## Analysis of LAS Scheduling for Job Size Distributions with High Variance (2003)

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Citations: | 53 - 8 self |

### BibTeX

@MISC{Rai03analysisof,

author = {Idris A. Rai and Guillaume Urvoy-keller and Ernst W. Biersack},

title = {Analysis of LAS Scheduling for Job Size Distributions with High Variance},

year = {2003}

}

### Years of Citing Articles

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### Abstract

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.

### Citations

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Citation Context ...ning of the drop rate of high priority and low priority packets, PS-w can reduce the response time of medium-sized flows that have 50-200 packets by up to 80% compared to random early detection (RED) =-=[11]-=- queue management policy without significantly penalizing the large flows. The response times of flows of sizes less than 20 packets are similar for PS-w and RED. In [3], a short flow differentiating ... |

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Citation Context ...e time. 1. INTRODUCTION Internet traffic studies revealed that Internet traffic consists of many short flows and that a tiny fraction of the largest flows constitutes more than half of the total load =-=[6, 21]-=-. It is interesting to study the performance of scheduling policies in the light of these findings to see if one can improve the performance of short jobs without penalizing too much the long jobs. We... |

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Citation Context ...e time. 1. INTRODUCTION Internet traffic studies revealed that Internet traffic consists of many short flows and that a tiny fraction of the largest flows constitutes more than half of the total load =-=[6, 21]-=-. It is interesting to study the performance of scheduling policies in the light of these findings to see if one can improve the performance of short jobs without penalizing too much the long jobs. We... |

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Citation Context ...f LAS needs to know the amount of service it has delivered to each job, which can be easily obtained from the server. LAS is also known in the literature under the names of foreground-background (FB) =-=[17]-=- or shortest elapsed time (SET) first scheduling [4]. The expression for the conditional mean response time E[T (x)] for an M/G/1 queue served using LAS has been originally derived in [24], and were r... |

240 | Dynamics of IP traffic: A study of the role of variability and the impact of control
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Citation Context ...y shown in Figure 8 where C1-C5 are clients initiating a series of Web sessions, each retrieving some Web pages from a server randomly chosen from a pool of S1-S5 as proposed in the ns-2 Web model in =-=[9]-=-. Each Web page contains a certain number of objects. Each time an object is requested, a new TCP connection is established. We refer to the packets that belong to one TCP connection as a flow. We set... |

235 |
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Citation Context ...ying E[ ~ R(x)]LAS E[R(x)]SRPT : E[ ~ R(x)]LAS E[R(x)]SRPT = x 1 (x) Z x 0 dt 1 (t) = Z x 0 dt 1 (x) Z x 0 dt 1 (t) = Z x 0 (x) (t) 1 (x) 1 1 (t) dt Applying the Chebyshev integral inequality [19] to f(t) = (x) (t) 1 (x) , which is a decreasing function of t and g(t) = 1 1 (t) , which is an increasing function of t, we get E[ ~ R(x)]LAS E[R(x)]SRPT 1 x Z x 0 (x) (t) 1 (x) dt Z x 0 dt ... |

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Citation Context ... half of the load is due to a tiny fraction of the largest flows. Different distributions have been shown to model the empirical Internet traffic given their coefficient of variation is larger than 1 =-=[1, 6, 10]-=-. These distributions include Pareto, bounded Pareto, lognormal distributions, hyper-exponential, Weilbull, inverse Gaussian, and hybrid of lognormal and Pareto distributions. The bounded Pareto (BP) ... |

157 | Analysis of srpt scheduling: Investigating unfairness. To appear
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Citation Context ...job size distribution exhibits the high variability property if less than 1% of the largest jobs account for more than half of the load. This property has also been referred to as heavy-tail property =-=[7, 2]-=-, but it is not restricted to heavy-tail distributions [12]. In this paper, we analyze the impact of the high variability property of job size distributions on the performance of the LAS scheduling po... |

123 | Size-based scheduling to improve web performance. mimeo
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Citation Context ...ean slowdown under SRPT than under PS. Nevertheless, SRPT has the drawback that it needs to know the size of the jobs. While the job size is known, for instance, in a Web server with static Web pages =-=[14]-=-, it is generally not known in environments such as in Internet routers or Web servers with dynamic pages. The least attained service (LAS) scheduling policy is a multilevel scheduling policy that fav... |

