269 research outputs found
Diffusion limits for shortest remaining processing time queues
We present a heavy traffic analysis for a single server queue with renewal
arrivals and generally distributed i.i.d. service times, in which the server
employs the Shortest Remaining Processing Time (SRPT) policy. Under typical
heavy traffic assumptions, we prove a diffusion limit theorem for a
measure-valued state descriptor, from which we conclude a similar theorem for
the queue length process. These results allow us to make some observations on
the queue length optimality of SRPT. In particular, they provide the sharpest
illustration of the well-known tension between queue length optimality and
quality of service for this policy.Comment: 19 pages; revised, fixed typos. To appear in Stochastic System
QUANTIFYING FAIRNESS IN QUEUING SYSTEMS: PRINCIPLES, APPROACHES, AND APPLICABILITY
In this article we discuss fairness in queues, view it in the context of social justice at large, and survey the recently published research work and publications dealing with the issue of measuring fairness of queues. The emphasis is placed on the underlying principles of the different measurement approaches, on reviewing their methodology, and on examining their applicability and intuitive appeal. Some quantitative results are also presented. The article has three major parts (sections) and a short concluding discussion. In the first part we discuss fairness in queues and its importance in the broader context of the prevailing conception of social justice at large, and the distinction between fairness of the queue and fairness at large is illuminated. The second part is dedicated to explaining and discussing three main properties expected of a fairness measure: conformity to the general concept of social justice, granularity, and intuitive appeal and rationality. The third part reviews the fairness of the queue evaluating and measuring approaches proposed and studied in recent years. We describe the underlying principles of the different approaches, present some of their results, and review them in context of the three main properties expected from a measure. The short discussion that follows centers on future research issue
New Cross-Layer Channel Switching Policy for TCP Transmission on 3G UMTS Downlink
In 3G UMTS, two main transport channels have been provided for downlink data
transmission: a common FACH channel and a dedicated DCH channel. The
performance of TCP in UMTS depends much on the channel switching policy used.
In this paper, we propose and analyze three new basic threshold-based channel
switching policies for UMTS that we name as QS (Queue Size), FS (Flow Size) and
QSFS (QS & FS combined) policy. These policies significantly improve over a
modified threshold policy in [1] by about 17% in response time metrics. We
further propose and evaluate a new improved switching policy that we call
FS-DCH (at-least flow-size threshold on DCH) policy. This policy is biased
towards short TCP flows of few packets and is thus a cross-layer policy that
improves the performance of TCP by giving priority to the initial few packets
of a flow on the fast DCH channel. Extensive simulation results confirm this
improvement for the case when number of TCP connections is low
Scheduling for todayâs 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 todayâs 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
Minimizing the Worst Slowdown: Off-Line and On-Line
Minimizing the slowdown (expected sojourn time divided by job size) is a key concern of fairness in scheduling and queuing problems where job sizes are very heterogeneous. We look for protocols (service disciplines) capping the worst slowdown (called here liability) a job may face no matter how large (or small) the other jobs are. In the scheduling problem (all jobs released at the same time), allowing the server to randomize the order of service cuts almost in half the liability profiles feasible under deterministic protocols. The same statement holds if cash transfers are feasible and users have linear waiting costs.
Heavy-Tailed Limits for Medium Size Jobs and Comparison Scheduling
We study the conditional sojourn time distributions of processor sharing
(PS), foreground background processor sharing (FBPS) and shortest remaining
processing time first (SRPT) scheduling disciplines on an event where the job
size of a customer arriving in stationarity is smaller than exactly k>=0 out of
the preceding m>=k arrivals. Then, conditioning on the preceding event, the
sojourn time distribution of this newly arriving customer behaves
asymptotically the same as if the customer were served in isolation with a
server of rate (1-\rho)/(k+1) for PS/FBPS, and (1-\rho) for SRPT, respectively,
where \rho is the traffic intensity. Hence, the introduced notion of
conditional limits allows us to distinguish the asymptotic performance of the
studied schedulers by showing that SRPT exhibits considerably better asymptotic
behavior for relatively smaller jobs than PS/FBPS.
Inspired by the preceding results, we propose an approximation to the SRPT
discipline based on a novel adaptive job grouping mechanism that uses relative
size comparison of a newly arriving job to the preceding m arrivals.
Specifically, if the newly arriving job is smaller than k and larger than m-k
of the previous m jobs, it is routed into class k. Then, the classes of smaller
jobs are served with higher priorities using the static priority scheduling.
The good performance of this mechanism, even for a small number of classes m+1,
is demonstrated using the asymptotic queueing analysis under the heavy-tailed
job requirements. We also discuss refinements of the comparison grouping
mechanism that improve the accuracy of job classification at the expense of a
small additional complexity.Comment: 26 pages, 2 figure
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