Random trees in queueing systems with deadlines

AbstractWe survey our research on scheduling aperiodic tasks in real-time systems in order to illustrate the benefits of modelling queueing systems by means of random trees. Relying on a discrete-time single-server queueing system, we investigated deadline meeting properties of several scheduling algorithms employed for servicing probabilistically arriving tasks, characterized by arbitrary arrival and execution time distributions and a constant service time deadline T. Taking a non-queueing theory approach (i.e., without stable-stable assumptions) we found that the probability distribution of the random time sT where such a system operates without violating any task's deadline is approximately exponential with parameter λT = 1μT, with the expectation E[sT] = μT growing exponentially in T. The value μT depends on the particular scheduling algorithm, and its derivation is based on the combinatorial and asymptotic analysis of certain random trees. This paper demonstrates that random trees provide an efficient common framework to deal with different scheduling disciplines and gives an overview of the various combinatorial and asymptotic methods used in the appropriate analysis

Stability of Service under Time-of-Use Pricing

We consider "time-of-use" pricing as a technique for matching supply and demand of temporal resources with the goal of maximizing social welfare. Relevant examples include energy, computing resources on a cloud computing platform, and charging stations for electric vehicles, among many others. A client/job in this setting has a window of time during which he needs service, and a particular value for obtaining it. We assume a stochastic model for demand, where each job materializes with some probability via an independent Bernoulli trial. Given a per-time-unit pricing of resources, any realized job will first try to get served by the cheapest available resource in its window and, failing that, will try to find service at the next cheapest available resource, and so on. Thus, the natural stochastic fluctuations in demand have the potential to lead to cascading overload events. Our main result shows that setting prices so as to optimally handle the {\em expected} demand works well: with high probability, when the actual demand is instantiated, the system is stable and the expected value of the jobs served is very close to that of the optimal offline algorithm.Comment: To appear in STOC'1

A Stochastic Resource-Sharing Network for Electric Vehicle Charging

We consider a distribution grid used to charge electric vehicles such that voltage drops stay bounded. We model this as a class of resource-sharing networks, known as bandwidth-sharing networks in the communication network literature. We focus on resource-sharing networks that are driven by a class of greedy control rules that can be implemented in a decentralized fashion. For a large number of such control rules, we can characterize the performance of the system by a fluid approximation. This leads to a set of dynamic equations that take into account the stochastic behavior of EVs. We show that the invariant point of these equations is unique and can be computed by solving a specific ACOPF problem, which admits an exact convex relaxation. We illustrate our findings with a case study using the SCE 47-bus network and several special cases that allow for explicit computations.Comment: 13 pages, 8 figure

Taming Uncertainties In Real-Time Routing For Wireless Networked Sensing And Control

Real-time routing is a basic element of closed-loop, real-time sensing and control, but it is challenging due to dynamic, uncertain link/path delays. The probabilistic nature of link/path delays makes the basic problem of computing the probabilistic distribution of path delays NP-hard, yet quantifying probabilistic path delays is a basic element of real-time routing and may well have to be executed by resource-constrained devices in a distributed manner; the highly-varying nature of link/path delays makes it necessary to adapt to in-situ delay conditions in real-time routing, but it has been observed that delay-based routing can lead to instability, estimation error, and low data delivery performance in general. To address these challenges, we propose the emph{Multi-Timescale Estimation (MTE)} method; by accurately estimating the mean and variance of per-packet transmission time and by adapting to fast-varying queueing in an accurate, agile manner, MTE enables accurate, agile, and efficient estimation of probabilistic path delay bounds in a distributed manner. Based on MTE, we propose the emph{Multi-Timescale Adaptation (MTA)} routing protocol; MTA integrates the stability of an ETX-based directed-acyclic-graph (DAG) with the agility of spatiotemporal data flow control within the DAG to ensure real-time data delivery in the presence of dynamics and uncertainties. We also address the challenges of implementing MTE and MTA in resource-constrained devices such as TelosB motes. We evaluate the performance of MTA using the NetEye and Indriya sensor network testbeds. We find that MTA significantly outperforms existing protocols, e.g., improving deadline success ratio by 89% and reducing transmission cost by a factor of 9.7

Stochastic scheduling and workload allocation : QoS support and profitable brokering in computing grids

