Equilibrieum allocation of processor time with linear utility functions

We consider a model for the processor time market in a multiprocessor system. The processes differ in speed and expences. Each user has one job, whose volume and budget are known, and a utility function depending linearly on the share of the job completed during the period to be allocated. The budget of each job coincides with a monetary estimate of its utility for the user. We show that under these assumptions the equilibrium prices and distribution of processor time between the jobs can be obtained from certain linear programming problems.