# Optimal Cluster Expansion-Based Intrusion Tolerant System to Prevent Denial of Service Attacks
## 1 Introduction  
Internet access and mobile communication technologies have developed very rapidly, and have enabled users to access useful services. This accessibility provides convenience to the users, but simultaneously makes users vulnerable to malicious attacks. Many security countermeasures have been introduced, such as firewalls, intrusion detection systems (IDSs), and intrusion prevention systems (IPSs) [1, 2]. However, these systems are still vulnerable to evolving malicious attacks, such as zero-day attacks that can target publicly known but unpatched vulnerabilities. To alleviate this problem, an intrusion-tolerant system (ITS) has been recently introduced in the literature. The goal of ITS is to provide reliability and survivability by maintaining quality of service even while under attack [3]. When designing an ITS, the fundamental principles are redundancy, diversity, and recovery [4, 5]. Redundancy refers to the duplication of elements or services in a system. Redundant systems provide stable services by using duplicated elements or services as substitutes when the original elements or services are attacked. Diversity refers to the variety of attributes of an element or service; thus, the duplicated substitutes can have the same function for redundancy, while having different attributes for diversity. Recovery refers to the restoration process of an element or service, and conserves resources.  
As cloud computing techniques evolve, virtual machine (VM)-based ITSs have attracted the attention of researchers [6, 7]. Multiple VMs are used in a host to provide redundancy principles instead of using a backup system. One well-known ITS is a self-cleansing intrusion tolerance (SCIT) system [8, 9], which uses VM snapshots to periodically recover the system. Hence, the exposure time to attackers is reduced. A SCIT system consists of a central controller and several hosts. Each host contains duplicated VMs. Each VM provides service during the designated exposed time, and then undergoes the recovery process. Every VM follows a four-step circular process: active-grace period-cleansing-livespare. During the active state period, a VM provides service by receiving and processing incoming requests. Therefore, this period is referred to as the exposed window time. This four-step process can be divided into two groups: online VMs and offline VMs, as shown in Figure 1. However, an SCIT system can be significantly affected by a massive-scale attack like a denial of service (DoS) or distributed DoS (DDoS), because the number of online VMs providing services are fixed in a SCIT system. That is, the total number of processing packets is limited [6; 8; 9].  
To alleviate those problems, an adaptive cluster expansion scheme is necessary to preserve system QoS by rapidly and adaptively increasing the number of online VMs according to a massive packet attack. Moreover, the performance of a cluster expansion scheme must consider a waste-of-resources analysis. That is, the total number of VMs from the cluster expansion must be compared with the appropriate number of VMs necessary for preserving QoS. Therefore, in this paper, we propose an optimal cluster expansion-based ITS scheme that can optimally increase or decrease the number of online VMs to preserve system QoS. The optimal cluster size is computed using queuing theory [10], and resource waste efficiency is also considered.  
The remainder of this paper is structured as follows: in the next section, we discuss related work. In Section 3, we propose an optimal cluster expansion-based ITS. The performance results for the proposed system and findings are presented in Section 4. A discussion of the proposed system is presented in Section 5. Finally, we conclude the paper and give some future works in Section 6.