  Cloud-computing shares a common pool of resources across customers at a scale
that is orders of magnitude larger than traditional multi-user systems.
Constituent physical compute servers are allocated multiple "virtual machines"
(VM) to serve simultaneously. Each VM user should ideally be unaffected by
others' demand. Naturally, this environment produces new challenges for the
service providers in meeting customer expectations while extracting an
efficient utilization from server resources. We study a new cloud service
metric that measures prolonged latency or delay suffered by customers. We model
the workload process of a cloud server and analyze the process as the customer
population grows. The capacity required to ensure that average workload does
not exceed a threshold over long segments is characterized. This can be used by
cloud operators to provide service guarantees on avoiding long durations of
latency. As part of the analysis, we provide a uniform large-deviation
principle for collections of random variables that is of independent interest.
