10 research outputs found
A large-deviations analysis of the GI/GI/1 SRPT queue
We consider a GI/GI/1 queue with the shortest remaining processing time
discipline (SRPT) and light-tailed service times. Our interest is focused on
the tail behavior of the sojourn-time distribution. We obtain a general
expression for its large-deviations decay rate. The value of this decay rate
critically depends on whether there is mass in the endpoint of the service-time
distribution or not. An auxiliary priority queue, for which we obtain some new
results, plays an important role in our analysis. We apply our SRPT-results to
compare SRPT with FIFO from a large-deviations point of view.Comment: 22 page
On the impact of heterogeneity and back-end scheduling in load balancing designs
Load balancing is a common approach for task
assignment in distributed architectures. In this paper, we show
that the degree of inefficiency in load balancing designs is highly
dependent on the scheduling discipline used at each of the backend
servers. Traditionally, the back-end scheduler can be modeled
as Processor Sharing (PS), in which case the degree of inefficiency
grows linearly with the number of servers. However, if the back-end
scheduler is changed to Shortest Remaining Processing Time
(SRPT), the degree of inefficiency can be independent of the
number of servers, instead depending only on the heterogeneity
of the speeds of the servers. Further, switching the back-end
scheduler to SRPT can provide significant improvements in
the overall mean response time of the system as long as the
heterogeneity of the server speeds is small
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
On the average sojourn time under M/M/1/SRPT
We study an M/M/1 queueing system under the shortest remaining processing time (SRPT) policy. We show that the average sojourn time varies as T((µ(1-¿) ln(e/(1-¿)))-1), where ¿ is the system load. Thus, SRPT o2ers a T(ln(e/(1-¿))) factor improvement over policies that ignore knowledge of job sizes while scheduling
On the average sojourn time under M/M/1/SRPT
We study an M/M/1 queueing system under the shortest remaining processing time (SRPT) policy. We show that the average sojourn time varies as Theta((mu(1-rho)ln(e/(1-rho)))(-1)), where rho is the system load. Thus, SRPT offers a Theta(ln(e/(1-rho))) factor improvement over policies that ignore knowledge of job sizes while scheduling
Heavy-traffic analysis of sojourn time under the foreground–background scheduling policy
We consider the steady-state distribution of the sojourn time of a job entering an M/GI/1 queue with the foreground–background scheduling policy in heavy traffic. The growth rate of its mean as well as the limiting distribution are derived under broad conditions. Assumptions commonly used in extreme value theory play a key role in both the analysis and the results
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