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November 456, 2013 Workshop on YEQT VII "Scheduling and priorities in queueing systems"
SUMMARY
The Young European Queueing Theorists (YEQT) workshops are
organized on a yearly basis at Eurandom, Eindhoven.
During the workshop there will be time and space available to
present scientific posters. We especially invite young researchers to come
forward with a poster on their recent work. Please email
Patty Koorn with your request
and we will do our best to accommodate your poster. ORGANISERS
LIST OF SPEAKERSKEYNOTE:
TUTORIAL
INVITED SPEAKERS
(please note: this is a preliminary programme. It will be updated as soon as we have confirmation of the speakers) MONDAY NOVEMBER 4
TUESDAY NOVEMBER 5
WEDNESDAY NOVEMBER 6
ABSTRACTSAhmad Al Hanbali Approximations for the waiting time distribution in
an M/G/c priority queue We investigate the use of priority mechanisms when assigning service engineers to customers as a tool for service differentiation. To this end, we analyze a nonpreemptive 𝑀/𝐺/𝑐 priority queue with various customer classes. For this queue, we present various accurate and fast methods to estimate the first two moments of the waiting time per class given that all servers are occupied. These waiting time moments allow us to characterize the overall waiting time distribution per class. We subsequently apply these methods to reallife data in a case study. Rami Atar (Keynote) Moderate deviation approach to heavy traffic There is a vast literature on heavy traffic analysis of controlled queueing models at the diffusion scale. In this talk I will describe recent developments on the alternative approach that considers these models at the moderate deviation scale. Ioannis Dimitriou Multiclass retrial queues with preemptive priorities Retrial queueing systems are characterized by the feature that an arriving customer who finds all the servers busy leaves the system and repeats his demand after a random amount of time. In such a case we assume that the blocked customer joins a virtual queue, called the orbit queue. In this work we study a single server retrial queueing system accepting n types of customers. We assume that customers of type i have preemptive priority over customers of type j, i < j. Customers of type 1 are queued in an infinite capacity ordinary queue and served in a FIFO discipline. An arriving type 1 customer who finds the server busy with a customer of type i (i = 2, ..., n) pushes him in his own orbit and occupy the server. The behavior of customers of type i, i = 2, ..., n is described as follows. If a newly arriving customer of type i, i = 2, ..., n finds the server busy with a customer of type j, where i < j, pushes the customer in service in his own orbit and occupy the server. Otherwise the newly arriving customer of type i, is blocked and routed to a seperate type i orbit queue. Both blocked and interrupted customers of type i, i = 2, ..., n, leave the system and repeat their demand individually after an exponentially distributed amount of time. Such a queueing system serves as a model for competing job streams in a carrier sensing multiple access system. We study the queueing system using multidimensional probability generating functions. For such a model we obtain the mean number of type i (i = 1, 2, ..., n) customers in steady state and use them to draw conclusions from numerical calculations. Martin Erausquin Job scheduling in a singleserver in a random environment We discuss the problem of scheduling stochastic jobs in a singleserver system, where the capacity of the system varies over time. The Gittins' index policy, which is known to be optimal in systems with constant capacity, turns out to be suboptimal in the general case. However, Glazebrook 87 showed the optimality of Gittins' index in ONOFF systems with geometric ON periods. We give an alternative proof for this result, provide a new expression for the index, and use it to characterize the optimal policy when the service time distributions have some specific properties. Ragavendran Gopalakrishnan Staffing and Routing to Incentivize Servers in ManyServer Systems Traditionally, research focusing on the design of scheduling and staffing policies for service systems has modeled servers as having fixed (possibly heterogeneous) service rates. However, service systems are often staffed by people. Then, the rate a server chooses to work may be impacted by the scheduling and staffing policies used by the system. We present a model for such "strategic servers'' that choose their service rate in order to maximize a tradeoff between an "effort cost'', which captures the idea that servers exert more effort when working at a faster rate, and a "value of idleness'', which assumes that servers prefer to be idle as much as possible. We revisit routing and staffing questions for an M/M/N system in this strategic server framework. First, we establish the conditions for the existence of a symmetric equilibrium service rate under any idletimeorderbased routing policy. Then, we find the staffing level that asymptotically minimizes linear staffing and waiting costs as the arrival rate grows large. An important interesting insight is that that asymptotically optimal staffing level staffs many more servers (of the order of the arrival rate more) than the common squareroot staffing policy that has been shown to be asymptotically optimal in the conventional M/M/N setting, when servers are not strategic. Anindya Goswami Risksensitive cost for a Markovian multiclass queue with priority A multiclass M/M/1 system, with service rate $\mu_in$ for class$i$
customers, is considered with the risksensitive cost criterion $n^{1}\log
E\exp\sum_ic_iX^n_i(T)$, where $c_i>0$, $T>0$ are constants, and $X^n_i(t)$
denotes the class$i$ queuelength at time $t$, assuming the system starts
empty. An asymptotic upper bound (as $n>\infinity$) on the performance
under a fixed priority policy is attained, implying that the policy is
asymptotically optimal when $c_i$ are sufficiently large. The analysis is
based on the study of an underlying differential game. Dynamic Scheduling in Heavy Traffic Maialen Larranaga Dynamic fluidbased scheduling in a multiclass abandonment queue We
investigate how to share a common resource among multiple classes of
customers in the presence of abandonments. We consider two different models:
(1) customers can abandon both while waiting in the queue and while being
served, (2) only customers that are in the queue can abandon. Given the
complexity of the stochastic optimization problem we propose a fluid model
as a deterministic approximation. For the overload case we directly obtain
that the $\tilde c \mu$rule is optimal. For the underload case we use
Pontryagin's Maximum Principle to obtain the optimal solution for two
classes of customers; there exists a switching curve that splits the
twodimensional statespace into two regions such that when the number of
customers in both classes is sufficiently small the optimal policy follows
the $\tilde c \mu$rule and when the number of customers is sufficiently
large the optimal policy follows the $\tilde c
μrule.
