An Efficient Δ–Causal Distributed Algorithm for Synchronous Cooperative Systems in Unreliable Networks

Algoritmo Eficiente Distribuido Δ–Causal para Sistemas Cooperativos Síncronos sobre Redes no Fiables

Saúl E. Pomares Hernández, Eduardo López Domínguez and Gustavo Rodríguez Gómez

Department of Computer Science, National Institute of Astrophysics, Optics and Electronics (INAOE) Luis Enrique Erro No. 1, Tonantzintla, Puebla, Mexico, C.P. 72840 spomares@ccc.inaoep.mx, edominguez@ccc.inaoep.mx, grodrig@ccc.inaoep.mx

Abstract

In cooperative systems causal ordering delivery has been used to resolve problems of coherency of type producer–consumer. Causal order delivery is important for distributed systems since it allows an asynchronous execution to participants. When time delivery constraints are considered, ensuring causal delivery becomes more complex, as is the case for synchronous cooperative systems, such as Telemedicine and Teleimmersion. In these systems, the messages (units of data of continuous and discrete media) have an associated lifetime that determines the period of useful time in which the messages must be delivered. On the other hand, generally in these systems there is no time for retransmit them when messages are lost. Causal order with time constraints has previously been addressed, and it is called Δ–causal order. In this paper, we present an efficient Δ–causal distributed algorithm for unreliable networks that is characterized by the use of a forward error correction (FEC) scheme and a distributed method to calculate the message lifetime based on relative time points (i.e. no global time is used). We show the efficiency of our Δ–causal algorithm in terms of the control information attached per message.

Keywords: Cooperative systems, Group communication, Causal order.

Resumen

En los sistemas cooperativos el ordenamiento causal ha sido usado para resolver problemas de coherencia de tipo productor–consumidor. La entrega de orden causal es importante en general para los sistemas distribuidos debido a que permite a los participantes una ejecución asíncrona. Cuando las restricciones de entrega en tiempo real son contempladas, asegurar la entrega causal se vuelve más complejo, como es el caso para los sistemas cooperativos síncronos, tales como Telemedicina y Teleinmersión. En estos sistemas, los mensajes (datos continuos y discretos) tienen asociado un tiempo de vida que determina el periodo de tiempo útil en cual los mensajes deben ser entregados, y por el otro lado, en general en estos sistemas, cuando los mensajes son perdidos no existe tiempo para retransmitirlos. El orden causal con restricciones de tiempo ha sido previamente estudiado, y es nombrado orden Δ–causal. En este trabajo, presentamos un algoritmo distribuido Δ–causal eficiente sobre redes no fiables, nuestro algoritmo se caracteriza por el uso de un esquema de corrección de errores hacia delante (FEC) y un método distribuido para calcular el tiempo de vida de un mensaje basado en puntos de tiempo relativo (ningún tiempo global es utilizado). Mostramos la eficiencia de nuestro algoritmo Δ–causal en términos de la información de control unida a cada mensaje.

Palabras clave: Sistemas cooperativos, Comunicación en grupo, Orden causal.

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