Heavy Tails and Instabilities in Large-Scale Systems with Failures

Modern engineering systems, e.g., wireless communication networks, distributed computing systems, etc., are characterized by high variability and susceptibility to failures. Failure recovery is required to guarantee the successful operation of these systems. One straight- forward and widely used mechanism is to restart the interrupted jobs from the beginning after a failure occurs. In network design, retransmissions are the primary building blocks of the network architecture that guarantee data delivery in the presence of channel failures. Retransmissions have recently been identified as a new origin of power laws in modern information networks. In particular, it was discovered that retransmissions give rise to long tails (delays) and possibly zero throughput. To this end, we investigate the impact of the ‘retransmission phenomenon’ on the performance of failure prone systems and propose adaptive solutions to address emerging instabilities. The preceding finding of power law phenomena due to retransmissions holds under the assumption that data sizes have infinite support. In practice, however, data sizes are upper bounded 0 ≤ L ≤ b, e.g., WaveLAN’s maximum transfer unit is 1500 bytes, YouTube videos are of limited duration, e-mail attachments cannot exceed 10MB, etc. To this end, we first provide a uniform characterization of the entire body of the distribution of the number of retransmissions, which can be represented as a product of a power law and the Gamma distribution. This rigorous approximation clearly demonstrates the transition from power law distributions in the main body to exponential tails. Furthermore, the results highlight the importance of wisely determining the size of data fragments in order to accommodate the performance needs in these systems as well as provide the appropriate tools for this fragmentation. Second, we extend the analysis to the practically important case of correlated channels using modulated processes, e.g., Markov modulated, to capture the underlying dependencies. Our study shows that the tails of the retransmission and delay distributions are asymptotically insensitive to the channel correlations and are determined by the state that generates the lightest tail in the independent channel case. This insight is beneficial both for capacity planning and channel modeling since the independent model is sufficient and the correlation details do not matter. However, the preceding finding may be overly optimistic when the best state is atypical, since the effects of ‘bad’ states may still downgrade the performance. Third, we examine the effects of scheduling policies in queueing systems with failures and restarts. Fair sharing, e.g., processor sharing (PS), is a widely accepted approach to resource allocation among multiple users. We revisit the well-studied M/G/1 PS queue with a new focus on server failures and restarts. Interestingly, we discover a new phenomenon showing that PS-based scheduling induces complete instability in the presence of retransmissions, regardless of how low the traffic load may be. This novel phenomenon occurs even when the job sizes are bounded/fragmented, e.g., deterministic. This work demonstrates that scheduling one job at a time, such as first-come-first-serve, achieves a larger stability region and should be preferred in these systems. Last, we delve into the area of distributed computing and study the effects of commonly used mechanisms, i.e., restarts, fragmentation, replication, especially in cloud computing services. We evaluate the efficiency of these techniques under different assumptions on the data streams and discuss the corresponding optimization problem. These findings are useful for optimal resource allocation and fault tolerance in rapidly developing computing networks. In addition to networking and distributed computing systems, the aforementioned results improve our understanding of failure recovery management in large manufacturing and service systems, e.g., call centers. Scalable solutions to this problem increase in significance as these systems continuously grow in scale and complexity. The new phenomena and the techniques developed herein provide new insights in the areas of parallel computing, probability and statistics, as well as financial engineering

Ο ρόλος της συνεργασίας των εκπαιδευτικών στη διδασκαλία και μάθηση των Μαθηματικών

