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18
The foregroundbackground queue: a survey
, 2006
"... Computer systems researchers have begun to apply the ForegroundBackground (FB) scheduling discipline to a variety of applications, and as a result, there has been a resurgence in theoretical research studying FB. In this paper, we bring together results from both of these research streams to prov ..."
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Cited by 22 (8 self)
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Computer systems researchers have begun to apply the ForegroundBackground (FB) scheduling discipline to a variety of applications, and as a result, there has been a resurgence in theoretical research studying FB. In this paper, we bring together results from both of these research streams to provide a survey of stateoftheart theoretical results characterizing the performance of FB. Our emphasis throughout is on the impact of these results on computer systems.
Preventing large sojourn times using SMART scheduling
 Operations Research
, 2005
"... Recently, the class of SMART scheduling policies has been introduced in order to formalize the common heuristic of “biasing toward small jobs. ” We study the tail of the sojourntime (responsetime) distribution under both SMART policies and the ForegroundBackground policy (FB) in the GI/GI/1 queue ..."
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Cited by 17 (8 self)
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Recently, the class of SMART scheduling policies has been introduced in order to formalize the common heuristic of “biasing toward small jobs. ” We study the tail of the sojourntime (responsetime) distribution under both SMART policies and the ForegroundBackground policy (FB) in the GI/GI/1 queue. We prove that these policies behave very well under heavytailed service times. Specifically, we show that the sojourntime tail under all SMART policies and FB is similar to that of the servicetime tail, up to a constant, which makes the SMART class superior to FirstComeFirstServed (FCFS). In contrast, for lighttailed service times, we prove that the sojourntime tail under FB and SMART is larger than that under FCFS. However, we show that the sojourntime tail for a job of size y under FB and all SMART policies still outperforms FCFS as long as y is not too large.
Mean delay analysis of multi level processor sharing disciplines
 In Proc. of IEEE Infocom 2006
"... scheduling disciplines permit to model a wide variety of nonanticipating scheduling disciplines. Such disciplines have recently attracted attention in the context of the Internet as an appropriate flowlevel model for the bandwidth sharing obtained when priority is given to short TCP connections. I ..."
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Cited by 9 (3 self)
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scheduling disciplines permit to model a wide variety of nonanticipating scheduling disciplines. Such disciplines have recently attracted attention in the context of the Internet as an appropriate flowlevel model for the bandwidth sharing obtained when priority is given to short TCP connections. In this paper, we compare the mean delay in an M/G/1 queue among MLPS disciplines under the assumption that the service time distribution belongs to class Decreasing Hazard Rate (DHR). We are able to prove that, given an MLPS discipline, the mean delay is reduced whenever a level is added by splitting an existing one in several cases. The exceptions concern splitting the upper levels with PS internal discipline. Our numerical examples, however, indicate that the level splitting be advantageous even in these cases. Furthermore, we characterize the effect on the mean delay of changing internal disciplines within levels. By numerical means we demonstrate that the mean delay of an MLPS discipline can get close to the minimum optimal delay with just a few levels. As the number of levels increases in an MLPS discipline, the MLPS queue mimics closer and closer the behavior of a ForegroundBackground queue, which is known to minimize the mean delay among all disciplines. Thus, our result provides a constructive way to demonstrate the optimality of FB. I.
Beyond processor sharing
 SIGMETRICS Perform. Eval. Rev
"... While the (Egalitarian) ProcessorSharing (PS) discipline offers crucial insights in the performance of fair resource allocation mechanisms, it is inherently limited in analyzing and designing differentiated scheduling algorithms such as Weighted Fair Queueing and Weighted RoundRobin. The Discrimin ..."
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Cited by 8 (2 self)
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While the (Egalitarian) ProcessorSharing (PS) discipline offers crucial insights in the performance of fair resource allocation mechanisms, it is inherently limited in analyzing and designing differentiated scheduling algorithms such as Weighted Fair Queueing and Weighted RoundRobin. The Discriminatory ProcessorSharing (DPS) and Generalized ProcessorSharing (GPS) disciplines have emerged as natural generalizations for modeling the performance of such service differentiation mechanisms. A further extension of the ordinary PS policy is the Multilevel ProcessorSharing (MLPS) discipline, which has captured a pivotal role in the analysis, design and implementation of sizebased scheduling strategies. We review various key results for DPS, GPS and MLPS models, highlighting to what extent these disciplines inherit desirable properties from ordinary PS or are capable of delivering service differentiation.
Modelling Restricted Processor Sharing
"... In principle unrestricted processor sharing can be very useful when jobs with widely varying CPU requirements are competing for the same processor. Even if there are several processors available, processor sharing can be useful. However, in practice it must be implemented by roundrobin, and there i ..."
