Driven by emerging tolerance-critical use cases of future communication networks, the demand on cloud computing service providers for their reliable and timely service delivery is to dramatically increase in the upcoming era. Advanced techniques to resolve the congestion of task queues are therefore called for. In this study we propose to rely on the impatient behavior of cloud service tenants towards a distributed risk-based queue management, which enables a profitability-sensitive task dropping while protecting the tenants data privacy. Regarding the service providers data privacy, we propose a dynamic online learning scheme, which allows the tenant to learn the queue dynamics from an adaptive number of observations on its own position in queue, so as to make a rational decision of impatient behavior.