Measuring the Impact of Adversarial Errors on Packet Scheduling Strategies

In this paper we explore the problem of achieving efficient packet transmission over unreliable links with worst case occurrence of errors. In such a setup, even an omniscient offline scheduling strategy cannot achieve stability of the packet queue, nor is it able to use up all the available bandwidth. Hence, an important first step is to identify an appropriate metric for measuring the efficiency of scheduling strategies in such a setting. To this end, we propose a relative throughput metric which corresponds to the long term competitive ratio of the algorithm with respect to the optimal. We then explore the impact of the error detection mechanism and feedback delay on our measure. We compare instantaneous error feedback with deferred error feedback, that requires a faulty packet to be fully received in order to detect the error. We propose algorithms for worst-case adversarial and stochastic packet arrival models, and formally analyze their performance. The relative throughput achieved by these algorithms is shown to be close to optimal by deriving lower bounds on the relative throughput of the algorithms and almost matching upper bounds for any algorithm in the considered settings. Our collection of results demonstrate the potential of using instantaneous feedback to improve the performance of communication systems in adverse environments

On Packet Scheduling with Adversarial Jamming and Speedup

In Packet Scheduling with Adversarial Jamming packets of arbitrary sizes arrive over time to be transmitted over a channel in which instantaneous jamming errors occur at times chosen by the adversary and not known to the algorithm. The transmission taking place at the time of jamming is corrupt, and the algorithm learns this fact immediately. An online algorithm maximizes the total size of packets it successfully transmits and the goal is to develop an algorithm with the lowest possible asymptotic competitive ratio, where the additive constant may depend on packet sizes. Our main contribution is a universal algorithm that works for any speedup and packet sizes and, unlike previous algorithms for the problem, it does not need to know these properties in advance. We show that this algorithm guarantees 1-competitiveness with speedup 4, making it the first known algorithm to maintain 1-competitiveness with a moderate speedup in the general setting of arbitrary packet sizes. We also prove a lower bound of $\phi+1\approx 2.618$ on the speedup of any 1-competitive deterministic algorithm, showing that our algorithm is close to the optimum. Additionally, we formulate a general framework for analyzing our algorithm locally and use it to show upper bounds on its competitive ratio for speedups in $[1,4)$ and for several special cases, recovering some previously known results, each of which had a dedicated proof. In particular, our algorithm is 3-competitive without speedup, matching both the (worst-case) performance of the algorithm by Jurdzinski et al. and the lower bound by Anta et al.Comment: Appeared in Proc. of the 15th Workshop on Approximation and Online Algorithms (WAOA 2017

On packet scheduling with adversarial jamming and speedup

In Packet Scheduling with Adversarial Jamming, packets of arbitrary sizes arrive over time to be transmitted over a channel in which instantaneous jamming errors occur at times chosen by the adversary and not known to the algorithm. The transmission taking place at the time of jamming is corrupt, and the algorithm learns this fact immediately. An online algorithm maximizes the total size of packets it successfully transmits and the goal is to develop an algorithm with the lowest possible asymptotic competitive ratio, where the additive constant may depend on packet sizes. Our main contribution is a universal algorithm that works for any speedup and packet sizes and, unlike previous algorithms for the problem, it does not need to know these parameters in advance. We show that this algorithm guarantees 1-competitiveness with speedup 4, making it the first known algorithm to maintain 1-competitiveness with a moderate speedup in the general setting of arbitrary packet sizes. We also prove a lower bound of ϕ+1≈2.618 on the speedup of any 1-competitive deterministic algorithm, showing that our algorithm is close to the optimum. Additionally, we formulate a general framework for analyzing our algorithm locally and use it to show upper bounds on its competitive ratio for speedups in [1, 4) and for several special cases, recovering some previously known results, each of which had a dedicated proof. In particular, our algorithm is 3-competitive without speedup, matching both the (worst-case) performance of the algorithm by Jurdzinski et al. (Proceedings of the 12th workshop on approximation and online algorithms (WAOA), LNCS 8952, pp 193–206, 2015. http://doi.org/10.1007/978-3-319-18263-6_17) and the lower bound by Anta et al. (J Sched 19(2):135–152, 2016. http://doi.org/10.1007/s10951-015-0451-z)

An Online Approach to Dynamic Channel Access and Transmission Scheduling

Making judicious channel access and transmission scheduling decisions is essential for improving performance as well as energy and spectral efficiency in multichannel wireless systems. This problem has been a subject of extensive study in the past decade, and the resulting dynamic and opportunistic channel access schemes can bring potentially significant improvement over traditional schemes. However, a common and severe limitation of these dynamic schemes is that they almost always require some form of a priori knowledge of the channel statistics. A natural remedy is a learning framework, which has also been extensively studied in the same context, but a typical learning algorithm in this literature seeks only the best static policy, with performance measured by weak regret, rather than learning a good dynamic channel access policy. There is thus a clear disconnect between what an optimal channel access policy can achieve with known channel statistics that actively exploits temporal, spatial and spectral diversity, and what a typical existing learning algorithm aims for, which is the static use of a single channel devoid of diversity gain. In this paper we bridge this gap by designing learning algorithms that track known optimal or sub-optimal dynamic channel access and transmission scheduling policies, thereby yielding performance measured by a form of strong regret, the accumulated difference between the reward returned by an optimal solution when a priori information is available and that by our online algorithm. We do so in the context of two specific algorithms that appeared in [1] and [2], respectively, the former for a multiuser single-channel setting and the latter for a single-user multichannel setting. In both cases we show that our algorithms achieve sub-linear regret uniform in time and outperforms the standard weak-regret learning algorithms.Comment: 10 pages, to appear in MobiHoc 201

