Themistoklis Charalambous

Self-adaptive and self-configured CPU resource provisioning for virtualized servers using Kalman filters

Data center virtualization allows cost-effective server consolidation which can increase system throughput and reduce power consumption. Resource management of virtualized servers is an important and challenging task, especially when dealing with fluctuating workloads and complex multi-tier server applications. Recent results in control theory-based resource management have shown the potential benefits of adjusting allocations to match changing workloads.n This paper presents a new resource management scheme that integrates the Kalman filter into feedback controllers to dynamically allocate CPU resources to virtual machines hosting server applications. The novelty of our approach is the use of the Kalman filter-the optimal filtering technique for state estimation in the sum of squares sense-to track the CPU utilizations and update the allocations accordingly. Our basic controllers continuously detect and self-adapt to unforeseen workload intensity changes.n Our more advanced controller self-configures itself to any workload condition without any a priori information. Indicatively, it results in within 4.8% of the performance of workload-aware controllers under high intensity workload changes, and performs equally well under medium intensity traffic. In addition, our controllers are enhanced to deal with multi-tier server applications: by using the pair-wise resource coupling between application components, they provide a 3% on average server performance improvement when facing large unexpected workload increases when compared to controllers with no such resource-coupling mechanism. We evaluate our techniques by controlling a 3-tier Rubis benchmark web site deployed on a prototype Xen-virtualized cluster.

Contractive Interference Functions and Rates of Convergence of Distributed Power Control Laws

The standard interference functions introduced by Yates have been very influential on the analysis and design of distributed power control laws. While powerful and versatile, the framework has some drawbacks: the existence of fixed-points has to be established separately, and no guarantees are given on the rate of convergence of the iterates. This paper introduces contractive interference functions, a slight reformulation of the standard interference functions that guarantees the existence and uniqueness of fixed-points along with linear convergence of iterates. We show that many power control laws from the literature are contractive and derive, sometimes for the first time, analytical convergence rate estimates for these algorithms. We also prove that contractive interference functions converge when executed totally asynchronously and, under the assumption that the communication delay is bounded, derive an explicit bound on the convergence time penalty due to increased delay. Finally, we demonstrate that although standard interference functions are, in general, not contractive, they are all para-contractions with respect to a certain metric. Similar results for two-sided scalable interference functions are also derived.

On the stability of the Foschini-Miljanic algorithm with time-delays

Many of the distributed power control algorithms for wireless networks in the literature ignore the fact that while the algorithms necessitate communication among users, propagation delays exist in the network. This problem is of vital importance, since propagation delays are omnipresent in wireless networks. The Foschini-Miljanic algorithm is provably stable if there are no time-delays in the execution of the algorithm. However, since the interference measurements are fed back to the transmitter by its corresponding receiver, time-delays are inevitably introduced into the system. This work presents a more realistic version of the well known Foschini-Miljanic algorithm for distributed power control since it considers the time-delays introduced to the system due to propagation delays. In both the continuous and discrete time cases we prove global stability of the system in the presence of propagation delays.

Stability and Performance of Continuous-Time Power Control in Wireless Networks

This paper develops a comprehensive stability analysis framework for general classes of continuous-time power control algorithms under heterogeneous time-varying delays. Our first set of results establish global asymptotic stability of power control laws involving two-sided scalable interference functions, and include earlier work on standard interference functions as a special case. We then consider contractive interference functions and demonstrate that the associated continuous-time power control laws always have unique fixed points which are exponentially stable, even under bounded heterogeneous time-varying delays. For this class of interference functions, we present explicit bounds on the decay rate that allow us to quantify the impact of delays on the convergence time of the algorithm. When interference functions are linear, we also prove that contractivity is necessary and sufficient for exponential stability of continuous-time power control algorithms with time-varying delays. Finally, numerical simulations illustrate the validity of our theoretical results.

Asymptotic stability and decay rates of positive linear systems with unbounded delays

There are several results on the stability analysis of positive linear systems in the presence of constant or time-varying delays. However, most existing results assume that the delays are bounded. This paper studies the stability of discrete-time positive linear systems with unbounded delays. We provide a set of easily verifiable necessary and sufficient conditions for delay-independent stability of positive linear systems subject to a general class of heterogeneous time-varying delays. For two particular classes of unbounded delays, explicit expressions that bound the decay rate of the system are presented. We demonstrate that the best bound on the decay rate that our results can guarantee can be found via convex optimization. Finally, the validity of the results is demonstrated via a numerical example.

Contractive interference functions and rates of convergence of distributed power control laws

The standard interference functions introduced by Yates have been very influential on the analysis and design of distributed power control laws. While powerful and versatile, the framework has some drawbacks: the existence of fixed-points has to be established separately, and no guarantees are given on the rate of convergence of the iterates. This paper introduces contractive interference functions, a slight reformulation of the standard interference functions that guarantees existence and uniqueness of fixed-points and geometric convergence rates. We show that many power control laws from the literature are contractive and derive, sometimes for the first time, convergence rate estimates for these algorithms. Finally, we show that although standard interference functions are not contractive, they are paracontractions with respect to a certain metric space. Extensions to two-sided scalable interference functions are also discussed.