for calculating the
limiting probability distribution of the queue length process. Based on these limiting probabilities, we present various performance measures for evaluating admission control and batch service policies, such as the loss probability for an arriving group of customers and for individual customers within a group. Finally, after presenting the algorithmic aspects of our solution method we shall illustrate how a large class of
well-known finite buffer single server queueing models are covered in this framework.

11.00-11.15 Break

11.15-12.15 Reading seminar by

• Andreas Löpker (Eurandom, TU/e, Eindhoven)
  
  He will present a review of duality for stochastic processes based on
  Continuous-time monotone stochastic recursions and duality, Karl Sigman, Reade Ryan (2000), Adv. Appl. Prob., Vol. 32, 426-445.

12.15-13.45 Lunch break

13.45-14.45 Problem Session by

• Liqiang Liu (Eurandom, Eindhoven)"Compact Picking Systems"

• Bert Zwart (CWI, Amsterdam) "Are symmetric queues only quasi-reversible or is there more to it?"

14.45-15.00 Break

15.00-16.00 Bernd Heidergott (Vrije Universiteit, Amsterdam) -to be announced.

First meeting October 7, 2009

Place: EURANDOM, Laplace Building, LG 1.110 (Yellow Room), Eindhoven

Time: 10.00 - 16.00 h.

Office space (LG 1.34, LG 1.115, LG 1.110 LG, LG 1.24) and notebooks are available.
                   
Programme

09.30-10.00 Coffee and tea

10.00-11.00 Gideon Weiss (The University of Haifa)
"Optimal Control of Manufacturing Systems: Solution of Fluid Approximation and Tracking by Queueing Model"

Abstract
We consider the optimal control of a large manufacturing  system, over a finite time horizon, e.g. a semiconductor wafer  fabrication plant. We model this as a multi-class queueing network.  We approximate the queueing network by a fluid network, and obtain an  optimal fluid solution by solving a separated continuous linear  program (SCLP). To track this fluid solution we model the deviations  of the real system from the fluid by a multi-class queueing network  with infinite virtual queues (IVQ). By keeping these deviations  stable we obtain an asymptotically optimal control policy. We shall  explain our motivation and the main features of this approach. We  will then introduce the two themes on which it is based: A novel  simplex like algorithm for the solution of SCLP, and the modeling  device of IVQs. While this talk combines ideas from Manufacturing,  Optimization and Queueing, it should be accessible to a wide audience.

11.00-11.15 Break

11.15-12.15 Reading seminar - Speaker: Matthieu Jonckheere (EURANDOM, TU/e)
He will present a review of the so-called ODE method for Markov chains based on the two following papers:

• Differential equation approximations for Markov chains, Darling, R., Norris J., (2008). Probability Surveys, Vol. 5, 37--79.

• The ODE method for stability of skip-free Markov chains with applications to MCMC, Fort, G., Meyn, S., Moulines, E. and Priouret, P. (2008). Ann. Appl. Probab., Vol. 18, 664-707.

12.15-13.45 Lunch break

13.45-14.45 Problem Session - First speaker: Jan Tijmen Udding (TU/e)
"Dispatching strategies for Straddle Carriers in a Container Terminal"

Abstract
We consider the discharging process in a Container Terminal.  In this  process Quay Cranes take containers from a vessel and put them on the  Quay. Straddle Carriers are then dispatched to pick up those  containers and move them to their final positions in the yard. Quite  often Straddle Carriers are dispatched to the Quay Crane that needs a  container to be moved most urgently, in order not to become idle.  This strategy, however, turns out to favor particular Quay Cranes  depending on the speed with which they operate. The question is  whether we can quantify this phenomenon

Second speaker: Maria Vlasiou (TU/e)
"Lindley-type connections between warehousing and independent sets in random graphs"

14.45-15.00 Break

15.00-16.00 Pieter Trapman (VU)
"A birth and death model for the spread of SIR epidemics: a relation with queueing theory"

Abstract
In this talk I will discuss a relation between the spread of infectious diseases and the dynamics of so called M/G/1 queues with processor sharing. The relation between the spread of epidemics and branching processes, which is well known in epidemiology, and the relation between M/G/1 queues and birth death processes, which is well known in queueing theory, will be exploited. In particular, I will consider the number of infectious individuals in a standard SIR (Susceptible, Infectious, Removed) epidemic model at the moment of the first detection of the epidemic, where infectious individuals are detected at a constant per capita rate. I will use a result from the literature on queueing processes to show that this number of infectious individuals is geometrically distributed. This result has important consequences for statistical inference of infectious disease data, such as data on the spread of the hospital bacteria MRSA.

Last modified: 11-10-11
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