The energy usage of computer systems is becoming an important consideration, especially for batteryoperated systems. Various methods for reducing energy consumption have been investigated, both at the circuit level and at the operating systems level. In this paper, we propose a simple model of job scheduling aimed at capturing some key aspects of energy minimization. In this model, each job is to be executed between its arrival time and deadline by a single processor with variable speed, under the assumption that energy usage per unit time, P , is a convex function of the processor speed s. We give an off-line algorithm that computes, for any set of jobs, a minimum-energy schedule. We then consider some on-line algorithms and their competitive performance for the power function P ( s ) = s p where p 3 2. It is shown that one natural heuristic, called the Average Rate heuristic, uses at most a constant times the minimum energy required. The analysis involves bounding the largest eigenvalue in matrices of a special type.

When a database is replicated at many sites, maintaining mutual consistency among the sites in the face of updates is a significant problem. This paper describes several randomized algorithms for distributing updates and driving the replicas toward consistency. The algorithms are very simple and require few guarantees from the underlying communication system, yet they ensure that the effect of every update is eventually reflected in all replicas. The cost and performance of the algorithms are tuned by choosing appropriate distributions in the randomization step. The algorithms are closely analogous to epidemics, and the epidemiology literature aids in understanding their behavior. One of the algorithms has been implemented in the Clearinghouse servers of the Xerox Corporate Internet. solving long-standing problems of high traffic and database inconsistency.

We discuss gateway queueing algorithms and their role in controlling congestion in datagram networks. A fair queueing aJgorithm, based on an earlier suggestion by Nagle, is proposed. An.alysis and simulations are used to compare this algorithm to other congestion control schemes. We find. that fair queueing provides several important advantages over the usual first-come-first-serve queueing algorithm: fair allocation of bandwidth, lower delay for sources using less than their full share of bandwidth, and protection from ill-behaved sources.

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