Survey of scalability of computational systems

Notions of scalability have helped in evaluation of the performance of algorithms and of parallel and distributed systems, including multi-agent systems. Algorithm analysis and computational complexity address primarily the scalability of solutions, where we may intuitively associate the scalability of a solution with its “reasonable” performance regardless of problem size. Performance and scalability of concurrent systems and models is a research area lacking a standard authoritative body of literature. Some algorithms are favored precisely because they scale better than others, and problems are called intractable precisely because their best solutions don’t scale well. O(n) solutions scale better than O(n) ones; problems in class P (polynomial-time) have solutions that scale acceptably, whereas NP-hard problems have no known solutions that scale acceptably. The objective of previous work on scalability of parallel systems was to use scalability analysis to select algorithm-architecture combinations, to predict performance of systems or algorithms, to determine optimal number of processors for a task, or to predict the effect of changes in hardware technology on performance [2]. Previous work on scalability in distributed systems and MASs has been based on the work on scalability in parallel systems. Notions of scalability to date have been based on the assumption that the complexity of algorithm execution is the object of study. Scalability notions are also related to efficiency, which may be defined as speedup divided by the number of processors, so that ideal efficiency is 1.0. Speedup for an algorithm running on a system is serial time (running time on one processor) divided by parallel time for the algorithm. Research has identified a metric to determine scalability, isoefficiency. The isoefficiency of an algorithm executing on an architecture is the ratio of problem size to the minimum number of processors p necessary to obtain an increase in speedup proportional to p. For cost-optimal algorithms, fixed running time for arbitrary problem size is obtainable if and only if the isoefficiency of the algorithm is Θ(p) [4]. A system may be described as scalable if an isoefficiency function exists; i.e., when efficiency can be maintained as p rises if problem size W rises sufficiently. Communication overhead among processors may prevent linear speedup in parallel systems, hence isoefficiency, hence scalability. In particular, global communication, which includes broadcast, one-to-all, and all-to-all personalized communication, is an obstacle. On parallel machines with message-passing latency,