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259
Analysis of SRPT scheduling: Investigating unfairness
 In Proceedings of ACM SIGMETRICS
, 2001
"... The ShortestRemainingProcessingTime (SRPT) scheduling policy has long been known to be optimal for minimizing mean response time (sojourn time). Despite this fact, SRPT scheduling is rarely used in practice. It is believed that the performance improvements of SRPT over other scheduling policies s ..."
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Cited by 158 (15 self)
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The ShortestRemainingProcessingTime (SRPT) scheduling policy has long been known to be optimal for minimizing mean response time (sojourn time). Despite this fact, SRPT scheduling is rarely used in practice. It is believed that the performance improvements of SRPT over other scheduling policies stem from the fact that SRPT unfairly penalizes the large jobs in order to help the small jobs. This belief has led people to instead adopt “fair ” scheduling policies such as ProcessorSharing (PS), which produces the same expected slowdown for jobs of all sizes. This paper investigates formally the problem of unfairness in SRPT scheduling as compared with PS scheduling. The analysis assumes an M/G/1 model, and emphasizes job size distributions with a heavytailed property, as are characteristic of empirical workloads. The analysis shows that the degree of unfairness under SRPT is surprisingly small. The M/G/1/SRPT and M/G/1/PS queues are also analyzed under overload and closedform expressions for mean response time as a function of job size are proved in this setting.
Systems with finite communication bandwidth constraints—I: State estimation problems
 Stanford University, Stanford, CA
, 1997
"... Abstract—In this paper a new class of feedback control problems is introduced. Unlike classical models, the systems considered here have communication channel constraints. As a result, the issue of coding and communication protocol becomes an integral part of the analysis. Since these systems cannot ..."
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Cited by 144 (2 self)
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Abstract—In this paper a new class of feedback control problems is introduced. Unlike classical models, the systems considered here have communication channel constraints. As a result, the issue of coding and communication protocol becomes an integral part of the analysis. Since these systems cannot be asymptotically stabilized if the underlying dynamics are unstable, a weaker stability concept called containability is introduced. A key result connects containability with an inequality equation involving the communication data rate and the rate of change of the state. Index Terms — Asymptotic stability, containability, feedback control, Kraft inequality.
Analysis of LAS Scheduling for Job Size Distributions with High Variance
, 2003
"... Recent studies of Internet traffic have shown that flow size distributions often exhibit a high variability property in the sense that most of the flows are short and more than half of the total load is constituted by a small percentage of the largest flows. In the light of this observation, it is ..."
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Cited by 53 (8 self)
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Recent studies of Internet traffic have shown that flow size distributions often exhibit a high variability property in the sense that most of the flows are short and more than half of the total load is constituted by a small percentage of the largest flows. In the light of this observation, it is interesting to revisit scheduling policies that are known to favor small jobs in order to quantify the benefit for small and the penalty for large jobs. Among all scheduling policies that do not require knowledge of job size, the least attained service (LAS) scheduling policy is known to favor small jobs the most.
On some inequalities for the gamma and psi functions
 MATH. COMP
, 1997
"... We present new inequalities for the gamma and psi functions, and we provide new classes of completely monotonic, starshaped, and superadditive functions which are related to Γ and ψ. Euler’s gamma function Γ(x) = ..."
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Cited by 44 (2 self)
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We present new inequalities for the gamma and psi functions, and we provide new classes of completely monotonic, starshaped, and superadditive functions which are related to Γ and ψ. Euler’s gamma function Γ(x) =
Several integral inequalities
 ONLINE: http://jipam.vu.edu.au/article.php?sid=113
"... Communicated by J. Pecarić ABSTRACT. In this article, an open problem posed in [12] is studied once again, and, following closely theorems and methods from [5], some extensions of several integral inequalities are obtained. ..."
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Cited by 36 (4 self)
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Communicated by J. Pecarić ABSTRACT. In this article, an open problem posed in [12] is studied once again, and, following closely theorems and methods from [5], some extensions of several integral inequalities are obtained.
