Coupling from the past in hybrid models for file sharing peer to peer systems

International audienceIn this paper we show how file sharing peer to peer systems can be modeled by hybrid systems with a continuous part corresponding to a fluid limit of files and a discrete part corresponding to customers. Then we show that this hybrid system is amenable to perfect simulations (i.e. simulations providing samples of the system states which distributions have no bias from the asymptotic distribution of the system). An experimental study is carried to show the respective influence that the different parameters (such as time-to-live, rate of requests, connection time) play on the behavior of large peer to peer systems, and also to show the effectiveness of this approach for numerical solutions of stochastic hybrid systems

Analysis of randomized join-the-shortest-queue (JSQ) schemes in large heterogeneous processor-sharing systems

In this paper, we investigate the stability and performance of randomized dynamic routing schemes for jobs based on the Join-the-Shortest Queue (JSQ) criterion in a heterogeneous system of many parallel servers. In particular, we consider servers that use processor sharing but with different server rates, and jobs are routed to the server with the smallest occupancy among a finite number of randomly sampled servers. We focus on the case of two servers that is often referred to as a Power-of-Two scheme. We first show that in the heterogeneous setting, uniform sampling of servers can cause a loss in the stability region and thus such randomized dynamic schemes need not outperform static randomized schemes in terms of mean delay in opposition to the homogeneous case of equal server speeds where the stability region is maximal and coincides with that of the static randomized routing. We explicitly characterize the stationary distributions of the server occupancies and show that the tail distribution of the server occupancy has a super-exponential behavior as in the homogeneous case as the number of servers goes to infinity. To overcome the stability issue, we show that it is possible to combine the static state-independent scheme with a randomized JSQ scheme that allows us to recover the maximal stability region combined with the benefits of JSQ, and such a scheme is preferable in terms of average delay. The techniques are based on a mean field analysis where we show that the stationary distributions coincide with those obtained under asymptotic independence of the servers and, moreover, the stationary distributions are insensitive to the job-size distribution

Data Parallel Hypersweeps for in Situ Topological Analysis

The contour tree is a tool for understanding the topological structure of a scalar field. Recent work has built efficient contour tree algorithms for shared memory parallel computation, driven by the need to analyze large data sets in situ while the simulation is running. Unfortunately, methods for using the contour tree for practical data analysis are still primarily serial, including single isocontour extraction, branch decomposition and simplification. We report data parallel methods for these tasks using a data structure called the hyperstructure and a general purpose approach called a hypersweep. We implement and integrate these methods with a Cinema database that stores features as depth images and with a web server that reconstructs the features for direct visualization

Worst-Case Input Generation for Concurrent Programs under Non-Monotone Resource Metrics

Worst-case input generation aims to automatically generate inputs that exhibit the worst-case performance of programs. It has several applications, and can, for example, detect vulnerabilities to denial-of-service attacks. However, it is non-trivial to generate worst-case inputs for concurrent programs, particularly for resources like memory where the peak cost depends on how processes are scheduled. This article presents the first sound worst-case input generation algorithm for concurrent programs under non-monotone resource metrics like memory. The key insight is to leverage resource-annotated session types and symbolic execution. Session types describe communication protocols on channels in process calculi. Equipped with resource annotations, resource-annotated session types not only encode cost bounds but also indicate how many resources can be reused and transferred between processes. This information is critical for identifying a worst-case execution path during symbolic execution. The algorithm is sound: if it returns any input, it is guaranteed to be a valid worst-case input. The algorithm is also relatively complete: as long as resource-annotated session types are sufficiently expressive and the background theory for SMT solving is decidable, a worst-case input is guaranteed to be returned. A simple case study of a web server's memory usage demonstrates the utility of the worst-case input generation algorithm

Session Coalgebras: A Coalgebraic View on Session Types and Communication Protocols

Compositional methods are central to the development and verification of software systems. They allow to break down large systems into smaller components, while enabling reasoning about the behaviour of the composed system. For concurrent and communicating systems, compositional techniques based on behavioural type systems have received much attention. By abstracting communication protocols as types, these type systems can statically check that programs interact with channels according to a certain protocol, whether the intended messages are exchanged in a certain order. In this paper, we put on our coalgebraic spectacles to investigate session types, a widely studied class of behavioural type systems. We provide a syntax-free description of session-based concurrency as states of coalgebras. As a result, we rediscover type equivalence, duality, and subtyping relations in terms of canonical coinductive presentations. In turn, this coinductive presentation makes it possible to elegantly derive a decidable type system with subtyping for $\pi$-calculus processes, in which the states of a coalgebra will serve as channel protocols. Going full circle, we exhibit a coalgebra structure on an existing session type system, and show that the relations and type system resulting from our coalgebraic perspective agree with the existing ones.Comment: 36 pages, submitte

Randomized Assignment of Jobs to Servers in Heterogeneous Clusters of Shared Servers for Low Delay

We consider the job assignment problem in a multi-server system consisting of $N$ parallel processor sharing servers, categorized into $M$ ($\ll N$) different types according to their processing capacity or speed. Jobs of random sizes arrive at the system according to a Poisson process with rate $N \lambda$. Upon each arrival, a small number of servers from each type is sampled uniformly at random. The job is then assigned to one of the sampled servers based on a selection rule. We propose two schemes, each corresponding to a specific selection rule that aims at reducing the mean sojourn time of jobs in the system. We first show that both methods achieve the maximal stability region. We then analyze the system operating under the proposed schemes as $N \to \infty$ which corresponds to the mean field. Our results show that asymptotic independence among servers holds even when $M$ is finite and exchangeability holds only within servers of the same type. We further establish the existence and uniqueness of stationary solution of the mean field and show that the tail distribution of server occupancy decays doubly exponentially for each server type. When the estimates of arrival rates are not available, the proposed schemes offer simpler alternatives to achieving lower mean sojourn time of jobs, as shown by our numerical studies

Timely-Throughput Optimal Scheduling with Prediction

Motivated by the increasing importance of providing delay-guaranteed services in general computing and communication systems, and the recent wide adoption of learning and prediction in network control, in this work, we consider a general stochastic single-server multi-user system and investigate the fundamental benefit of predictive scheduling in improving timely-throughput, being the rate of packets that are delivered to destinations before their deadlines. By adopting an error rate-based prediction model, we first derive a Markov decision process (MDP) solution to optimize the timely-throughput objective subject to an average resource consumption constraint. Based on a packet-level decomposition of the MDP, we explicitly characterize the optimal scheduling policy and rigorously quantify the timely-throughput improvement due to predictive-service, which scales as $\Theta(p\left[C_{1}\frac{(a-a_{\max}q)}{p-q}\rho^{\tau}+C_{2}(1-\frac{1}{p})\right](1-\rho^{D}))$, where $a, a_{\max}, \rho\in(0, 1), C_1>0, C_2\ge0$ are constants, $p$ is the true-positive rate in prediction, $q$ is the false-negative rate, $\tau$ is the packet deadline and $D$ is the prediction window size. We also conduct extensive simulations to validate our theoretical findings. Our results provide novel insights into how prediction and system parameters impact performance and provide useful guidelines for designing predictive low-latency control algorithms.Comment: 14 pages, 7 figure