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Workshop
YEQT-III
(Young European Queueing Theorists) Thursday November 19
Friday November 20
Saturday November 20
Abstracts Sandjai Bhulai Optimal Scheduling Policies for the Limited Processor Sharing Queue We study a limited processor sharing queue (LPS with Poisson arrivals and phase type service times. The processor can admit a limited number of requests for service. We present a new decomposition-based approach to analyze monotonicity properties that lead to a complete characterization for the optimal scheduling policy providing new fundamental insights into the optimal control of LPS queues. The results show that a considerable gain can be obtained by using the dynamic policy. Matthieu Feuillet Modeling Networks under the Law of the Jungle In this talk we seek to characterize the behavior of the Internet in the absence of congestion control. More specifically, we assume all sources transmit at their maximum rate and recover from packet loss by the use of some ideal erasure coding scheme. We estimate the efficiency of resource utilization in terms of the maximum load the network can sustain, accounting for the random nature of traffic. We introduce stochastic processes describing the Law of the Jungle and we present results concerning resource utilization, fairness and the impact of access rates. Contrary to common belief, there is generally no congestion collapse. Efficiency remains high in most cases as long as maximum source rates are smaller than link capacities by one or two orders of magnitude. Itai Gurvich On Optimality Gaps of Asymptotically Optimal Policies in the Many-server Heavy-traffic Regime Optimality gaps in many-server asymptotic optimality results are typically shown to be of a smaller order of magnitude than the square-root of the demand rate but a more refined characterization of these gaps is usually not provided. Our work is concerned with characterizing and improving these gaps. First, we show that, in some cases, the optimality gaps that are provided in the literature can be tightened significantly without changing the prescribed control. For other cases, we discuss how to modify the limiting diffusion control problem (and the resulting control) so as to improve on the optimality gap. The analysis relates the optimality gaps to the connection between preemptive and non-preemptive controls and between diffusion control problems and dynamic programming. This is joint work with Baris Ata. Bruce Hajek Collecting Coupons with Continuous Arrivals of Collectors Distributed protocols for peer-to-peer file sharing over the Internet, such as BitTorrent, have been highly successful in recent years. The idea is that files to be shared are broken into chunks. As new peers enter the system they strive to obtain a complete collection from other peers. The problem of chunk collection is much like the classical coupon collector problem, but different collectors can make copies of coupons for each other. An interesting aspect is the effect of continuous arrivals of collectors who depart upon completing their collections. The theory for understanding the success of peer-to-peer systems has lagged far behind practice, and there is also much room to understand the relative strengths of different protocols in a variety of applications. In this talk I shall discuss some stochastic models and present some recent results on the theory of peer-to-peer file sharing. Based in part on joint work with Ji Zhu. Moshe Haviv Strategic Customers behavior in Memoryless and non Memorylesss queues
Part 1: The whereabouts of customers in a
queuing system interact. If more customers join the queue, one's waiting
time may increase, up to a level that one may prefer not to join at all.
This logic applies of course to the other customers, but if all stay out one
may better join. So who are those to join and who are those not to join?
Also, if too many packets are routed along one path, then an individual
packet might be better assigned to some other path. But who will select this
path, the individual himself or a central planner? Their objectives may not
coincide: a self optimizer customer ignores the externalities that may
results from any of his decisions and which effect others. For another
decision problem, suppose acquiring the information which line or path is
shorter, comes with some cost. Clearly, one has an incentive to pay for this
information. Yet, one's incentive goes down with the fraction of those who
acquire Nidhi Hegde Scheduling Mobile Users in Wireless Networks We consider the performance evaluation of scheduling schemes in wireless networks with mobile users. We first establish properties of optimal scheduling schemes in a static environment, without user mobility. We then extend the framework to networks with mobile users. The impact of mobility on the network capacity and user throughput will be examined. Building on these results, we offer design principles for scheduling mobile users. David Hodge Optimal index policies for multi-product make-to-stock queues: if resources are more costly would we use less? We consider a key structural property of optimal inventory replenishment policies in a model with diminishing returns for resource effort. Our bottleneck lies in the limit on the replenishment rate. One could imagine that in communications networks the replenishment is analogous to packaging up processed jobs which are then placed in a queue to be distributed to customers according to a stochastic delivery process. We target indexability, namely statewise monotonicity of the optimal policy in the resource cost, for both the standard lost sales model and a back-order model. We demonstrate conditions for indexability together with some surprising counterexamples. In the cases of non-indexability we are able to establish a notion of asymptotic indexability – with monotonic policies over a wide range of replenishment cost values. The work provides an easy algorithm for the more general multi-product replenishment problem via the derived indices. We then numerically evaluate the efficiency of this algorithm for tackling the general multi-product inventory replenishment problem with diminishing returns in a wide variety of examples. Peter