# Service Level Agreement Violations in Cloud Storage: Insurance and Compensation Sustainability
## 1 Introduction  
Service Level Agreements (SLA) are typically employed by cloud providers to provide guarantees on the quality of their services to end customers [1; 2; 3; 4; 5; 6]. Those agreements, which form a contract or a contract-like relationship between the parties, state the obligations imposed on the cloud provider, through a set of service quality metrics and constraints to be met.  
The compliance of cloud providers with those contractual or contractual-like commitments has to be monitored, and several tools have been proposed in the literature for that purpose [7; 8; 9] or for acting on the basis of monitoring results to reach for compliance [10]. Any tool has to measure a set of parameters related to the quality of service and compare their values against SLAs' provisions. The foremost among them is availability [11], defined roughly as the percentage of time that the cloud is available.  
As it happens, the obligations underwritten in SLAs may not be fulfilled. In that case, the cloud provider is expected to pay penalties, if the contract so prescribes [12], or anyway to compensate its customers for the loss incurred. If violations take place on a wide scale, penalties and compensations may endanger the economic balance of the cloud provider.  
The cloud provider should therefore protect itself against such an occurrence. It can basically act in two ways:  
* reduce the risk due to unavailability periods;
* be indemnified against possible losses.  
The first countermeasure is technical in nature. Reducing the probability of occurrence and/or the amount of damages calls for investments in the infrastructure and better cloud management processes.  
The second countermeasure instead relies on buying an insurance policy, whereby the insurer takes on the risk of paying all claims by customers in return for the premium to be paid by the cloud provider, which acts as the insured. The insurance approach to deal with possible excessive claims by cloud users in the framework of a Service Level Agreement has been proposed in [13]. A major problem lies in the definition of the right premium of an insurance policy. In that paper, the correct premium has been computed for the case where the outage phenomenon is described by a Poisson process for occurrence of outages and by the generalized Pareto distribution for their duration. However, an alternative model has been recently introduced in the literature, based on an extensive measurement campaign on a private cloud [14] belonging to a small/medium company. In that paper, the interarrival time between successive outages is modelled through a Pareto distribution, while the duration of an outage is modelled by a lognormal distribution.  
In this paper, we again consider the problem of correctly determining the insurance premium against cloud outages. We adopt the expected utility paradigm as in [13], but we consider the outage model recently proposed in [14] in addition to the exponential-Pareto (a.k.a. Poisson-Pareto) examined in [13]. Both outage models are here examined under three QoS metrics. Our main new results are the following:  
* we obtain closed formulas for the insurance premiums for all the combinations of outage model and QoS metric (rather than just for the exponential-Pareto model as in [13];
* we obtain a closed formula to set the unit compensation offered to customers so as to avoid compensations (through the resulting premium) eroding the profit margins;
* we show that the maximum unit compensation is related to the service fee through an approximate inverse square law.  
The paper is structured as follows. Section 2 is devoted to describing the two models for outages. The quality of service metrics are instead described in Section 3. The statistics of losses resulting from the models of outages are computed in Section 4. The fair premium is derived in Section 5. Finally, the conditions to make the refund process sustainable are derived in Section 6.