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In data centres, there exist several techniques for energy efficiency purposes. When applied, most of those techniques have impact on the quality (e.g. performance) of the underlying services. A careful study is required in order to optimise such an energy-performance trade-off. In this paper, we study the speed scaling as an energy efficiency technique within the scope of high-performance computing (HPC) data centres. We propose a methodology based on threelevels: analytic, simulation and technical. At the analytical level, the matrix-analytic method (MAM) allows one to obtain energyperformance measures explicitly for a small-scale system. At the simulation level, discrete-event simulation (DES) based on the generalised semi-Markov processes (GSMP) is used to derive the corresponding estimates. Finally, at the technical level, a real small-scaled system in a controlled environment is used. The preliminary results demonstrate that simulation and technical models go well together with the theoretical one with an accuracy of more than 95%. CCS CONCEPTS• Hardware → Enterprise level and data centers power issues; • Mathematics of computing → Queueing theory; • Computing methodologies → Discrete-event simulation.

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In this paper, we consider a queuing inventory system with heterogeneous customers of K types arriving according to a marked Markovian arrival process. Each class of customers differs by nature of the service they seek and different priorities are assigned for each class resulting in different levels of inventory admitted to exhaust for customers of each class. A single service node is provided for each class with exponential services having class-dependent service rates. All classes of customers are served from a single source of inventory replenished according to (s,S) policy with exponentially distributed lead time. Stability condition and steady state probabilities are obtained by matrix-analytic method. Some important performance measures are also derived. Inventory recycle time was analyzed in detail. Useful cost function and numerical illustrations are also given. The optimization problem is interesting and can be solved in similar real scenario.

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