Low latency via redundancy

Low latency is critical for interactive networked applications. But while we know how to scale systems to increase capacity, reducing latency --- especially the tail of the latency distribution --- can be much more difficult. In this paper, we argue that the use of redundancy is an effective way to convert extra capacity into reduced latency. By initiating redundant operations across diverse resources and using the first result which completes, redundancy improves a system's latency even under exceptional conditions. We study the tradeoff with added system utilization, characterizing the situations in which replicating all tasks reduces mean latency. We then demonstrate empirically that replicating all operations can result in significant mean and tail latency reduction in real-world systems including DNS queries, database servers, and packet forwarding within networks

Streamability of nested word transductions

We consider the problem of evaluating in streaming (i.e., in a single left-to-right pass) a nested word transduction with a limited amount of memory. A transduction T is said to be height bounded memory (HBM) if it can be evaluated with a memory that depends only on the size of T and on the height of the input word. We show that it is decidable in coNPTime for a nested word transduction defined by a visibly pushdown transducer (VPT), if it is HBM. In this case, the required amount of memory may depend exponentially on the height of the word. We exhibit a sufficient, decidable condition for a VPT to be evaluated with a memory that depends quadratically on the height of the word. This condition defines a class of transductions that strictly contains all determinizable VPTs

Kinetic Intersections as a Source of Information on Rate Coefficients

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Compositional Performance Modelling with the TIPPtool

Stochastic process algebras have been proposed as compositional specification formalisms for performance models. In this paper, we describe a tool which aims at realising all beneficial aspects of compositional performance modelling, the TIPPtool. It incorporates methods for compositional specification as well as solution, based on state-of-the-art techniques, and wrapped in a user-friendly graphical front end. Apart from highlighting the general benefits of the tool, we also discuss some lessons learned during development and application of the TIPPtool. A non-trivial model of a real life communication system serves as a case study to illustrate benefits and limitations

Tropical Fourier-Motzkin elimination, with an application to real-time verification

We introduce a generalization of tropical polyhedra able to express both strict and non-strict inequalities. Such inequalities are handled by means of a semiring of germs (encoding infinitesimal perturbations). We develop a tropical analogue of Fourier-Motzkin elimination from which we derive geometrical properties of these polyhedra. In particular, we show that they coincide with the tropically convex union of (non-necessarily closed) cells that are convex both classically and tropically. We also prove that the redundant inequalities produced when performing successive elimination steps can be dynamically deleted by reduction to mean payoff game problems. As a complement, we provide a coarser (polynomial time) deletion procedure which is enough to arrive at a simply exponential bound for the total execution time. These algorithms are illustrated by an application to real-time systems (reachability analysis of timed automata).Comment: 29 pages, 8 figure

Adaptive Route Choice in Stochastic Time-Dependent Networks: Routing Algorithms and Choice Modeling

Transportation networks are inherently uncertain due to random disruptions; meanwhile, real-time information potentially helps travelers adapt to realized traffic conditions and make better route choices under such disruptions. Modeling adaptive route choice behavior is essential in evaluating Advanced Traveler Information Systems (ATIS) and related policies to better provide travelers with real-time information. This dissertation contributes to the state of the art by estimating the first latent-class routing policy choice model using revealed preference (RP) data and providing efficient computer algorithms for routing policy choice set generation. A routing policy is defined as a decision rule applied at each link that maps possible realized traffic conditions to decisions on the link to take next. It represents a traveler\u27s ability to look ahead in order to incorporate real-time information not yet available at the time of decision. A case study is conducted in Stockholm, Sweden and data for the stochastic time-dependent network are generated from hired taxi Global Positioning System (GPS) traces through the methods of map-matching and non-parametric link travel time estimation. A latent-class Policy Size Logit model is specified with two additional layers of latency in the measurement equation. The two latent classes of travelers are policy users who follow routing policies and path users who follow fixed paths. For the measurement equation of the policy user class, the choice of a routing policy is latent and only its realized path on a given day can be observed. Furthermore, when GPS traces have relatively long gaps between consecutive readings, the realized path cannot be uniquely identified. Routing policy choice set generation is based on the generalization of path choice set generation methods, and utilizes efficient implementation of an optimal routing policy (ORP) algorithm based on the two-queue data structure for label correcting. Systematic evaluation of the algorithm in random networks as well as in two large scale real-life networks is conducted. The generated choice sets are evaluated based on coverage and adaptiveness. Coverage is the percentage of observed trips included in the generated choice sets based on a certain threshold of overlapping between observed and generated routes, and adaptiveness represents the capability of a routing policy to be realized as different paths over different days. It is shown that using a combination of methods yields satisfactory coverage of 91.2%. Outlier analyses are then carried out for unmatching trips in choice set generation. The coverage achieves 95% for 100% threshold after correcting GPS errors and breaking up trips with intermediate stops, and further achieves 100% for 90% threshold. The latent-class routing policy choice model is estimated against observed GPS traces based on the three different sample sizes resulting from coverage improvement, and the estimates appear consistent across different sample sizes. Estimation results show the policy user class probability increases with trip length, and the latent-class routing policy choice model fits the data better than a single-class path choice model or routing policy choice model. This suggests that travelers are heterogeneous in terms of their ability and willingness to plan ahead and utilize real-time information. Therefore, a fixed path model as commonly used in the literature may lose explanatory power due to its simplified assumptions on network stochasticity and travelers\u27 utilization of real-time information