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Cited by 7 (0 self)
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In principle unrestricted processor sharing can be very useful when jobs with widely varying CPU requirements are competing for the same processor. Even if there are several processors available, processor sharing can be useful. However, in practice it must be implemented by roundrobin, and there is an overhead cost (e.g., cache thrashing) to implementing this scheme. Furthermore, the overhead may depend on the number of jobs that are active, and can be significant. Therefore restricted processor sharing, which only allows a limited number of jobs to share the processors, may be a more appropriate strategy. In this paper we present a comprehensive analytic model to study the interplay among the number of parallel processors, the maximum degree of processor sharing, the overhead, and the job arrival rate. We examine how the CPU time distribution affects mean system time (or response time), under what conditions two slow processors are better than one double fast one, and when it pays to invoke restricted processor sharing.
Optimal scheduling of jobs with a DHR tail in the M/G/1 queue
"... We consider the mean delay optimization in the M/G/1 queue for jobs with a service time distribution that has a tail with decreasing hazard rate (DHR). If the DHR property is valid for the whole distribution, then it is known that the ForegroundBackground (FB) discipline, which gives priority to th ..."
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We consider the mean delay optimization in the M/G/1 queue for jobs with a service time distribution that has a tail with decreasing hazard rate (DHR). If the DHR property is valid for the whole distribution, then it is known that the ForegroundBackground (FB) discipline, which gives priority to the job with least amount of attained service, is optimal among nonanticipating scheduling disciplines. However, FB may fail to be optimal if the DHR property is valid only for the tail of the distribution. An important example is the Pareto distribution bounded away from zero. In this paper we show that for a class of service time distributions with a DHR tail (including the Pareto distribution), the optimal nonanticipating discipline is a combination of FCFS and FB disciplines, which gives priority to the jobs with attained service less than some fixed threshold θ ∗. These priority jobs are served in the FCFS manner. If there are no jobs with attained service less than θ ∗ , priority is given to the job with least amount of attained service.
Inducing Optimal Scheduling with Selfish Users
"... It is well known that scheduling jobs according to the ShortestRemainingProcessingTime (SRPT) policy is optimal for minimizing mean response time in a singleserver system with online arrivals. Unfortunately, SRPT scheduling requires users to provide their job size (service requirement). Recent l ..."
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Cited by 2 (1 self)
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It is well known that scheduling jobs according to the ShortestRemainingProcessingTime (SRPT) policy is optimal for minimizing mean response time in a singleserver system with online arrivals. Unfortunately, SRPT scheduling requires users to provide their job size (service requirement). Recent literature considers the problem of optimal scheduling when job sizes are either entirely unknown or partially unknown. We extend this work by additionally considering users who know their job size, but are selfish in that they are willing to lie about their size, if that affords them a delay advantage (e.g., pretending that their job is small). It is not at all obvious how to schedule such selfish users, given that they are mixed in with users who genuinely don’t know their size, and that the system administrator cannot differentiate between the two types. To address this question, we develop a novel approach for inducing users into selfscheduling themselves according to (an approximation of) SRPT and also revealing the size of their job. We achieve this by defining a game that users play, whereby users are allowed to apply priorityboosting tokens to portions of their job. For a given number of tokens, we characterize the features of a unique equilibrium selfscheduling policy. We prove that the equilibrium policy is a dominant
Comparison of Strategies for Serving Two Streams of Jobs
"... Highly varying job demands generally consist of many short jobs mixed with several long jobs. In this paper, we consider a simple scenario where two job streams with different level of demands must be processed by the same server. We study the performance of several roundrobin variants and FCFSP in ..."
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Highly varying job demands generally consist of many short jobs mixed with several long jobs. In this paper, we consider a simple scenario where two job streams with different level of demands must be processed by the same server. We study the performance of several roundrobin variants and FCFSP in such a scenario. The simulation results show that on the one hand, by employing immediate preemption to favor newly arrived jobs, roundrobin can effectively reduce the mean response time for the shortjob stream, while only slightly increasing the response time for the longjob stream. On the other hand, by assuming the availability of job stream information and always favoring the shortjob stream, FCFSP may improve performance. However, to further improve performance, other information if available (e.g., the characteristics of each individual stream) should be considered. Keywords: Firstcomefirstserved with priority (FCFSP), roundrobin (RR), lastcomefirstserved with preemptive resume (LCFSPR), leastattainedtime (LAT) 1
unknown title
, 2007
"... Optimal scheduling of service requirements with a DHR tail in the M/G/1 queue ..."
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Optimal scheduling of service requirements with a DHR tail in the M/G/1 queue