As Small Medium Enterprises (SMEs) adopt Cloud technologies to provide high value customer offerings, uptime is considered important. Cloud outages represent a challenge to SMEs and micro teams to maintain a services platform. If a Cloud platform suffers from downtime this can have a negative effect on business revenue. Additionally, outages can divert resources from product development/delivery tasks to reactive remediation. These challenges are immediate for SMEs or micro teams with a small levels of resources. In this paper we present a framework that can model the arrival of Cloud outage events. This framework can be used by DevOps teams to manage their scarce pool of resources to resolve outages, thereby minimising impact to service delivery. We analysed over 300 Cloud outage events from an enterprise data set. We modelled the inter-arrival and service times of each outage event and found a Pareto and a lognormal distribution to be a suitable fit. We used this result to produce a special case of the G/G/1 queue system to predict busy times of DevOps personnel. We also investigated dependence between overlapping outage events. Our predictive queuing model compared favourably with observed data, 72% precision was achieved using one million simulations.