On Name Resolution in PeertoPeer Networks
 In Proceedings of the 2nd ACM Worskhop on Principles of Mobile Commerce (POMC
, 2002
"... An efficient name resolution scheme is the cornerstone of any peertopeer network. The foundation of an efficient name resolution scheme is a dynamic network topology that determines the neighbor relationships to be maintained by the nodes in the network. The name resolution scheme proposed by P ..."
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Cited by 33 (4 self)
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An efficient name resolution scheme is the cornerstone of any peertopeer network. The foundation of an efficient name resolution scheme is a dynamic network topology that determines the neighbor relationships to be maintained by the nodes in the network. The name resolution scheme proposed by Plaxton, Rajaraman, and Richa, which we hereafter refer to as the PRR scheme, is a scalable scheme that also provides provable locality properties on a certain class of growthrestricted metric spaces. On arbitrary metric spaces, however, some performance bounds of PRR are significantly weakened. In this paper, we define a class of network topologies called hyperdelta networks and observe that the PRR topology may be viewed as a random hyperdelta network. We then propose SPRR (simplified PRR), a variant of the PRR scheme that performs well on arbitrary metric spaces. SPRR imposes additional constraints on PRR neighbor selection by placing the nodes on a cycle. Although SPRR does not provide as strong locality properties as PRR, it exploits locality heuristically yet effectively. Finally, a significant level of fault tolerance can be achieved in SPRR without adding much complexity.
SelfAlignment in Words and their Applications
 J. Algorithms
, 1992
"... Some quantities associated with periodicities in words are analyzed within the Bernoulli probabilistic model. In particular, the following problem is addressed. Assume that a string X is given, with symbols emitted randomly but independently according to some known distribution of probabilities. T ..."
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Cited by 27 (8 self)
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Some quantities associated with periodicities in words are analyzed within the Bernoulli probabilistic model. In particular, the following problem is addressed. Assume that a string X is given, with symbols emitted randomly but independently according to some known distribution of probabilities. Then, for each pair (W , Z) of distinct suffixes of X, the expected length of the longest common prefix of W and Z is sought. The collection of these lengths, that are called here selfalignments, plays a crucial role in several algorithmic problems on words, such as building suffix trees or inverted files, detecting squares and other regularities, computing substring statistics, etc. The asymptotically best algorithms for these problems are quite complex and thus risk to be unpractical. The present analysis of selfalignments and related measures suggests that, in a variety of cases, more straightforward algorithmic solutions may yield comparable or even better performances. Key words and ph...
SelfSimilar Asymptotics for Linear and Nonlinear Diffusion Equations
 Studies in Applied Mathematics
, 1985
"... . The longtime asymptotic solutions of initial value problems for the heat equation and the nonlinear porous medium equation are selfsimilar spreading solutions. The symmetries of the governing equations yield three parameter families of these solutions given in terms of their mass, center of mass ..."
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Cited by 25 (4 self)
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. The longtime asymptotic solutions of initial value problems for the heat equation and the nonlinear porous medium equation are selfsimilar spreading solutions. The symmetries of the governing equations yield three parameter families of these solutions given in terms of their mass, center of mass and variance. Unlike the mass and center of mass, the variance, or "timeshift," of a solution is not a conserved quantity for the nonlinear problem. We derive an optimal linear estimate of the longtime variance. Newman's Lyapunov functional is used to produce a maximum entropy timeshift estimate. Results are applied to nonlinear merging and timedependent, inhomogeneously forced diffusion problems. Key words. porous medium equation, similarity solutions, longtime asymptotics, nonlinear diffusion 1. Introduction. In many dissipative systems, the solution approaches a selfsimilar form at long times. Barenblatt has called this behavior intermediate asymptotics [6, 10]; independent of the ...
Local estimates for some fully nonlinear elliptic equations
, 2005
"... We present a method to derive local estimates for some classes of fully nonlinear elliptic equations. The advantage of our method is that we derive Hessian estimates directly from C 0 estimates. Also, the method is flexible and can be applied to a large class of equations. ..."
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Cited by 24 (2 self)
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We present a method to derive local estimates for some classes of fully nonlinear elliptic equations. The advantage of our method is that we derive Hessian estimates directly from C 0 estimates. Also, the method is flexible and can be applied to a large class of equations.