About | Research | Events | People | Reports | Alumni | Contact | Home
Special Edition of the Queueing Colloquium
on the occasion of
Onno Boxma's 60th Birthday
June 21, 2012
SUMMARY | REGISTRATION | SPEAKERS |
ABSTRACTS |
PARTICIPANTS |
The Queueing Colloquium is a series of one-day seminars, with 4-6 speakers presenting work on a wide variety of queueing-related topics. The Queueing Colloquium meetings were initiated on February 2, 1978, at Utrecht University, organized by J.W. Cohen, A. Hordijk and H.C. Tijms, (please click here for the original list of 22 participants!) and subsequently moved to CWI where they have been held in different formats and at various intervals ever since.
On June 21st, a special edition of the Queueing Colloquium will take place at Eurandom, on the occasion of the 60th birthday of one of its former organizers, most devoted attendees, and most prominent ambassadors of the Dutch queueing community, Onno Boxma.
Seven eminent speakers have kindly agreed to give talks at this celebratory event, five close collaborators of Onno's from abroad as well as two former students and current organizers of the regular Queueing Colloquium.
Sem Borst (TU Eindhoven)
Johan van Leeuwaarden (TU Eindhoven)
SPEAKERS
Hansjoerg Albrecher | Université de Lausanne |
Sergey Foss | Heriot Watt University |
Offer Kella | Hebrew University of Jerusalem |
Rudesindo Núñez Queija | UvA/CWI |
David Perry | University of Haifa |
Uri Yechiali | Tel Aviv University |
Bert Zwart | CWI |
To make plannning for catering etc. easier, we ask all speakers and participants register with
the online form.
Registration is free of charge, however a non-attendence fee of 15 euros will be
charged in case of no-show.
Please use the online Registration form (you will be redirected to the TU/e website).
PROGRAMME (tentative)
10.00 - 10.30 | Registration and coffee/tea | |
10.30 - 10.40 | Opening by Remco van der Hofstad | |
10.40 - 11.20 | H.-J. Albrecher | Insurance risk, bankruptcy and queues |
11.20 - 12.00 | R. Núñez Queija | Stationary Joint Queue Lengths for Widely Heterogeneous Traffic Classes |
12.00 - 12.40 | O. Kella | Exponentializing in Lévy processes and random walks is helpful |
12.40 - 13.45 | Lunch | |
13.45 - 14.25 | B. Zwart | Layered queues |
14.25 - 15.05 | D. Perry | Perishable Inventory Systems with Random Replenishments |
15.05 - 15.30 | Break | |
15.30 - 16.10 | S. Foss | On the Greedy server and Greedy walk problems |
16.10 - 16.50 | U. Yechiali | The Israeli Queue with an Infinite Number of Families |
16.50 - 18.30 | Reception |
ABSTRACTS
Hansjoerg Albrecher
Insurance risk, bankruptcy and queues
In this talk I will focus on insurance risk models and their links with queuing models, a topic that has triggered several joint research projects with Onno Boxma over the last years. A relaxation of the ruin concept in insurance risk theory will be discussed, which smoothes the classical ruin probability and still allows for explicit analysis. Some simple identities will be presented.
Sergey Foss
On the Greedy server and Greedy walk
problems
We consider a queueing system in which arriving customers are placed
on a circle and wait for service. A traveling server moves at constant speed on
the circle, stopping at the location of the customers until service completion.
The server is greedy: always moving in the direction of the nearest customer.
Coffman and Gilbert conjectured that this system is stable if the traffic
intensity is smaller than 1; however, a proof or counterexample remains unknown.
In this talk, we present a picture of the current state of this conjecture and
suggest new related open problems.
Offer Kella
Exponentializing in Lévy processes and random walks is helpful
The talk will be about two models. The first is a general reflected Lévy process (resp., random walk) which is started off at an independent exponential state and is stopped at an independent exponential (resp., geometric) time. Results regarding the joint Laplace-Stieltjes transform (LST) of the reflected process and the regulator are expressed in terms of the marginal LST’s of the maximum and minimum processes at exponential times associated with the Lévy process started at zero. Some consequences are examined. The second model is about a new reasoning implying the decomposition results for the G/G/1 queue with server vacations and their Lévy process counterparts. In both models it is NOT assumed the processes have no positive or no negative jumps (there may be jumps in both directions). The first model is based on join work with Michel Mandjes and the second is joint with Jevgenij Ivanovs.
