Cloud infrastructures are becoming a common platform for storage and workload operations for industries. With increasing rate of data generation, the cloud storage industry has already grown into a multibillion dollar industry. This industry offers services with very strict service level agreements (SLAs) to insure a high Quality of Service (QoS) for its clients. A breach of these SLAs results in a heavy economic loss for the service provider. We study a queueing model of data backup systems with a focus on the age of data. The age of data is roughly defined as the time for which data has not been backed up and is therefore a measure of uncertainty for the user. We precisely define the performance measure and compute the generating function of its distribution. It is critical to ensure that the tail probabilities are small so that the system stays within SLAs with a high probability. Therefore, we also analyze the tail distribution of the age of data by performing dominant singularity analysis of its generating function. Our formulas can help the service providers to set the system parameters adequately

Introduction

In the past few years, cloud data services have become one of the important pillars of the Information and Technology (IT) industry. Companies such as Amazon, Microsoft and IBM started offering computing services as IaaS (Infrastructure As A Service) which enables smaller businesses to enter market and generate revenue more quickly (see Deloitte [1]). By outsourcing the requirement of infrastructure setup and management to cloud service providers, the cost and difficulty of setup significantly reduces. Moreover, unlike local storage, these platforms offer remarkable features such as reliability, availability of data, protection from geographical calamities, etc (see Chang and Wills [2] for more details). Cloud storage industry was worth US$25.171 billion in 2017 and is expected to be worth US$92.488 billion in 2022 [3]. This growth has been driven by the huge volume of data that is being generated every day (Shadroo and Rahmani [4]). Recently, studies have shown that this amount is continuing to grow exponentially. A study by the international data corporation (Reinsel et al. [5]) has estimated that the amount of data generated would reach 163ZB by 2025 which is approximately 10 times the data generated in 2016. Industries have started adopting public clouds for storage and operations. Arul Elumalai and Tandon [6] estimate that about 37% of the companies will be using public IaaS for at least one workload by 2018. Therefore, it is important to study and analyze cloud infrastructure systems and processes.