Analysis of SRPT scheduling: investigating unfairness
Proceedings of the 2001 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Classifying scheduling policies with respect to unfairness in an M/GI/1
SIGMETRICS '03 Proceedings of the 2003 ACM SIGMETRICS international conference on Measurement and modeling of computer systems
Multi-layered round robin routing for parallel servers
Queueing Systems: Theory and Applications
A large-deviations analysis of the GI/GI/1 SRPT queue
Queueing Systems: Theory and Applications
The Fluid Limit of an Overloaded Processor Sharing Queue
Mathematics of Operations Research
State-dependent response times via fluid limits in shortest remaining processing time queues
ACM SIGMETRICS Performance Evaluation Review
State-dependent response times via fluid limits in shortest remaining processing time queues
ACM SIGMETRICS Performance Evaluation Review
Queueing Systems: Theory and Applications
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We consider a single-server queue with renewal arrivals and i.i.d. service times in which the server uses the shortest remaining processing time policy. To describe the evolution of this queue, we use a measure-valued process that keeps track of the residual service times of all buffered jobs. We propose a fluid model (or formal law of large numbers approximation) for this system and, under mild assumptions, prove the existence and uniqueness of fluid model solutions. Furthermore, we prove a scaling limit theorem that justifies the fluid model as a first-order approximation of the stochastic model. The state descriptor of the fluid model is a measure-valued function whose dynamics are governed by certain inequalities in conjunction with the standard workload equation. In particular, these dynamics determine the evolution of the left edge (infimum) of the state descriptor's support, which yields conclusions about response times. We characterize the evolution of this left edge as an inverse functional of the initial condition, arrival rate, and service time distribution. This characterization reveals the manner in which the growth rate of the left edge depends on the service time distribution. By considering varying examples, the authors show that the rate can vary from logarithmic to polynomial.