115 | Connection Scheduling in Web Servers
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Citation Context ...job size distribution exhibits the high variability property if less than 1% of the largest jobs account for more than half of the load. This property has also been referred to as heavy-tail property =-=[7, 2]-=-, but it is not restricted to heavy-tail distributions [12]. In this paper, we analyze the impact of the high variability property of job size distributions on the performance of the LAS scheduling po... |

78 | What TCP/IP protocol headers can tell us about the web
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Citation Context ...ted, a new TCP connection is established. We refer to the packets that belong to one TCP connection as a flow. We set the Web parameters as shown in Table 1. These values are based on the findings of =-=[27-=-] and summarized by [3]. The density function of the Pareto distribution is obtained from Equation (7) when p !1. Here, we use the Pareto distribution with mean of 12, = 1:2, and k = 1. The coefficie... |

47 | Online scheduling to minimize average stretch
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Citation Context ...c to analyze fairness [2]. Processor Sharing (PS) is known to be a fair policy since it offers the same slowdown to all jobs. The shortest remaining processing time (SRPT) scheduling policy is proven =-=[20, 25]-=- to be the optimal policy for minimizing the mean response time. It has been known for a long time that for negative exponentially distributed job sizes, SRPT severely penalizes large jobs. However, B... |

43 | Asymptotic convergence of scheduling policies with respect to slowdown
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(Show Context)
Citation Context ... M=G=1=LAS queue at steady state was done by Schassberger [22, 23]. However, Schassberger did not evaluate the impact of the variance of the service time distribution. In a recent work, Balter et al. =-=[15]-=- show that for an M/G/1 queue, the conditional mean slowdown of all work-conserving scheduling policies, which includes LAS, asymptotically converges to the conditional mean slowdown of PS, i.e. limx!... |

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Citation Context ...meters of the BP distribution, i.e., k, , and p. The C value of exponential distribution is always 1. The variability of a distribution can be determined by using the mass-weighted function (Mw (x)) [=-=-=-8], which (for a job of size x) is defined as the fraction of the total load constituted by jobs of size less than or equal to x or Mw (x) , (x) . We plot Mw (x) as a function of F (x) to see the fra... |

26 | On the Tails of Web File Size Distributions
- Gong, Liu, et al.
- 2001
(Show Context)
Citation Context ...if less than 1% of the largest jobs account for more than half of the load. This property has also been referred to as heavy-tail property [7, 2], but it is not restricted to heavy-tail distributions =-=[12]-=-. In this paper, we analyze the impact of the high variability property of job size distributions on the performance of the LAS scheduling policy. Response time and slowdown are commonly used as perfo... |

24 |
The queue M/G/1 with feedback to lower priority queues
- Schrage
- 1967
(Show Context)
Citation Context ...ground (FB) [17] or shortest elapsed time (SET) first scheduling [4]. The expression for the conditional mean response time E[T (x)] for an M/G/1 queue served using LAS has been originally derived in =-=[24]-=-, and were re-derived in [28, 4, 18] as well. However, the expression for E[T (x)] is complex and difficult to evaluate numerically, and therefore very little has been done to evaluate the performance... |

22 | Preferential treatment for short flows to reduce web latency,” Computer Networks: The
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Citation Context ...ng congestion and will drop packets from the largest flows that currently have a packet in the queue. The idea of giving preferential treatment to short flows has been considered by other researchers =-=[3, 13]-=-, who propose DiffServ like models where edge routers mark packets as belonging to short or long flows and core routers utilize the marking to give preferential treatment to short flows. The first pro... |

19 | Differentiated control of web traffic: A numerical analysis
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(Show Context)
Citation Context ...ng congestion and will drop packets from the largest flows that currently have a packet in the queue. The idea of giving preferential treatment to short flows has been considered by other researchers =-=[3, 13]-=-, who propose DiffServ like models where edge routers mark packets as belonging to short or long flows and core routers utilize the marking to give preferential treatment to short flows. The first pro... |