The same structure is observed numerically in the optimal policy of the
stochastic model for an arbitrary number of classes. Based on this we
develop a heuristic and by numerical experiments we evaluate its performance
and compare it to several index policies. We observe that the suboptimality
gap of our solution is small. Mihalis Markakis Delay Analysis of the MaxWeight Policy under HeavyTailed Traffic via Fluid Approximations We consider a singlehop switched
queueing network with a mix of heavytailed (i.e., arrival processes with
infinite variance) and lighttailed traffic, and study the delay performance
of the MaxWeight policy, known for its throughput optimality and asymptotic
delay optimality properties. Prajwal Osti Optimal dynamic TDD intercell coordination for elastic traffic We consider the intercell coordination problem between two interfering cells combined with dynamic TDD. In dynamic TDD, each station selects whether it is serving uplink (u) or downlink (d) traffic. Thus, the system has four possible operation modes (uu, du, ud, dd). The amount of intercell interference between the stations clearly depends on the operation mode. Traffic in our model consists of elastic data flows in both cells (cells 1 and 2) and in both directions (uplink and downlink), i.e., there are four traffic classes. Flows in each class are served according to the processor sharing (PS) queueing discipline. We first characterize the maximal stability region, and then determine the optimal static (i.e., stateindependent) policy to choose the operation mode for various scenarios. We also consider further optimizing the performance by dynamic policies, where the chosen operation mode depends on the instantaneous state of the system. We define several dynamic priority policies and also consider the policy resulting from applying the first policy iteration algorithm to the optimal static policy. In addition, as a reference policy, we have the wellknown maxweight policy. We show that certain simple priority policies are, in fact, stochastically optimal in some special cases, but which policy is optimal depends on the setting. In the general case, we simulate the performance of the dynamic policies and give insight into how the policies perform relative to each other and what is the ultimate gain achieved by the dynamic policies. Georgios Paschos Stability via Evacuation Times and Applications A first order performance characterization of queueing systems is the
stability region. We study the relation of system stability to minimal
evacuation times, i.e. the necessary time to clear specific snapshots of
packets. It is shown that under certain conditions the stability region is
completely characterized by the asymptotic growth of the evacuation
function. This in turn can be determined in closed form for specific
systems, which makes the proposed tool very useful. Liron Ravner Equilibrium Arrival Times to Congested Queues Customers are often faced with a choice of when to arrive to a congested queue with some desired service at the end. Suppose the server operates for a certain time interval, and customers are served according to their arrival order. Typically, customers wish to avoid waiting in the queue for a long time, but arriving too late or too early may also incur high costs. We model the interaction between the customers arriving to the queue as a strategic game. Examples of such scenarios are arriving at a concert with unmarked seats, driving to work in the morning or going to lunch in the cafeteria. We will examine an example in which customers incur costs according to their order of arrival. Specifically, an arrival process that constitutes a Nash Equilibrium will be presented. Using Priorities and Selfish Scheduling to Obtain Global Optima Determining the structure, properties, and
particular values of optimal policies for minimizing a global (social)
objective function for scheduling and routing problems is often extremely
difficult using standard approaches such as dynamic programming. On the
other hand, given a priority order, individually optimal (selfish)
scheduling policies are often structurally obvious and easily computed. We
show how to make the social and selfish solutions coincide by assigning
appropriate priorities to individuals, and apply the approach to optimal
"green" scheduling (with both holding costs and energy usage costs) and to
marginal analysis of flexibility in service systems such as call centers. Jaron Sanders Scaled Control in the QED Regime We develop manyserver asymptotics in the QualityandEfficiencyDriven (QED) regime for models with admission control. The admission control, designed to reduce the incoming traffic in periods of congestion, scales with the size of the system. For a class of Markovian models with this scaled control, we identify the QED limits for two stationary performance measures. We also derive corrected QED approximations, generalizing earlier results for the Erlang B, C and A models. These results are useful for the dimensioning of large systems equipped with an active control policy. In particular, the corrected approximations can be leveraged to establish the optimality gaps related to squareroot staffing and asymptotic dimensioning with admission control. Halldora Thorsdottir A functional central limit theorem for a Markovmodulated infiniteserver queue We model the
production of new molecules in a chemical reaction network as a Poisson
process with a varying arrival rate, depending on an external Markov
process. It is assumed that the molecules decay after an exponential time,
independently of other molecules present. The goal is to analyze the
distributional properties of the number of molecules in the system, under a
specific timescaling. In this scaling, the background process is sped up by
a factor N^\alpha, for some \alpha>0, whereas the arrival rates are scaled
by N, for N large. Kurt Van Hautegem OPS/OBS Scheduling Algorithms: Incorporating a Wavelength Conversion Cost in the Performance Analysis
With everincreasing demands for bandwidth optical
packet/burst switching is used to utilise more of the available capacity of
optical networks. In current prototypes of optical switches time and
wavelength multiplexing are combined to resolve packet contentions, by means
of Fiber Delay Lines and wavelength converters in the switching elements.
