We consider a virtual computing environment that provides computational resources on demand to users with multiattribute task descriptions that include a valuation, resource (CPU) needs and a completion deadline. Achieving a high quality of service in this environment depends on finding a balance between processing high priority tasks before their deadlines expire, while maximizing resource utilization. The problem becomes more challenging in an economic setting, where the task valuation is private. We propose a bid-based server that publishes a history of the success rate table (SRT) for processed tasks. Clients use the history to optimize their bid for resources on a (single) multiprocessor server. The server schedules tasks in descending order of their bid - Highest Bid First (HBF) and backfills the schedule with smaller tasks when resources are still available. The scheduler follows a hard deadline model where tasks cannot be processed after their deadline. We propose three variat...