A priority scheme is proposed in which the prioritized customers get guaranteed Quality of Service (QoS) by the cloud computing system in terms of lesser response time. The concept of selection probability is introduced according to which the cloud metascheduler chooses the next query for execution. The prioritized customers are categorized into different priority queues which are modeled as M/M/1/K/K queues and an analytical model is developed for the calculation of selection probabilities. Two algorithms are proposed for explaining the processing at the users’ end and at the cloud computing server’s end. The results obtained are validated using the numerical simulations