We study the stability properties of a susceptible-infected-susceptible (SIS) diffusion model, so-called the n-intertwined Markov model, over arbitrary directed network topologies. As in the majority of the work on infection spread dynamics, this model exhibits a threshold phenomenon. When the curing rates in the network are high, the disease-free state is the unique equilibrium over the network. Otherwise, an endemic equilibrium state emerges, where some infection remains within the network. Using notions from positive systems theory, we provide novel proofs for the global asymptotic stability of the equilibrium points in both cases over strongly connected networks based on the value of the basic reproduction number, a fundamental quantity in the study of epidemics. When the network topology is weakly connected, we provide conditions for the existence, uniqueness, and global asymptotic stability of an endemic state, and we study the stability of the disease-free state. Finally, we demonstrate that the n-intertwined Markov model can be viewed as a best-response dynamical system of a concave game among the nodes. This characterization allows us to cast new infection spread dynamics; additionally, we provide a sufficient condition for the global convergence to the disease-free state, which can be checked in a distributed fashion. Several simulations demonstrate our results.

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Cloud service providers (CSPs) enable tenants to elastically scale their resources to meet their demands. In fact, there are various types of resources offered at various price points. While running applications on the cloud, a tenant aiming to minimize cost is often faced with crucial trade-off considerations. For instance, upon each arrival of a query, a web application can either choose to pay for CPU to compute the response fresh, or pay for cache storage to store the response so as to reduce the compute costs of future requests. The Ski-Rental problem abstracts such scenarios where a tenant is faced with a to-rent-or-to-buy trade-off; in its basic form, a skier should choose between renting or buying a set of skis without knowing the number of days she will be skiing. In this paper, we introduce a variant of the classical Ski-Rental problem in which we assume that the skier knows the first (or second) moment of the distribution of the number of ski days in a season. We demonstrate that utilizing this information leads to achieving the best worst-case expected competitive ratio (CR) performance. Our method yields a new class of randomized algorithms that provide arrivals-distribution-free performance guarantees. Further, we apply our solution to a cloud file system and demonstrate the cost savings obtained in comparison to other competing schemes. Simulations illustrate that our scheme exhibits robust average-cost performance that combines the best of the well-known deterministic and randomized schemes previously proposed to tackle the Ski-Rental problem. • Recompute the query from scratch. This involves the CPU and I/O costs, if any, for using the disk.

In this work, we study the problem of power allocation in teams. Each team consists of two agents who try to split their available power between the tasks of communication and jamming the nodes of the other team. The agents have constraints on their total energy and instantaneous power usage. The cost function is the difference between the rates of erroneously transmitted bits of each team. We model the problem as a zero-sum differential game between the two teams and use Isaacs' approach to obtain the necessary conditions for the optimal trajectories. This leads to a continuous-kernel power allocation game among the players. Based on the communications model, we present sufficient conditions on the physical parameters of the agents for the existence of a pure strategy Nash equilibrium (PSNE). Finally, we present simulation results for the case when the agents are holonomic.

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