Abstract: The Grid can be seen as a collection of services each of which performs some functionality. Users of the Grid seek to use combinations of these services to perform the overall task they need to achieve. In general this can be seen as aset of services with a workflow document describing how these services should be combined. The user may also have certain constraints on the workflow operations, such as execution time or cost ----t~ th~ user, specified in the form of a Quality of Service (QoS) document. The users . submit their workflow to a brokering service along with the QoS document. The brokering service's task is to map any given workflow to a subset of the Grid services taking the QoS and state of the Grid into account -- service availability and performance. We propose an approach for generating constraint equations describing the workflow, the QoS requirements and the state of the Grid. This set of equations may be solved using Mixed-Integer Linear Programming (MILP), which is the traditional method. We further develop a novel 2-stage stochastic MILP which is capable of dealing with the volatile nature of the Grid and adapting the selection of the services during the lifetime of the workflow. We present experimental results comparing our approaches, showing that the . 2-stage stochastic programming approach performs consistently better than other traditional approaches. Next we addresses workload allocation techniques for Grid workflows in a multi-cluster Grid We model individual clusters as MIMIk. queues and obtain a numerical solutio~ for missed deadlines (failures) of tasks of Grid workflows. We also present an efficient algorithm for obtaining workload allocations of clusters. Next we model individual cluster resources as G/G/l queues and solve an optimisation problem that minimises QoS requirement violation, provides QoS guarantee and outperforms reservation based scheduling algorithms. Both approaches are evaluated through an experimental simulation and the results confirm that the proposed workload allocation strategies combined with traditional scheduling algorithms performs considerably better in terms of satisfying QoS requirements of Grid workflows than scheduling algorithms that don't employ such workload allocation techniques. Next we develop a novel method for Grid brokers that aims at maximising profit whilst satisfying end-user needs with a sufficient guarantee in a volatile utility Grid. We develop a develop a 2-stage stochastic MILP which is capable of dealing with the volatile nature . of the Grid and obtaining cost bounds that ensure that end-user cost is minimised or satisfied and broker's profit is maximised with sufficient guarantee. These bounds help brokers know beforehand whether the budget limits of end-users can be satisfied and. if not then???????? obtain appropriate future leases from service providers. Experimental results confirm the efficacy of our approach.Imperial Users onl

Datacenter Traffic Control: Understanding Techniques and Trade-offs

Datacenters provide cost-effective and flexible access to scalable compute and storage resources necessary for today's cloud computing needs. A typical datacenter is made up of thousands of servers connected with a large network and usually managed by one operator. To provide quality access to the variety of applications and services hosted on datacenters and maximize performance, it deems necessary to use datacenter networks effectively and efficiently. Datacenter traffic is often a mix of several classes with different priorities and requirements. This includes user-generated interactive traffic, traffic with deadlines, and long-running traffic. To this end, custom transport protocols and traffic management techniques have been developed to improve datacenter network performance. In this tutorial paper, we review the general architecture of datacenter networks, various topologies proposed for them, their traffic properties, general traffic control challenges in datacenters and general traffic control objectives. The purpose of this paper is to bring out the important characteristics of traffic control in datacenters and not to survey all existing solutions (as it is virtually impossible due to massive body of existing research). We hope to provide readers with a wide range of options and factors while considering a variety of traffic control mechanisms. We discuss various characteristics of datacenter traffic control including management schemes, transmission control, traffic shaping, prioritization, load balancing, multipathing, and traffic scheduling. Next, we point to several open challenges as well as new and interesting networking paradigms. At the end of this paper, we briefly review inter-datacenter networks that connect geographically dispersed datacenters which have been receiving increasing attention recently and pose interesting and novel research problems.Comment: Accepted for Publication in IEEE Communications Surveys and Tutorial

vSkyConf: Cloud-assisted Multi-party Mobile Video Conferencing

As an important application in the busy world today, mobile video conferencing facilitates virtual face-to-face communication with friends, families and colleagues, via their mobile devices on the move. However, how to provision high-quality, multi-party video conferencing experiences over mobile devices is still an open challenge. The fundamental reason behind is the lack of computation and communication capacities on the mobile devices, to scale to large conferencing sessions. In this paper, we present vSkyConf, a cloud-assisted mobile video conferencing system to fundamentally improve the quality and scale of multi-party mobile video conferencing. By novelly employing a surrogate virtual machine in the cloud for each mobile user, we allow fully scalable communication among the conference participants via their surrogates, rather than directly. The surrogates exchange conferencing streams among each other, transcode the streams to the most appropriate bit rates, and buffer the streams for the most efficient delivery to the mobile recipients. A fully decentralized, optimal algorithm is designed to decide the best paths of streams and the most suitable surrogates for video transcoding along the paths, such that the limited bandwidth is fully utilized to deliver streams of the highest possible quality to the mobile recipients. We also carefully tailor a buffering mechanism on each surrogate to cooperate with optimal stream distribution. We have implemented vSkyConf based on Amazon EC2 and verified the excellent performance of our design, as compared to the widely adopted unicast solutions.Comment: 10 page

Flexible Scheduling in Middleware for Distributed rate-based real-time applications - Doctoral Dissertation, May 2002

