We consider a network of parallel, non-observable queues and analyze the "price of anarchy", an index measuring the worst-case performance loss of a decentralized system with respect to its centralized counterpart in presence of non-cooperative users. Our analysis is undertaken from the new point of view where the router has the memory of previous dispatching choices, which significantly complicates the nature of the problem. In the regime where the demands proportionally grow with the network capacity, we provide a tight lower bound on the socially-optimal response time and a tight upper bound on the price of anarchy by means of convex programming. Then, we exploit this result to show, by simulation, that the billiard routing scheme yields a response time which is remarkably close to our lower bound, implying that billiards minimize response time. To study the added-value of non-Bernoulli routers, we introduce the "price of forgetting" and prove that it is bounded from above by two, which is tight in heavy-traffic. Finally, other structural properties are derived numerically for the price of forgetting. These claim that the benefit of having memory in the router is independent of the network size and heterogeneity, while monotonically depending on the network load only. These properties yield simple productforms well-approximating the socially-optimal response time. 1

Cloud computing is an emerging technology that allows to access computing resources on a pay-per-use basis. The main challenges in this area are the efficient performance management and the energy costs minimization.In this paper we model the service provisioning problem of Cloud Platform-as-aService systems as a Generalized Nash Equilibrium Problem and show that a potential function for the game exists. Moreover, we prove that the social optimum problem is convex and we derive some properties of social optima from the corresponding KarushKuhn-Tucker system. Next, we propose a distributed solution algorithm based on the best response dynamics and we prove its convergence to generalized Nash equilibria.Finally, we numerically evaluate equilibria in terms of their efficiency with respect to the social optimum of the Cloud by varying our algorithm initial solution. Numerical results show that our algorithm is scalable and very efficient and thus can be adopted for the run-time management of very large scale systems.

We analyze the behavior of closed product-form queueing networks when the number of customers grows to infinity and remains proportionate on each route (or class). First, we focus on the stationary behavior and prove the conjecture that the stationary distribution at non-bottleneck queues converges weakly to the stationary distribution of an ergodic, open product-form queueing network. This open network is obtained by replacing bottleneck queues with per-route Poissonian sources whose rates are determined by the solution of a strictly concave optimization problem. Then, we focus on the transient behavior of the network and use fluid limits to prove that the amount of fluid, or customers, on each route eventually concentrates on the bottleneck queues only, and that the long-term proportions of fluid in each route and in each queue solve the dual of the concave optimization problem that determines the throughputs of the previous open network.Keywords: closed queueing networks; product-form; asymptotic independence; fluid limit; large population. Acknowledgements June 2012AbstractWe analyze the behavior of closed product-form queueing networks when the number of customers grows to infinity and remains proportionate on each route (or class). First, we focus on the stationary behavior and prove the conjecture that the stationary distribution at non-bottleneck queues converges weakly to the stationary distribution of an ergodic, open product-form queueing network. This open network is obtained by replacing bottleneck queues with per-route Poissonian sources whose rates are determined by the solution of a strictly concave optimization problem. Then, we focus on the transient behavior of the network and use fluid limits to prove that the amount of fluid, or customers, on each route eventually concentrates on the bottleneck queues only, and that the long-term proportions of fluid in each route and in each queue solve the dual of the concave optimization problem that determines the throughputs of the previous open network.

We investigate the trade-off between performance and power consumption in servers hosting virtual machines running IT services. The performance behavior of such servers is modeled through Generalized Processor Sharing (GPS) queues enhanced with a green speed-scaling mechanism that controls the processing capacity to use depending on the number of active virtual machines. When the number of virtual machines grows large, we show that the stochastic evolution of our model converges to a system of ordinary differential equations for which we derive a closed-form formula for its unique stationary point. This point is a function of the capacity and the shares that characterize the GPS mechanism. It allows us to show that speed-scaling mechanisms can provide large reduction in power consumption having only small performance degradation in terms of the delays experienced in the virtual machines. In addition, we derive the optimal choice for the shares of the GPS discipline, which turns out to be non-trivial. Finally, we show how our asymptotic analysis can be applied to the dimensioning and service partitioning in data-centers. Experimental results show that our asymptotic formulas are accurate even when the number of virtual machines is small.

Motivated by revenue maximization in server farms with admission control, we investigate optimal scheduling in parallel processor-sharing queues. Incoming customers are distinguished in multiple classes and we define revenue as a weighted sum of class throughputs. Under these assumptions, we describe a heavy-traffic limit for the revenue maximization problem and study the asymptotic properties of the optimization model as the number of clients increases. Our main result is a simple heuristic that is able to provide tight guarantees on the optimality gap of its solutions. In the general case with M queues and R classes, we prove that our heuristic is (1 + 1 M −1 )-competitive in heavy-traffic. Experimental results indicate that the proposed heuristic is remarkably accurate, despite its negligible computational costs, both in random instances and using service rates of a web application measured on multiple cloud deployments. 1

The Web service composition (WSC) is the process of building an instance of an abstract workflow by combining appropriate Web services that satisfies given QoS requirements. In general, QoS requirements consists of a number of constraints. The selection process requires global optimization and can be formalized as a mixed integer linear programming problem which cannot be solved in polynomial time. However, since the number of submitted workflows is large and the QoS is highly dynamic, the fast selection of composite Web Services is particularly important.In this paper, we present a QoS broker-based framework for Web services execution in autonomic grid environments. The main goal of the framework is to support the broker in selecting Web services based on the required QoS. To achieve this goal, we propose a novel approach: since successive composed Web services requests can have the same task to Web service assignment, we address the Multiple Instance WSC (MI-WSC) problem optimizing simultaneously the set of requests which will be submitted to the system in the successive time interval instead of independently computing a solution for each incoming request.Experimental results show that the proposed algorithm has better performance with respect to existing techniques. Moreover, the qualities of the selected composite Web services are not significantly different from the optimal ones.

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This article proposes a model to study the interaction of price competition and congestion in the cloud computing marketplace. Specifically, we propose a three-tier market model that captures a marketplace with users purchasing services from Software-as-a-Service (SaaS) providers, which in turn purchase computing resources from either Provider-as-a-Service (PaaS) or Infrastructure-as-a-Service (IaaS) providers. Within each level, we define and characterize market equilibria. Further, we use these characterizations to understand the relative profitability of SaaSs and PaaSs/IaaSs and to understand the impact of price competition on the user experienced performance, that is, the “price of anarchy” of the cloud marketplace. Our results highlight that both of these depend fundamentally on the degree to which congestion results from shared or dedicated resources in the cloud.