Online scheduling in fault-prone systems: performance optimization and energy efficiency

Mención Internacional en el título de doctorEveryone is familiar with the problem of online scheduling (even if they are not aware of it), from the way we prioritize our everyday decisions to the way a delivery service must decide on the route to follow in order to cover the ongoing requests. In computer science, this is a problem of even greater importance. This thesis considers two main families of online scheduling problems in computer science, and aims to provide an extended clear framework for their analysis, presenting at the same time some common characteristics that connect these problems. The first and main family of online scheduling problems considered, is task scheduling in fault-prone computing systems. As the number of clients and the possibilities offered by the rapid development of computing systems, grow with time, the increase of demands of computationally intensive tasks is inevitable. Uniprocessors are no longer capable of coping with the escalation of these demands, which among others, has led to the development of multicore-based parallel machines, Internet-based computing platforms and co-operational distributed systems. Nonetheless, the challenges of these systems, even of the simplest ones, are numerous: They have to deal with continuous dynamic requests from the clients, which are probably not of the same nature (require different amount of computational resources). The processing elements (i.e., machines) may suffer from unpredictable failures, either malicious or due to overload. Furthermore, depending on the size of these systems and the exact processing units, their power consumption may be of significant amount; even equal to the electricity needed for a small town. Hence, limiting their power consumption is another challenge. To analyze such a system one must consider the online nature of the problem; the dynamic task arrivals (client requests) of different sizes (computational demands), and the unpredictable machine crashes and restarts (failures). It is important to give guarantees for the performance of the algorithms used in these systems, thus the thesis conducts worst-case competitive analysis and covers a significant level of the three dimensions of the problem. More precisely, it studies the effects of the number of machines, the number of different task sizes and the speed of the machines – which as will be explained through the thesis, affects the power consumption of the system – on the efficiency of online scheduling algorithms. As performance measures, this thesis uses the completed load, the pending load and the latency competitiveness of the algorithms. In some cases, it considers the long-term competitiveness versions of these measures as well. One of the most important results shown, is that resource augmentation in the form of increasing the machine speedup, is necessary in order to achieve some competitiveness, or to reach optimal competitiveness. The sufficient amount of speedup is found, and online algorithms that achieve the desired competitiveness are proposed and analyzed. Apart from the algorithms designed, some of the most widely used algorithms in scheduling are also analyzed in the model considered for the first time; namely, Longest In System (LIS), Shortest In System (SIS), Largest Processing Time (LPT), and Smallest Processing Time (SPT). Nonetheless, deciding on the best algorithm between them, is not easy. Each algorithm behaves better with respect to a different evaluation metric and under different model parameters. The second family of problems considered, is packet scheduling over an unreliable wireless communication link. As claimed, these problems have a strong connection to the task scheduling problem, especially when considering one machine and no speedup, hence some of the results can be shared. A setting with a single pair of nodes is considered, connected through an unreliable wireless channel. The sending station transmits packets to a receiving station over the channel, which can be jammed and hence corrupt the packet being transmitted. First, worst-case scenarios are assumed for the channel jams, modeled by a malicious adversarial entity. The packet arrivals however, follow a stochastic distribution and competitive analysis of scheduling algorithms is pursued giving matching bounds for the most pessimistic scenarios of channel jams. The aim of the algorithms is to find the schedule (or order or transmission of the arriving packets) in order to maximize the asymptotic throughout, which corresponds to the long-term competitive ratio of total length of successfully transmitted packets. Then, a slightly different problem is considered, assuming infinite amount of data to be transmitted over the same unreliable communication link. This time however, an adversarial entity with constrained power is assumed for the channel jams. The constrained power is modeled by an Adversarial Queueing Theory (AQT) approach, defined with two main parameters; "the error availability rate", and, the maximum batch of errors available to the adversary at any time. This is the first time AQT is used to model channel jams; it has been mostly used to model the packet arrivals in networking problems. In this problem, the scheduling algorithms must decide on the length of the packets to be transmitted, with the objective of maximizing the goodput rate; the rate of successfully transmitted load. It is seen, that even for the simplest settings, the analysis and results are not trivial.This work has been supported by IMDEA Networks InstitutePrograma Oficial de Doctorado en Ingeniería TelemáticaPresidente: María Serna Iglesias.- Secretario: Vincenzo Mancuso.- Vocal: Leszek Antoni Gasieni