Resource allocation in a cloud under virus attacks

How should you place your resources on the cloud sustain potential failures, due to technical problems or malicious attacks? The question should be addressed within the domain of resource allocation strategies in cloud computing, which have been widely studied over the past years (see survey in [3]). In prior studies, the resource allocation problem was addressed under a framework where the servers are 100 percent reliable (see for example, [1], [2]). That is, if a server is allocated then it operates with probability 1. As suggested above, however, system designers must account for server failures that may be caused by various reasons, such as viruses or breakdowns. In 2015 alone, 230,000 new malwares were launched every day. As a consequence, cyber security and network resilience are a major concern for internet service providers. The maliciously caused failures and the occasional breakdowns lead us to divert from the traditional models of deterministic servers and propose a new model where resource allocation is conducted under the assumption whereby the number of operating servers is stochastic. Our model distinguishes between two values regarding the servers. The first is the number of allocated servers, which is the number of servers placed by the system operator; this number is deterministic. The second is the number of surviving servers after a possible failure. This is a random value since the outcome of a failure is uncertain. We refer to the number of the placed servers as placement, whereby these are our decision variables. The number of remaining servers is a random variable and it is referred to as the supply variable. Service providers may use different types of servers within the same networks. For example, separate servers for Linux and Windows or separate servers for production and development. More common types of servers are: Web servers, Email servers, FTP servers and identity servers. Many networks on the internet employ a client-server networking model integrating websites and communication services. Usually, it comes with a limited types of servers. An alternative model peer-to-peer (P2P) networking allows all devices on a network to function as either a server or client as needed. Those networks are characterized with a multiple types of servers. For example, video streaming applications, where each movie is a different server type. In this study, we focus on a multi-type system that the number of resources are limited. There is a random demand for each type, and the goal is to reach the maximum expected revenue of satisfied demand across all regions. We provide the model details in Section 2. The main challenge is to deal with a decision variables that are inherent in a stochastic factor. We show that under a condition on the supply distribution, the objective function is concave. Thus one can use a greedy algorithm to solve the problem. Moreover, we show that this condition is both sufficient and necessary in order for the concavity property to hold (for any given demand ). What turns out to play a major role in our analysis is some kind of a cumulative function of the supply cdf, which we call cumcum. The cucmcum function of a random variable is defined as follows: Let X be a discrete random variable, with a support {0, 1, 2, ..., w} and let FX(·) be it’s cdf. Then, the cucmum function of the random variable X at k is ∑k j=0 FX(j) for k ≤ w, and ∑w j=0 FX(j) for k > w. We denote the cumcum function of X as FFX(·). We later show that the condition for the desired concavity property can be defined through the cumcum function.