Although optical switches have lower energy consumption than their
electronic counterparts, it remains substantial. Since wavelength converters
contribute significantly to the switches overall energy consumption, they
should be used sparingly, rather than continuously. Current scheduling
algorithms however do not take the usage of wavelength converters (and the
related effectiveness) into account. To this end, we developed and evaluated
new costbased scheduling algorithms, which take both gap and delay into
account to schedule an incoming packet. The performance improvement of these
algorithms over existing algorithms can be traded off for a significant
reduction in uptime of the wavelength converters by introducing a
conversion cost in the involved cost function. This is backed by Monte Carlo
simulation results, in which the algorithms are applied both in a
voidfilling and nonvoidfilling setting. The algorithms are of the same
implementation complexity as current algorithms, and thus of immediate value
to switch designers. Joris Walraevens Tail Probabilities in Priority Queues Tail probabilities of the number of customers and
the customer delay of the lowpriority class in a twoclass infinite
priority queue are investigated. The tool used is singularity analysis of
probability generating functions, by which it is shown that different (types
of) singularities of the respective probability generating function might
play a role, leading to distinct asymptotics. We categorize the possible
asymptotics either as (i) exponential, (ii) power law or (iii) power law
with exponential cutoff. The analytic work is complemented by stochastic
intuition, in that the different types of asymptotics are the result of the
dominance of different effects in the queue, namely, resp. a queueing
effect, a singleevent effect and a priority effect. We also look at what
happens when the queue is near the instability bound, and at the influence
of finite highpriority buffer capacity. Bandit processes and index policies We consider the problem of optimal control for a number of alternative Markov decision processes, where at each moment in time exactly one process must be "continued" while all other processes are "frozen". Only the process that is continued produces any reward and changes its state. The aim is to maximize expected total discounted reward. A familiar example would be the problem of optimally scheduling the processing of jobs that reside in a singleserver queue. A each moment one of the jobs is processed by the server, while all the other jobs are made to wait. Our aim is to minimize the expected total holding cost incurred until all jobs are complete. Another example is that of hunting for an apartment; we must choose the order in which to view apartments and decide when to stop viewing and rent the best apartment of those that have been viewed. This type of problem has a beautiful and surprising solution in terms of Gittins indices. In this tutorial I will review the theory of bandit processes and Gittins indices, describe some applications in scheduling and queueing, and tell you about some frontiers of research in the field. Part 1 : Index policies. Interchange arguments. Stopping problems. Bandit processes. Gittins index theorem. Calibration. Target processes. Playing golf with more than one ball. Pandora's problem. Branching bandits. Optimal scheduling in the M/G/1 queue. Part 2 : Restless bandits. Whittle indexability. Fluid models and asymptotic optimality. Large deviations and risksensitive optimal control. Bo Zhang Distributed Data Backup Scheduling: Modeling and Optimization In this talk I will first discuss some general ideas
on modeling and optimization of data backup scheduling, an increasingly
important problem domain in which no formal mathematical model has been
proposed before. Then I will present some queueingtype results on
distributed data backup scheduling that we obtained motivated by a
realworld project at IBM. Specifically, we developed a novel Markov chain
model to describe the distributed data backup process and analyzed its
stability conditions and stationary behavior. In the context of our proposed
model, we also formulated an optimization problem for choosing a scheduling
policy that strikes the right balance between performing frequent backups to
improve data safety and reducing backup costs.
PRACTICAL INFORMATION● VenueEurandom, Mathematics and Computer Science Dpt, TU Eindhoven, Den Dolech 2, 5612 AZ EINDHOVEN, The Netherlands
Eurandom is located on the campus of
Eindhoven University of
Technology, in the
brand new
TU/e
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).
● RegistrationTo register for the workshop, please fill out the registration form. There is no fee for participation.
● 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 meetingroom 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 daytoday 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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