A computing device retrieves historical data regarding one or more historical time periods during which cloud application instances were provisioned. A probability distribution of a number of queries received by the historical cloud application instances during each of the one or more historical time periods is determined by the computing device. A probability distribution of a number of received queries completed by each of the one or more historical cloud application instances during each of the one or more historical time periods is determined by the computing device. A new provisioning plan for further time periods is generated via application of a stochastic optimization model based upon the probability distribution of the number of received queries during each of the one or more historical time periods and the probability distribution of the number of received queries completed by each of the one or more cloud application instances.