Queueing Model of a Data Center With Resource Pool Constraints

We consider a data center where servers are grouped into pools and jobs can be processed in parallel by servers of different pools under some constraints imposed by the service provider. Specifically, each job is assigned a class, corresponding to the customer that generates this job or the requested service, and is imposed two types of constraints, each depending on its class: individual constraints that limit the number of servers that this job can use within each pool and collective constraints that limit the number of servers that the whole class can use within each pool. All servers of a pool have the same service capacity and process the jobs sequentially in FCFS order under the above constraints. We show that the corresponding queuing system is a special case of Order Independent queues, which are known to be quasi-reversible. We give the stability condition of the queue and prove that the resulting average resource allocation is balanced fairness under the individual and collective constraints. We also derive recursive formulas for the efficient calculation of some key performance metrics like the mean service rate of a job. Numerical results illustrate the behavior of the system in some simple scenarios.