95 research outputs found
Optimal Scheduling in the Multiserver-job Model under Heavy Traffic
Multiserver-job systems, where jobs require concurrent service at many
servers, occur widely in practice. Essentially all of the theoretical work on
multiserver-job systems focuses on maximizing utilization, with almost nothing
known about mean response time. In simpler settings, such as various known-size
single-server-job settings, minimizing mean response time is merely a matter of
prioritizing small jobs. However, for the multiserver-job system, prioritizing
small jobs is not enough, because we must also ensure servers are not
unnecessarily left idle. Thus, minimizing mean response time requires
prioritizing small jobs while simultaneously maximizing throughput. Our
question is how to achieve these joint objectives.
We devise the ServerFilling-SRPT scheduling policy, which is the first policy
to minimize mean response time in the multiserver-job model in the heavy
traffic limit. In addition to proving this heavy-traffic result, we present
empirical evidence that ServerFilling-SRPT outperforms all existing scheduling
policies for all loads, with improvements by orders of magnitude at higher
loads.
Because ServerFilling-SRPT requires knowing job sizes, we also define the
ServerFilling-Gittins policy, which is optimal when sizes are unknown or
partially known.Comment: 32 pages, to appear in ACM SIGMETRICS 202
Discrete-Event Modeling of a High-Performance Computing Cluster with Service Rate Control
We present a stochastic recursion based discrete-event model of a high-performance computing cluster with service rate switching capabilities. The model is easily adopted to many common settings of modern supercomputers, such as specific scheduling disciplines and various control policies. We also provide some illustrative numerical experiments and discuss further generalizations of the model
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
EUROPEAN CONFERENCE ON QUEUEING THEORY 2016
International audienceThis booklet contains the proceedings of the second European Conference in Queueing Theory (ECQT) that was held from the 18th to the 20th of July 2016 at the engineering school ENSEEIHT, Toulouse, France. ECQT is a biannual event where scientists and technicians in queueing theory and related areas get together to promote research, encourage interaction and exchange ideas. The spirit of the conference is to be a queueing event organized from within Europe, but open to participants from all over the world. The technical program of the 2016 edition consisted of 112 presentations organized in 29 sessions covering all trends in queueing theory, including the development of the theory, methodology advances, computational aspects and applications. Another exciting feature of ECQT2016 was the institution of the Takács Award for outstanding PhD thesis on "Queueing Theory and its Applications"
Nested Fork-Join Queuing Networks and Their Application to Mobility Airfield Operations Analysis
A single-chain nested fork-join queuing network (FJQN) model of mobility airfield ground processing is proposed. In order to analyze the queuing network model, advances on two fronts are made. First, a general technique for decomposing nested FJQNs with probabilistic forks is proposed, which consists of incorporating feedback loops into the embedded Markov chain of the synchronization station, then using Marie\u27s Method to decompose the network. Numerical studies show this strategy to be effective, with less than two percent relative error in the approximate performance measures in most realistic cases. The second contribution is the identification of a quick, efficient method for solving for the stationary probabilities of the λn/Ck/r/N queue. Unpreconditioned Conjugate Gradient Squared is shown to be the method of choice in the context of decomposition using Marie\u27s Method, thus broadening the class of networks where the method is of practical use. The mobility airfield model is analyzed using the strategies described above, and accurate approximations of airfield performance measures are obtained in a fraction of the time needed for a simulation study. The proposed airfield modeling approach is especially effective for quick-look studies and sensitivity analysis
Overlap Times in the Queue
Overlap times have been studied as a way of understanding the time of
interaction between customers in a service facility. Most of the previous
analysis relies on the single jump assumption for arrivals, which implies the
queue increases by one for each arrival epoch. In this paper, we relax the
single arrival assumption and explore the impact of having batch arrivals.
Unfortunately, with batch arrivals it is not clear how one measures an overlap
time between batches of customers. Thus, we develop two ways of capturing the
notion of an overlap time in a batch setting and derive exact results in the
infinite server queue with batch arrivals. Finally, we derive new results for
analyzing overlap times of more than two batches
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
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