# Modeling and Evaluation of Power-Aware Software Rejuvenation in Cloud Systems
## 1 Introduction
Therefore, in order to match real-world systems as much as possible, we consider two categories of VMs in this paper: (1) small VMs, which are VMs that need to be served for a short while and therefore utilize a small share of resources, and (2) big VMs, which are the VMs that need to be executed for a longer period of time and thus use a significant share of system resources. Over the course of their life, larger VMs have a greater impact on software aging of their host VMMs in contrast to the smaller VMs. In this paper, we present a Stochastic Activity Networks (SAN) model for cloud data centers and provide a strategy for applying rejuvenation to candidate VMMs at the appropriate time. Model-based studies are amongst the most prevalent analyses that researches completed to study software aging and software rejuvenation [21]. Since one of the main causes of failures of VMMs is the continuous execution of VMs running on VMMs [17], the type and the total number of VMs executed by a VMM serve as the measure for determining the appropriate time of rejuvenation. Therefore, we define an upper bound for the maximum number of VMs that a VMM can run, starting from its last boot time, and force a rejuvenation whenever the age of a VMM reaches this limit. The age of a VMM can be expressed as the cumulative workload that the VMM has served since its last failure or rejuvenation. By analyzing the proposed model with the rejuvenation scheme, the benefits of applying the rejuvenation to VMMs of an IaaS cloud provider in reducing the number of VM failures and improving the performance and availability in the steady-state are observed. In addition, the proposed model enables power-awareness in the cloud management system by migrating active VMs from lightly loaded VMMs to more heavily loaded ones and switching off free PMs. Evaluation of the proposed scheme demonstrates that this power saving mechanism improves the system's steady-state performance and availability. The formalism used in this paper to model the power-aware VMM rejuvenation scheme is SANs [22; 23; 24]. SANs are probabilistic extensions of activity networks that are equipped with a set of activity time distribution functions, reactivation predicates, and enabling rate functions. They were developed to facilitate performance and dependability evaluation and have features that permit the representation of parallelism, timeliness, fault tolerance, and degradable performance [25]. More detailed information about SANs can be found in the previous literature [26; 27; 28]. The main contributions of this paper are summarized as follows. (1) A SAN model is presented for performance evaluation of IaaS clouds that considers many details of real systems, including VM multiplexing, migration of VMs between VMMs, VM heterogeneity, failure of VMMs, failure of VM migration, and different probabilities for arrival of different VM request types. (2) Using the presented SAN, a two-threshold power-aware software rejuvenation scheme is proposed and compared with two baselines based on diverse performance, availability, and power consumption measures defined on the system. The rest of this paper is organized as follows. Section 2 reviews the previous work in the field of software rejuvenation in cloud systems. Section 3 provides a brief introduction to the SAN formalism. In Section 4, the general structure of our system is explained. In Section 5, the proposed SAN model and the rejuvenation scheme presented for the SAN are introduced in detail. Section 6 presents the output measures of interest and the results of the performance evaluation, and finally, Section 7 concludes the paper and provides some directions for future work.