Η παρούσα εργασία έχει ως αντικείμενο μελέτης τη συνεργασία των εκπαιδευτικών των Μαθηματικών και "άλλων" (κυρίως ερευνητών της Διδακτικής των Μαθηματικών). Έπειτα από μελέτη προηγούμενων ερευνών σχετικών με τη συνεργασία, τέθηκαν τρία ερευνητικά ερωτήματα κι ακολούθησε ανάλυση των δεδομένων μέσω grounded προσέγγισης. Έτσι, εξήχθησαν τα αποτελέσματα της μελέτης. Φάνηκε πως οι περισσότερες έρευνες εστιάζουν στα θετικά αποτελέσματα της συνεργασίας στη διδασκαλία και μάθηση των Μαθηματικών. Επίσης, οι περισσότερες από τις συνεργασίες γίνονται στα πλαίσια κοινοτήτων και προγραμμάτων επαγγελματικής ανάπτυξης. Τέλος, αναδείχθηκαν τα κύρια οφέλη της συνεργασίας για τους συμμετέχοντες και τους μαθητές παράλληλα με τα εμπόδια και τους περιορισμούς που μπορεί να υπάρξουν. Δόθηκαν προτάσεις για μελλοντική έρευνα σχετικά με τη συνεργασία.The present study is a review study that aims at the collaboration of teachers of mathematics and "others" (mainly researchers of Mathematics Education). Following a study of past collaborative research, three research questions were asked and the data were analysed with a grounded approach. So, the results of the study were exported. Most research seems to focus on the positive effects of collaborating on teaching and learning mathematics. Also, most forms of collaboration are made within communities and professional development programs. Finally, the main benefits of collaboration for the participants and the students have emerged alongside the obstacles and the limitations that may arise. Proposals were made for future research on collaboration

Software Defined Batteries

Abstract Different battery chemistries perform better on different axes, such as energy density, cost, peak power, recharge time, longevity, and efficiency. Mobile system designers are constrained by existing technology, and are forced to select a single chemistry that best meets their diverse needs, thereby compromising other desirable features. In this paper, we present a new hardware-software system, called Software Defined Battery (SDB), which allows system designers to integrate batteries of different chemistries. SDB exposes APIs to the operating system which control the amount of charge flowing in and out of each battery, enabling it to dynamically trade one battery property for another depending on application and/or user needs. Using microbenchmarks from our prototype SDB implementation, and through detailed simulations, we demonstrate that it is possible to combine batteries which individually excel along different axes to deliver an enhanced collective performance when compared to traditional battery packs

E.D.: Retransmissions over correlated channels

ABSTRACT Frequent failures characterize many existing communication networks, e.g. wireless ad-hoc networks, where retransmission-based failure recovery represents a primary approach for successful data delivery. Recent work has shown that retransmissions can cause power law delays and instabilities even if all traffic and network characteristics are super-exponential. While the prior studies have considered an independent channel model, in this paper we extend the analysis to the practically important dependent case. We use modulated processes, e.g. Markov modulated, to capture the channel dependencies. We study the number of retransmissions and delays when the hazard functions of the distributions of data sizes and channel statistics are proportional, conditionally on the channel state. Our results show that the tails of the retransmission and delay distributions are asymptotically insensitive to the channel correlations and are determined by the state that generates the lightest asymptotics. This insight is beneficial both for capacity planning and channel modeling since we do not need to account for the correlation details. However, these results may be overly optimistic when the best state is infrequent, since the effects of 'bad' states may be prevalent for sufficiently long to downgrade the expected performance

Uniform approximation of the distribution for the number of retransmissions of bounded documents

Retransmission-based failure recovery represents a primary approach in existing communication networks, on all protocol layers, that guarantees data delivery in the presence of channel failures. Contrary to the traditional belief that the number of retransmissions is geometrically distributed, a new phenomenon was discovered recently, which shows that retransmissions can cause long (-tailed) delays and instabilities even if all traffic and network characteristics are light-tailed, e.g., exponential or Gaussian. Since the preceding finding holds under the assumption that data sizes have infinite support, in this paper we investigate the practically important case of bounded data units 0 ≤ Lb ≤ b. To this end, we provide an explicit and uniform characterization of the entire body of the retransmission distribution P[Nb>n]inbothnand b. This rigorous approximation clearly demonstrates the previously observed transition from power law distributions in the main body to exponential tails. The accuracy of our approximation is validated with a number of simulation experiments. Furthermore, the results highlight the importance of wisely determining the size of data units in order to accommodate the performance needs in retransmission-based systems. From a broader perspective, this study applies to any other system, e.g., computing, where restart mechanisms are employed after a job processing failure