Jacko An Optimal Index Policy for the Multi-Armed Bandit Problem with Re-Initializing Bandits In the multi-armed bandit problem it is assumed that the bandits are freezing, i.e., they maintain their state when not played. This results to be a crucial condition for proving optimality of the index policy: "At every period play the bandit of highest Gittins index". Instead of the freezing assumption, we consider bandits that move to a re-initializing state when not played. Such dynamics is well known in reinforcement learning, where a system quits a trial and starts a new upon receiving negative feedback from the external critic, and also appears in the simplest variants of the Transmission Control Protocol implemented in the Internet. We prove that if for every re-initializing bandit there exist marginal productivity indices (which generalize those of Gittins) such that the re-initializing state has the highest index among all the bandit’s states, then the marginal-productivity-index policy is optimal. Using analogous ideas we also give a new proof of the classic problem with freezing bandits that yields complementary insights to the existing proofs. Matthieu Jonckheere Optimizing Admission Control in Balanced Networks
Consider a multiclass stochastic network
with state dependent service rates and arrival rates describing
bandwidth-sharing mechanisms as well as admission control and/or load
balancing schemes. Given Poisson arrival and exponential service
requirements, the number of customers in the network evolves as a
multi-dimensional birth-and-death process on a finite subset of N^k. We
assume that the death (i.e. service) rates and the birth rates depending on
the whole state of the system, satisfy a local balance condition. This makes
the resulting network a so-called Whittle network and the stochastic process
describing the state of the network is reversible with Yoav Kerner A queueing approach to a multi class M/G/1 make-to-stock with backlog A single machine produces an item according to a renewal process. Customers of each class arrive according to independent Poisson processes and differ from each other only in their waiting cost, which is assumed to be linear. We assume finite classes. We consider a linear (both in time and inventory level) holding cost. One would like to find a policy that minimizes the overall cost. An Inventory Rationing (IR) policy is defined by a base stock level and a finite sequence of thresholds, such that a class i customer receives an item if and only if the inventory level exceeds the threshold R_i. The IR policy can be presented as an M/G/1 priority system with state dependent arrival rates. In general, the IR policy is not optimal, even when the information given to the decision maker is only the queue lengths of various customers types. In this talk we will discuss cases in which the IR policy is optimal, and we will present an improvement when it is not. The analysis is based on busy period analysis of M/G/1 priority system and on obtaining the conditional residual service time in such a system. Iordanis Koutsopoulos Client and Server Games in Peer-to-Peer Networks
We consider a content sharing network of
non-cooperative peers. The strategy set of each peer comprises, (i) client
strategies, namely feasible request load splits to servers, and (ii) server
strategies, namely scheduling disciplines on requests. The performance
metric is average retrieval delay. First, we consider the request load
splitting game for given server strategies such as First-In-First-Out or
given absolute priority policies. A peer splits its request load to servers
to optimize its performance objective. We consider the class of best
response load splitting policies residing between the following extremes: a
truly selfish, or egotistic one, where a peer optimizes its own delay, and
a pseudo-selfish or altruistic one, where a peer also considers incurred
delays to others. We derive conditions for Nash equilibrium points (NEPs)
and discuss convergence to NEP and properties of the NEP. For both the
egotistic cases, the NEP is unique. For the altruistic case, each of the
multiple NEPs is an optimum, a global one for the FIFO case and a local one
otherwise. Pasi Lassila Minimizing the Mean Flow-Level Delay in Wireless Systems HSDPA/HDR systems allow the use of sophisticated opportunistic schedulers that can utilize information on instantaneous channel conditions. On the other hand, for elastic data traffic the size of the files can be used in size-dependent scheduling methods, e.g., the well known SRPT scheduler, to minimize the flow delay. We consider the use of both size and channel information for minimizing the flow delay in the dynamic setting with randomly arriving flows having random sizes and independent random channel rate variations. We start by considering the case where the scheduler is only aware of the mean rate of the user channels. In this case, the system can be modeled as an M/G/1 queue, for which the SRPT policy provides the optimal policy. In the case where both instantaneous rate and size information is available, the optimal policy is not known. In our work, we study simple index and priority policies, and use the well-known PF policy as the baseline. In this setting, the stability of the policies becomes an issue, especially when considering users with highly asymmetric channels. Erjen Lefeber Controller Design for Networks of Switching Servers with Setup Times
In this talk we consider the controller
design for networks of switching servers, e.g. manufacturing systems or
urban road networks (traffic light control). Control of these networks is
difficult, since using controllers that are stable for a server in isolation
might render the network unstable. We present an approach to controller
design which is inspired from control theory. To that end, instead of
starting from a policy and then analyzing the proposed policy, we start from
