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  Special Edition of the Queueing Colloquium

on the occasion of

Onno Boxma's 60th Birthday

June 21, 2012

 

 

 

SUMMARY REGISTRATION SPEAKERS

PROGRAMME

ABSTRACTS

PARTICIPANTS

SUMMARY

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.

 

 

 

ORGANIZERS

Sem Borst (TU Eindhoven)

Johan van Leeuwaarden (TU Eindhoven)

 

SPEAKERS

Hansjoerg Albrecher UniversitÚ de Lausanne
Sergey Foss Heriot Watt University
Offer Kella Hebrew University of Jerusalem
Rudesindo N˙˝ez Queija UvA/CWI
David Perry University of Haifa
Uri Yechiali Tel Aviv University
Bert Zwart CWI

   

                            

               

 

REGISTRATION

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. N˙˝ez Queija Stationary Joint Queue Lengths for Widely Heterogeneous Traffic Classes
12.00 - 12.40 O. Kella Exponentializing in  LÚvy 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  LÚvy processes and random walks is helpful

The talk will be about two models. The first is a general reflected LÚvy 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 LÚvy 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 LÚvy 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 N˙˝ez 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 Á, 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.


 


PRACTICAL INFORMATION

Conference Location
T
he 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