- Distributed Computing manuscript No(will be...

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Unformatted text preview: Distributed Computing manuscript No. (will be inserted by the editor) Indranil Gupta · Mahvesh Nagda · Christo Frank Devaraj The Design of Novel Distributed Protocols from Differential Equations Received: date / Accepted: date Abstract This paper proposes a framework to trans- late certain subclasses of differential equation systems into practical protocols for distributed systems. The gen- erated protocols are intended for large-scale distributed systems that contain several hundreds to thousands of processes. The synthesized protocols are state machines containing probabilistic transitions and actions, and they are proved to show equivalent stochastic behavior to the original equations. The protocols are probabilistically scalable and reliable, and have practical applications in large-scale distributed systems, e.g., peer to peer sys- tems. In order to illustrate the usefulness of the frame- work, it is used to generate new solutions for the prob- lems of (i) responsibility migration (giving rise to a novel model of dynamic replication), and (ii) majority selec- tion. We present mathematical analysis of these two pro- tocols, and experimental results from our implementa- tions. These two protocols are derived from natural analo- gies that are represented as differential equations - en- demics and the Lotka-Volterra model of competition re- spectively. We believe the design framework could be ef- fectively used in transforming, in a very systematic man- ner, well-known natural phenomena into protocols for distributed systems. This research was supported in part by NSF CAREER grant CNS-0448246 and in part by NSF ITR grant CMS-0427089. I. Gupta Department of Computer Science University of Illinois at Urbana-Champaign. 201 N. Goodwin Ave., Urbana, IL, USA 61801. Ph: 1 217 265 5517. Fax: 1 217 265 6494. E-mail: [email protected] M. Nagda Wolverine Asset Management. 3555 Scottsdale Circle, Naperville, IL 60564. E-mail: [email protected] C.F. Devaraj Microsoft Corporation. 2400 Elliott Ave, 214, Seattle, WA 98121. E-mail: [email protected] Keywords Science of Protocol Design, Differential Equations, Distributed Protocols, Scalability, Reliability, Replication, Endemics, Voting, LV, Probabilistic Protocols. 1 Introduction Much attention has been paid to studying the scalabil- ity and reliability of distributed protocols that run in- side large-scale distributed systems containing hundreds to thousands of processes, such as peer to peer systems, the Grid, the Internet, and the Web. However, the sci- ence of design of scalable, efficient, and reliable protocols for such large-scale distributed systems remains a diffi- cult problem. In this paper, we describe a framework to translate sets of differential equations (called a “sys- tem of differential equations”, or abbreviated as “equa- tion system”) into a protocol for a large-scale distrib- uted system. The techniques generate a state machine where states are derived from variables in the original...
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This note was uploaded on 12/08/2011 for the course CS 525 taught by Professor Gupta during the Spring '08 term at University of Illinois, Urbana Champaign.

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