A Process Calculus for Asynchronously Communication with Transmission Delay

Distributed systems consist of multiple processors which corporate with one another by sending messages over communication networks. These communication networks often have transmission delay which results in a physical and logical function of geographical distance, communication bandwidth, and communication protocol overhead. The delay essentially characterizes distributed systems and one of the most difficulty in developing correct distributed systems. For example, the delay often affects the arrival time of messages and thus causes inexpectabel causalities among events on different processors. From the reason of efficency, in distributd systems communication among processors is often realized as an asynchronous form in order to reduce synchronization cost including communication delay between a sender processor and a receiver one. In order to construct and verify programs for distributed systems, we must take this delay into consideration. The objective of this paper is to propose a framework for describing quantitatively communication delay and analyzing the influence of the delay upon interactions among distributed processes. The framework is formulated based on a process algebra, for example ACP [1], CCS [10], π-calculus [11]. There have indeed been some process algebras for distributed systems. Most of them are extensions of existing process algebras with some natures of distributed computing: process locations [4, 9], port passing [7, 10, ?], and local time, i.e., the inexistence of global time information [?], and not communication delay. In this paper, we dare to not introduce these natures, including process location in order to concentrating on investigating communication delay and its influence. 1 . The framework proposed in this paper is an extension of a timed process algebra [15] with the ability of expressing parallelism, communication delay, and asynchronous communication. Through its expressiveness power, we try to strictly analyze the influence of the delay upon the behavioral and temporal properties of interactions among distributed real-time processes.