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On the Gittins index in the M/G/1 queue
For an M/G/1 queue with the objective of minimizing the mean number of jobs in the system, the Gittins index rule is known to be optimal among the set of non-anticipating policies. We develop properties of the Gittins ...
Optimal policy for multi-class scheduling in a single server queue
In this paper we apply the Gittins optimality result to characterize the optimal scheduling discipline in a multi-class M/G/1 queue. We apply the general result to several cases of practical interest where the service time ...
Heavy-traffic analysis of the M/PH/1 Discriminatory Processor Sharing queue with phase-dependent weights
We analyze a generalization of the Discriminatory Processor Sharing (DPS) queue in a heavy-traffic setting. Customers present in the system are served simultaneously at rates controlled by a vector of weights. We assume ...