Time-shared Systems: a theoretical treatment
Journal of the ACM (JACM)
Sharing a Processor Among Many Job Classes
Journal of the ACM (JACM)
Asymptotic regimes and approximations for discriminatory processor sharing
ACM SIGMETRICS Performance Evaluation Review
A survey on discriminatory processor sharing
Queueing Systems: Theory and Applications
Bandwidth-sharing networks in overload
Performance Evaluation
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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 phase-type distributed service requirements and allow that customers have different weights in various phases of their service. We establish a state-space collapse for the queue length vector in heavy traffic. The result shows that in the limit, the queue length vector is the product of an exponentially distributed random variable and a deterministic vector. This generalizes a previous result by [2] who considered a DPS queue with exponentially distributed service requirements. We finally discuss some implications for residual service requirements and monotonicity properties in the ordinary DPS model.