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In this paper we prove a stability result for Hamilton-Jacobi equations with an integro-differential term for discontinuous Hamiltonians. This type of equations arises in various problems concerning, for example, the control of diffusion processes with jumps, the theory of large deviations for processes with jumps, and the theory of piecewise deterministic processes. 1. Introduction. The theory of viscosity solutions of Hamilton-Jacobi equations, introduced by M. G. Crandall and P. L. Lions [5], has given rise to numerous developments in such a way that from now on it covers all necessary tools for an effective use in applied mathematics. The case of Hamilton-Jacobi equations with continuous Hamiltonians was simplified by M. G. Crandall, L. C. Evans, and P. L. Lions [6] and thereafter extended, by P. L. Lions [8], to second order equations. The extension, of the notion of viscosity solutions to noncontinuous first order Hamiltonians, was first obtained by H. Ishii [4], and later by G. Barles and B. Perthame [2]. Short time after, A. Sayah [9] proved existence and uniqueness of viscosity solutions for the continuous Hamilton-Jacobi equations with an integro-differential term.In this paper we intend to prove a stability result for Hamilton-Jacobi equations with an integro-differential term for discontinuous Hamiltonians H defined by:

This paper deals with the reduction of energy consumption in large scale systems, especially by taking into account the impact of energy consumption for server consolidation. Decreasing the number of physical hosts used while ensuring a certain level of quality of services is the goal of our approach. We introduce a metric called energetic yield which represents the quality of a task placement on a subset of machines, while taking into account quality of service and energy efficiency aspects. It measures the difference between resources required by a job and what the system allocates ultimately, while trying to save energy. Our work aims at minimizing this difference. We propose placement heuristics that are compared to the optimal solution and to a related system. In this paper, we present a set of experiments showing the relevance of this metric in order to reduce significantly energy consumption.