16 | Size-based Adaptive bandwidth Allocation: Optimizing the Average QoS for Elastic Flows
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- 2002
(Show Context)
Citation Context ...take a high variance and thus it can exhibit the high variability property as observed in the Internet traffic and also because the maximum job size can be set to mimic the largest Internet flow size =-=[29, 7, 2-=-]. In this paper, we also use the bounded Pareto job size distribution for the same reasons. We denote the bounded Pareto distribution by BP (k; p; ), where k and p are the minimum and the maximum job... |

14 |
A proof of the optimality of the shortest remaining service time discipline
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Citation Context ...c to analyze fairness [2]. Processor Sharing (PS) is known to be a fair policy since it offers the same slowdown to all jobs. The shortest remaining processing time (SRPT) scheduling policy is proven =-=[20, 25]-=- to be the optimal policy for minimizing the mean response time. It has been known for a long time that for negative exponentially distributed job sizes, SRPT severely penalizes large jobs. However, B... |

12 |
The queue M/G/1 with the shortest processing remaining time discipline
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(Show Context)
Citation Context ... (x) , R x 0 tf(t)dt, and , (1) is the total load in the system. In most cases, this paper assumes an M/G/1 queue, where G is a c.f.m.f.v distribution. The expression of E[T (x)] for M/G/1/SRPT [26]=-=-=- can be decomposed into the conditional mean waiting time E[W (x)] (the time between the instant when a job arrives at the system until it receives the service for the first time) and the conditional ... |

6 |
The Network Simulator ns2
- edunsnamns
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Citation Context ...ltiplexed with packets from other flows. A flow therefore does not arrive at once in the system. To evaluate the performance of LAS in a packet network, we implement LAS in the ns-2 network simulator =-=[16]-=- and analyze it for Web-traffic with Pareto-distributed flow sizes. The simulation results for different load values show that more than 99% of the short flows generated during the simulation benefit ... |

6 |
The steady state distribution of spent service times present in the M/G/1 foreground-background processor-sharing queue
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Citation Context ... queue and observes that LAS offers lower waiting times to short jobs while large jobs see significantly higher waiting times. The analysis of M=G=1=LAS queue at steady state was done by Schassberger =-=[22, 23]-=-. However, Schassberger did not evaluate the impact of the variance of the service time distribution. In a recent work, Balter et al. [15] show that for an M/G/1 queue, the conditional mean slowdown o... |

6 |
Time sharing with priorities
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Citation Context ...elapsed time (SET) first scheduling [4]. The expression for the conditional mean response time E[T (x)] for an M/G/1 queue served using LAS has been originally derived in [24], and were re-derived in =-=[28, 4, 18]-=- as well. However, the expression for E[T (x)] is complex and difficult to evaluate numerically, and therefore very little has been done to evaluate the performance of LAS with respect to the variabil... |

4 |
Grundlagen der Betriebssysteme, Walter de Gruyter
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Citation Context ...elapsed time (SET) first scheduling [4]. The expression for the conditional mean response time E[T (x)] for an M/G/1 queue served using LAS has been originally derived in [24], and were re-derived in =-=[28, 4, 18]-=- as well. However, the expression for E[T (x)] is complex and difficult to evaluate numerically, and therefore very little has been done to evaluate the performance of LAS with respect to the variabil... |

2 |
A Detailed Steady State Analysis of the M/G/1 Queue under various Time Sharing Disciplines
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Citation Context ... queue and observes that LAS offers lower waiting times to short jobs while large jobs see significantly higher waiting times. The analysis of M=G=1=LAS queue at steady state was done by Schassberger =-=[22, 23]-=-. However, Schassberger did not evaluate the impact of the variance of the service time distribution. In a recent work, Balter et al. [15] show that for an M/G/1 queue, the conditional mean slowdown o... |

1 |
Analyzing the Waiting Time Process in Internet Queueing Systems With the Transform Approximation Method", The Telecommunications Review
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Citation Context ... half of the load is due to a tiny fraction of the largest flows. Different distributions have been shown to model the empirical Internet traffic given their coefficient of variation is larger than 1 =-=[1, 6, 10]-=-. These distributions include Pareto, bounded Pareto, lognormal distributions, hyper-exponential, Weilbull, inverse Gaussian, and hybrid of lognormal and Pareto distributions. The bounded Pareto (BP) ... |

1 | Analyzing the Waiting Time - Fischer, Gross, et al. - 2001 |