a priori Marc Lelarge Efficient Control of Epidemics over Random Networks. Motivated by the modeling of the spread of viruses or epidemics with coordination among agents, we introduce a new model generalizing both the basic contact model and the bootstrap percolation. We analyze this percolated threshold model when the underlying network is a random graph with fixed degree distribution. Our main results unify many results in the random graphs literature. In particular, we provide a necessary and sufficient condition under which a single node can trigger a large cascade. Then we quantify the possible impact of an attacker against a degree based vaccination and an acquaintance vaccination. We define a security metric allowing to compare the different vaccinations. The acquaintance vaccination requires no knowledge of the node degrees or any other global information and is shown to be much more efficient than the uniform vaccination in all cases. Seva Shneer Throughputs and fairness in slotted and non-slotted versions of CSMA We consider a system consisting of $n$ transmitters/receivers placed on a line. The channel used by transmitters is such that $2$ transmitters cannot send messages at the same time if the distance between them is not larger than $k$, where $k$ is a positive integer. The well-known CSMA protocol is often used to govern the behaviour of the transmitters in this scenario, and the performance of the system in this case is well-understood. We propose a discrete-time analogue of the CSMA protocol and in the case of a completely saturated system find exact formulas for the total throughput of the system governed by this algorithm and for individual throughputs of all transmitters. We then compare these throughputs with the throughputs achieved by the classical CSMA protocol. The fairness of both protocols is also compared. Finally, we discuss bounds for the throughput of a system where the first transmitter (source) is saturated and messages are relayed by the intermediate transmitters to the last one (destination). This is a joint work with Peter van de Ven (TU/e and EURANDOM). Slawomir Stanczak Efficient versus Fair Resource Allocation in Autonomous Wireless Interference Networks Wireless resources are scarce and the capacity of wireless links exhibits an ephemeral and dynamic nature, depending for instance on wireless channel characteristics and transmit powers of all interfering links. At the same time, wireless networks will have to support a wide range of applications having fundamentally different QoS requirements and traffic characteristics. All this requires a better understanding of the fundamental tradeoffs and interdependencies in wireless networks, with the goal of designing resource allocation strategies that exploit these interdependencies to achieve significant performance gains. In this talk, we will present a systematic summary of some recent results and algorithmic solutions for resource allocation and interference management in distributed wireless networks. The main focus is on a joint optimization of physical-layer signaling and the medium access control, including power control and link scheduling. A particular interest is attached to advanced multiple antenna and beam forming technologies. A distributed implementation of the algorithms is based on the concept of an adjoint network; this concept also has an interesting application in wireless sensor networks. Presentation (changed speaker) Ioannidis Stratis Scalable and Reliable Searching in Unstructured Peer-to-Peer Systems Searching in unstructured peer-to-peer systems poses a challenge because of high churn: both the topology and the content stored by peers can change quickly as peers arrive and depart, while the network formed under this churn process can be arbitrary at any point in time. Ideally, a search mechanism in a peer-to-peer system should be scalable: as, typically, peers have limited bandwidth, the traffic generated by queries should not grow significantly as the peer population increases. Moreover, a search mechanism should also be reliable: if certain content is in the system, searching should locate it with reasonable guarantees. These two goals can be conflicting, as generating more queries increases a mechanism's reliability but decreases its scalability. Hence, a fundamental question regarding searching in unstructured systems is whether a mechanism can exhibit both properties, despite the network's dynamic and arbitrary nature. We show this is indeed the case, by proposing a novel mechanism that is both scalable and reliable. To obtain this result, we model the evolution of the network as a Markov chain over the set of possible overlay graph configurations, whose transitions depend on the connection protocol followed by peer arrivals and departures.
Tolga Tezcan Control of Systems with Flexible Multi-server Pools: A Shadow Routing Approach A general model with multiple input flows (classes) and several flexible multi-server pools is considered. We propose a robust, generic scheme for routing new arrivals, which optimally balances server pools' loads, without the knowledge of the flow input rates and without solving any optimization problem. The scheme is based on Shadow routing in a virtual queuing system. We study the behavior of our scheme in the Halfin-Whitt (or, QED) asymptotic regime. |
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Jean Walrand Scheduling for Communication and Processing Networks The talk reviews the history and recent results on the scheduling of tasks that require access to a set of resources.
The first step was the discovery that
maximum weighted matching achieves the maximum throughput for a class of
such scheduling problems that includes wireless networks and packet switches
[1]. However, this algorithm is too complex to be directly applicable. Bert Zwart Scheduling Performance and Asymptotics Abstract: We give an overview of recent research on the performance of scheduling disciplines such as Processor Sharing and Shortest Remaining Processing time, motivated by recent problems in computer systems and communication networks. Emphasis is on the impact of the choice of the scheduling discipline on the occurrence of rare events, and the behavior under critical load. The aim is to give the audience an overview of the results in this area, to provide intuition behind these results, and to review some of the basic techniques behind them. See http://www.cs.cmu.edu/afs/cs.cmu.edu/user/harchol/www/Papers/boxma.pdf for some background.
P.O. Box 513, 5600 MB Eindhoven, The Netherlands |