608 research outputs found
SRPT Scheduling Discipline in Many-Server Queues with Impatient Customers
The shortest-remaining-processing-time (SRPT) scheduling policy has been extensively studied, for more than 50 years, in single-server queues with infinitely patient jobs. Yet, much less is known about its performance in multiserver queues. In this paper, we present the first theoretical analysis of SRPT in multiserver queues with abandonment. In particular, we consider the M/GI/s+GI queue and demonstrate that, in the many-sever overloaded regime, performance in the SRPT queue is equivalent, asymptotically in steady state, to a preemptive two-class priority queue where customers with short service times (below a threshold) are served without wait, and customers with long service times (above a threshold) eventually abandon without service. We prove that the SRPT discipline maximizes, asymptotically, the system throughput, among all scheduling disciplines. We also compare the performance of the SRPT policy to blind policies and study the effects of the patience-time and service-time distributions
Fluid Limits for Shortest Job First with Aging
We investigate fluid scaling of single server queueing systems under the
shortest job first with aging (SJFA) scheduling policy. We use the
measure-valued Skorokhod map to characterize the fluid limit for SJFA queues
with a general aging rule and establish convergence results to the fluid limit.
We treat in detail examples of linear and exponential aging
SEH: Size Estimate Hedging for Single-Server Queues
For a single server system, Shortest Remaining Processing Time (SRPT) is an
optimal size-based policy. In this paper, we discuss scheduling a single-server
system when exact information about the jobs' processing times is not
available. When the SRPT policy uses estimated processing times, the
underestimation of large jobs can significantly degrade performance. We propose
a simple heuristic, Size Estimate Hedging (SEH), that only uses jobs' estimated
processing times for scheduling decisions. A job's priority is increased
dynamically according to an SRPT rule until it is determined that it is
underestimated, at which time the priority is frozen. Numerical results suggest
that SEH has desirable performance when estimation errors are not unreasonably
large
Achievable performance of blind policies in heavy traffic
For a GI/GI/1 queue, we show that the average sojourn time under the (blind) Randomized Multilevel Feedback algorithm is no worse than that under the Shortest Remaining Processing Time algorithm times a logarithmic function of the system load. Moreover, it is verified that this bound is tight in heavy traffic, up to a constant multiplicative factor. We obtain this result by combining techniques from two disparate areas: competitive analysis and applied probability
Achievable performance of blind policies in heavy traffic
For a GI/GI/1 queue, we show that the average sojourn time under the (blind) Randomized Multilevel Feedback algorithm is no worse than that under the Shortest Remaining Processing Time algorithm times a logarithmic function of the system load. Moreover, it is verified that this bound is tight in heavy traffic, up to a constant multiplicative factor. We obtain this result by combining techniques from two disparate areas: competitive analysis and applied probability
The Epistemology of Simulation, Computation and Dynamics in Economics Ennobling Synergies, Enfeebling 'Perfection'
Lehtinen and Kuorikoski ([73]) question, provocatively, whether, in the context of Computing the Perfect Model, economists avoid - even positively abhor - reliance on simulation. We disagree with the mildly qualified affirmative answer given by them, whilst agreeing with some of the issues they raise. However there are many economic theoretic, mathematical (primarily recursion theoretic and constructive) - and even some philosophical and epistemological - infelicities in their descriptions, definitions and analysis. These are pointed out, and corrected; for, if not, the issues they raise may be submerged and subverted by emphasis just on the unfortunate, but essential, errors and misrepresentationsSimulation, Computation, Computable, Analysis, Dynamics, Proof, Algorithm
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