Rudesindo Núñez Queija
Stationary Joint Queue Lengths for Widely Heterogeneous Traffic Classes
(Based on joint work with M. Jonckheere and B. Prabhu)
We consider a service system with two traffic classes. The characteristics of
the two classes differ in traffic volumes, service requirement distributions,
quality of service needs and time-sharing priority discrimination. After
appropriate scaling, we examine the (transform of the) limiting joint queue
length distribution. One of the classes is assumed to be at a high level of
congestion with a corresponding low priority level to prevent the
"well-behaving" class from suffering inherited congestion. In the limit, the
ill-behaved class stabilizes at a deterministic level, which is determined by
the random characteristics of the other class.
Our modeling assumptions, in particular the fact that both dimensions are
unbounded as well as the mutual dependence of the dynamics in the limiting
regime, do not allow direct use of results from nearly-decomposable Markov Chain
theory and time-scale separation techniques. We use an alternative approach
based on stochastic comparison.
This work complements earlier results that we obtained for the transient instead
of the stationary regime.
David Perry
Perishable Inventory Systems with Random Replenishments
A guide to perishable inventory systems (PIS's) that are refilled by randomly arriving items and not by ordering decisions is introduced. The literature on this class of PIS's (for which a blood bank or an organ trans- plantation center are prominent examples) is sparse. The survey starts with the pioneering work on a prototype model in which item arrivals and demand arrivals form independent Poisson processes. We show how to compute all per- formance measures of interest for this PIS. Thereafter, extensions in several directions are reviewed, among them (i) PIS's with finite capacity and waiting demands; (ii) PIS's with renewal item arrival times; (iii) batch arrivals of items or demands; (iv) actuarial valuation; (v) optimization and control. Some novel contributions are also introduced.
Uri Yechiali
The Israeli
Queue with an Infinite Number of Families
The ”Israeli Queue” was
introduced in [1] by Boxma, v.d. Wal and Yechiali for a queueing system with a
finite number of ’families’, as a consequence of a polling system with N
stations and un-limited batch service, where the next station selected to be
served is the one with the customer having the longest waiting time. In this
work we study the Israeli Queue with a (possibly) infinite number of families.
Specifically, consider a single-server queue with Poisson arrival stream where
each customer, upon arrival, first searches for a member of his family. If he
finds one, he joins the group of his family members and receives service with
the entire group in a batch mode. Groups are formed as follows: each group has a
”leader” or a ”head” - the first one of the group to arrive to the system. New
arrivals see only the head of each group.
The probability of being friend with a group leader is p, and the groups are
statistically independent. We assume that an arriving customer can also join the
group that is in service. That is, if there are n group leaders in the system
(including the one in service), than the probability of joining the k − th
group, for 1 ≤ k ≤ n, is (1 − p)k−1 p, and the probability
of creating a new group is (1 − p)n .
We assume that service time of a batch is Exponentially distributed with
parameter µ, independent of the batch size, and analyze an M/M/1-
type queue, an M/M/c-type queue and a priority model with (at most) 1 M
high-priority classes and a single lower-priority class. In all models
we derive the steady-state probabilities of the queue length, and cal- culate
key performance measures.
(Based on a joint work with Nir Perel).
References
[1] Boxma, O.J., Wal, v.d. J. and Yechiali, U. (2008). Polling with
batch service. Stochastic Models 24(4), 604–625.
Bert Zwart
Layered queues
Queueing networks with a layered structure consist of entities which both act as server and as customer, and have not been studied extensively. In this talk we consider an example of a layered queue occurring in computer systems. We show that the performance of different layers may operate on different timescales when the system is critically loaded. This yields tractable heavy traffic limits. Joint work with Maria Vlasiou, Jiheng Zhang and Rob van der Mei.
Conference Location
The workshop location is Eurandom, Den Dolech 2, 5612 AZ
Eindhoven, Laplace Building, 1st floor, LG 1.105.
Eurandom is located on the campus of Eindhoven University of Technology, in the 'Laplacegebouw' building' (LG on the map). The university is located at 10 minutes walking distance from Eindhoven railway station (take the exit north side and walk towards the tall building on the right with the sign TU/e).
For all information on how to come to Eindhoven, please check http://www.eurandom.tue.nl/contact.htm
CONTACT
For more information please contact
Mrs. Patty Koorn,
Workshop officer of Eurandom
Last updated
15-06-12,
by
PK