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Data center workloads are composed of multiresource jobs requiring a variety of computational resources including CPU cores, memory, disk space, and hardware accelerators. Mod- ern servers can run multiple jobs in parallel, but a set of jobs can only run in parallel if the server has sufficient resources to satisfy the demands of each job. It is generally hard to find sets of jobs that perfectly utilize all server resources, and choosing the wrong set of jobs can lead to low resource uti- lization. This raises the question of how to allocate resources across a stream of arriving multiresource jobs to minimize the mean response time across jobs — the mean time from when a job arrives to the system until it is complete. Current policies for scheduling multiresource jobs are com- plex to analyze and hard to implement. We propose a class of simple policies, called Markovian Service Rate (MSR) policies. We show that the class of MSR policies is throughput- optimal, in that if a policy exists that can stabilize the sys- tem, then an MSR policy exists that stabilizes the system. We derive bounds on the mean response time under an MSR policy, and show how our bounds can be used to choose an MSR policy that minimizes mean response time.