3,268 research outputs found
Characterizing Policies with Optimal Response Time Tails under Heavy-Tailed Job Sizes
We consider the tail behavior of the response time distribution in an M/G/1 queue with heavy-tailed job sizes, specifically those with intermediately regularly varying tails. In this setting, the response time tail of many individual policies has been characterized, and it is known that policies such as Shortest Remaining Processing Time (SRPT) and Foreground-Background (FB) have response time tails of the same order as the job size tail, and thus such policies are tail-optimal. Our goal in this work is to move beyond individual policies and characterize the set of policies that are tail-optimal. Toward that end, we use the recently introduced SOAP framework to derive sufficient conditions on the form of prioritization used by a scheduling policy that ensure the policy is tail-optimal. These conditions are general and lead to new results for important policies that have previously resisted analysis, including the Gittins policy, which minimizes mean response time among policies that do not have access to job size information. As a by-product of our analysis, we derive a general upper bound for fractional moments of M/G/1 busy periods, which is of independent interest
On the Minimum Achievable Age of Information for General Service-Time Distributions
There is a growing interest in analysing the freshness of data in networked
systems. Age of Information (AoI) has emerged as a popular metric to quantify
this freshness at a given destination. There has been a significant research
effort in optimizing this metric in communication and networking systems under
different settings. In contrast to previous works, we are interested in a
fundamental question, what is the minimum achievable AoI in any
single-server-single-source queuing system for a given service-time
distribution? To address this question, we study a problem of optimizing AoI
under service preemptions. Our main result is on the characterization of the
minimum achievable average peak AoI (PAoI). We obtain this result by showing
that a fixed-threshold policy is optimal in the set of all randomized-threshold
causal policies. We use the characterization to provide necessary and
sufficient conditions for the service-time distributions under which
preemptions are beneficial
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
Scheduling for today’s computer systems: bridging theory and practice
Scheduling is a fundamental technique for improving performance in computer systems. From web servers
to routers to operating systems, how the bottleneck device is scheduled has an enormous impact on the performance of the system as a whole. Given the immense literature studying scheduling, it is easy to think that we already understand enough about scheduling. But, modern computer system designs have highlighted a number of disconnects between traditional analytic results and the needs of system designers.
In particular, the idealized policies, metrics, and models used by analytic researchers do not match the policies, metrics, and scenarios that appear in real systems.
The goal of this thesis is to take a step towards modernizing the theory of scheduling in order to provide
results that apply to today’s computer systems, and thus ease the burden on system designers. To accomplish
this goal, we provide new results that help to bridge each of the disconnects mentioned above. We will move beyond the study of idealized policies by introducing a new analytic framework where the focus is on scheduling heuristics and techniques rather than individual policies. By moving beyond the study of individual policies, our results apply to the complex hybrid policies that are often used in practice. For example, our results enable designers to understand how the policies that favor small job sizes are affected by the fact that real systems only have estimates of job sizes. In addition, we move beyond the study of mean response time
and provide results characterizing the distribution of response time and the fairness of scheduling policies.
These results allow us to understand how scheduling affects QoS guarantees and whether favoring small job sizes results in large job sizes being treated unfairly. Finally, we move beyond the simplified models traditionally used in scheduling research and provide results characterizing the effectiveness of scheduling in multiserver systems and when users are interactive. These results allow us to answer questions about the how to design multiserver systems and how to choose a workload generator when evaluating new scheduling designs
Performance of the Gittins Policy in the G/G/1 and G/G/k, With and Without Setup Times
How should we schedule jobs to minimize mean queue length? In the preemptive
M/G/1 queue, we know the optimal policy is the Gittins policy, which uses any
available information about jobs' remaining service times to dynamically
prioritize jobs. For models more complex than the M/G/1, optimal scheduling is
generally intractable. This leads us to ask: beyond the M/G/1, does Gittins
still perform well?
Recent results indicate that Gittins performs well in the M/G/k, meaning that
its additive suboptimality gap is bounded by an expression which is negligible
in heavy traffic. But allowing multiple servers is just one way to extend the
M/G/1, and most other extensions remain open. Does Gittins still perform well
with non-Poisson arrival processes? Or if servers require setup times when
transitioning from idle to busy?
In this paper, we give the first analysis of the Gittins policy that can
handle any combination of (a) multiple servers, (b) non-Poisson arrivals, and
(c) setup times. Our results thus cover the G/G/1 and G/G/k, with and without
setup times, bounding Gittins's suboptimality gap in each case. Each of (a),
(b), and (c) adds a term to our bound, but all the terms are negligible in
heavy traffic, thus implying Gittins's heavy-traffic optimality in all the
systems we consider. Another consequence of our results is that Gittins is
optimal in the M/G/1 with setup times at all loads.Comment: 41 page
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