Distributed rate-based real-time systems, such as process control and avionics mission computing systems, have traditionally been scheduled statically. Static scheduling provides assurance of schedulability prior to run-time overhead. However, static scheduling is brittle in the face of unanticipated overload, and treats invocation-to-invocation variations in resource requirements inflexibly. As a consequence, processing resources are often under-utilized in the average case, and the resulting systems are hard to adapt to meet new real-time processing requirements. Dynamic scheduling offers relief from the limitations of static scheduling. However, dynamic scheduling offers relief from the limitations of static scheduling. However, dynamic scheduling often has a high run-time cost because certain decisions are enforced on-line. Furthermore, under conditions of overload tasks can be scheduled dynamically that may never be dispatched, or that upon dispatch would miss their deadlines. We review the implications of these factors on rate-based distributed systems, and posits the necessity to combine static and dynamic approaches to exploit the strengths and compensate for the weakness of either approach in isolation. We present a general hybrid approach to real-time scheduling and dispatching in middleware, that can employ both static and dynamic components. This approach provides (1) feasibility assurance for the most critical tasks, (2) the ability to extend this assurance incrementally to operations in successively lower criticality equivalence classes, (3) the ability to trade off bounds on feasible utilization and dispatching over-head in cases where, for example, execution jitter is a factor or rates are not harmonically related, and (4) overall flexibility to make more optimal use of scarce computing resources and to enforce a wider range of application-specified execution requirements. This approach also meets additional constraints of an increasingly important class of rate-based systems, those with requirements for robust management of real-time performance in the face of rapidly and widely changing operating conditions. To support these requirements, we present a middleware framework that implements the hybrid scheduling and dispatching approach described above, and also provides support for (1) adaptive re-scheduling of operations at run-time and (2) reflective alternation among several scheduling strategies to improve real-time performance in the face of changing operating conditions. Adaptive re-scheduling must be performed whenever operating conditions exceed the ability of the scheduling and dispatching infrastructure to meet the critical real-time requirements of the system under the currently specified rates and execution times of operations. Adaptive re-scheduling relies on the ability to change the rates of execution of at least some operations, and may occur under the control of a higher-level middleware resource manager. Different rates of execution may be specified under different operating conditions, and the number of such possible combinations may be arbitrarily large. Furthermore, adaptive rescheduling may in turn require notification of rate-sensitive application components. It is therefore desirable to handle variations in operating conditions entirely within the scheduling and dispatching infrastructure when possible. A rate-based distributed real-time application, or a higher-level resource manager, could thus fall back on adaptive re-scheduling only when it cannot achieve acceptable real-time performance through self-adaptation. Reflective alternation among scheduling heuristics offers a way to tune real-time performance internally, and we offer foundational support for this approach. In particular, run-time observable information such as that provided by our metrics-feedback framework makes it possible to detect that a given current scheduling heuristic is underperforming the level of service another could provide. Furthermore we present empirical results for our framework in a realistic avionics mission computing environment. This forms the basis for guided adaption. This dissertation makes five contributions in support of flexible and adaptive scheduling and dispatching in middleware. First, we provide a middle scheduling framework that supports arbitrary and fine-grained composition of static/dynamic scheduling, to assure critical timeliness constraints while improving noncritical performance under a range of conditions. Second, we provide a flexible dispatching infrastructure framework composed of fine-grained primitives, and describe how appropriate configurations can be generated automatically based on the output of the scheduling framework. Third, we describe algorithms to reduce the overhead and duration of adaptive rescheduling, based on sorting for rate selection and priority assignment. Fourth, we provide timely and efficient performance information through an optimized metrics-feedback framework, to support higher-level reflection and adaptation decisions. Fifth, we present the results of empirical studies to quantify and evaluate the performance of alternative canonical scheduling heuristics, across a range of load and load jitter conditions. These studies were conducted within an avionics mission computing applications framework running on realistic middleware and embedded hardware. The results obtained from these studies (1) demonstrate the potential benefits of reflective alternation among distinct scheduling heuristics at run-time, and (2) suggest performance factors of interest for future work on adaptive control policies and mechanisms using this framework

A stochastic resource-sharing network for electric vehicle charging

We consider a distribution grid used to charge electric vehicles subject to voltage stability and various other constraints. We model this as a class of resource

A model for dynamic allocation of human attention among multiple tasks

The problem of multi-task attention allocation with special reference to aircraft piloting is discussed with the experimental paradigm used to characterize this situation and the experimental results obtained in the first phase of the research. A qualitative description of an approach to mathematical modeling, and some results obtained with it are also presented to indicate what aspects of the model are most promising. Two appendices are given which (1) discuss the model in relation to graph theory and optimization and (2) specify the optimization algorithm of the model