A resource-sharing game with relative priorities

Motivated by cloud-based computing resources operating with relative priorities, we investigate the strategic interaction between a fixed number of users sharing the capacity of a processor. Each user chooses a payment, which corresponds to his priority level, and submits jobs of variable sizes according to a stochastic process. These jobs have to be completed before some user-specific deadline. They are executed on the processor and receive a share of the capacity that is proportional to the priority level. The users’ goal is to choose priority levels so as to minimize their own payment, while guaranteeing that their jobs meet their deadlines. We fully characterize the solution of the game for two classes of users and exponential service times. For an arbitrary number of classes and general service times, we develop an approximation based on heavy-traffic and we characterize the solution of the game under the heavy-traffic assumption. Our experiments show that the approximate solution captures accurately the structure of the equilibrium in the original game.