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## Optimal Choice of Threshold in Two Level Processor Sharing

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748 | Queueing Systems
- Kleinrock
- 1975
(Show Context)
Citation Context ...amples of such applications are file size based differentiation in TCP/IP networks [3, 9] and Web server request differentiation [10, 11]. The Two Level Processor Sharing (TLPS) scheduling discipline =-=[12]-=- helps to overcome the above mentioned requirements. It uses the differentiation of jobs according to a threshold on the attained service and gives priority to the jobs with small sizes. A detail desc... |

199 | Fitting mixtures of exponentials to long-tail distributions to analyze network performance models. Performance Evaluation
- Feldmann, Whitt
(Show Context)
Citation Context ...ten could be modeled with a heavy-tailed distributions. It is known, that the heavy-tailed distribution could be approximated with a hyper-exponential distribution with a significant number of phases =-=[5, 8]-=-. Also in [7], it was shown that the hyper-exponential distribution models well the file size distribution in the Internet. Therefore, in the present work we analyze the TLPS system with hyper-exponen... |

138 | Size-based scheduling to improve web performance
- Harchol-Balter, Schroeder, et al.
- 2003
(Show Context)
Citation Context ...imes. These requirements are often not feasible in applications. The examples of such applications are file size based differentiation in TCP/IP networks [3, 9] and Web server request differentiation =-=[10, 11]-=-. The Two Level Processor Sharing (TLPS) scheduling discipline [12] helps to overcome the above mentioned requirements. It uses the differentiation of jobs according to a threshold on the attained ser... |

135 |
A proof of the optimality of the Shortest Remaining Processing Time Discipline
- Schrage
- 1968
(Show Context)
Citation Context ... time that a clever scheduling of tasks can significantly improve system performance. For instance, Shortest Remaining Processing Time (SRPT) scheduling discipline minimizes the expected sojourn time =-=[15]-=-. However, SRPT requires to keep track of all jobs in the system and also requires the knowledge of the remaining processing times. These requirements are often not feasible in applications. The examp... |

37 | Differentiation between short and long TCP flows: predictability of the response time
- Avrachenkov, Ayesta, et al.
- 2004
(Show Context)
Citation Context ...es the knowledge of the remaining processing times. These requirements are often not feasible in applications. The examples of such applications are file size based differentiation in TCP/IP networks =-=[3, 9]-=- and Web server request differentiation [10, 11]. The Two Level Processor Sharing (TLPS) scheduling discipline [12] helps to overcome the above mentioned requirements. It uses the differentiation of j... |

37 | Fitting world-wide web request traces with the EM-algorithm. Performance Evalutation, 52:175
- Khayari, Sadre, et al.
- 2003
(Show Context)
Citation Context ...eled with a heavy-tailed distributions. It is known, that the heavy-tailed distribution could be approximated with a hyper-exponential distribution with a significant number of phases [5, 8]. Also in =-=[7]-=-, it was shown that the hyper-exponential distribution models well the file size distribution in the Internet. Therefore, in the present work we analyze the TLPS system with hyper-exponential job size... |

31 |
Mixed scheduling disciplines for network flows
- Feng, Misra
- 2003
(Show Context)
Citation Context ...es the knowledge of the remaining processing times. These requirements are often not feasible in applications. The examples of such applications are file size based differentiation in TCP/IP networks =-=[3, 9]-=- and Web server request differentiation [10, 11]. The Two Level Processor Sharing (TLPS) scheduling discipline [12] helps to overcome the above mentioned requirements. It uses the differentiation of j... |

21 | Differentiated control of web traffic: A numerical analysis
- Guo, Matta
- 2002
(Show Context)
Citation Context ...imes. These requirements are often not feasible in applications. The examples of such applications are file size based differentiation in TCP/IP networks [3, 9] and Web server request differentiation =-=[10, 11]-=-. The Two Level Processor Sharing (TLPS) scheduling discipline [12] helps to overcome the above mentioned requirements. It uses the differentiation of jobs according to a threshold on the attained ser... |

10 |
Analysis of the M/G/1 processor-sharing queue with bulk arrivals
- Bansal
- 2003
(Show Context)
Citation Context ...former parameters. 3.2 Explicit form for the expected sojourn time To find T T LP S (x) we need to solve the integral equation (7). To solve (7) we use the Laplace transform based method described in =-=[6]-=-. Theorem 1. The expected sojourn time in the TLPS system with the hyper-exponential job size distribution with two phases is given by T (θ) = X1 θ + W (θ)F (θ) + 1 − ρθ m − X1 θ 1 − ρ + � b(θ) µ1µ2(m... |

9 | Mean delay analysis of multi-level processorsharing disciplines
- Aalto, Ayesta
- 2006
(Show Context)
Citation Context ...h small sizes. A detail description of the TLPS discipline is presented in the ensuing section. Of course, TLPS provides a sub-optimal mechanism in comparison with SRPT. Nevertheless, as was shown in =-=[1]-=-, when the job size distribution has a decreasing hazard rate, the performance of TLPS with appropriate choice of threshold is very close to optimal. It turns out that the distribution of file sizes i... |

8 | The Processor-Sharing Queueing Model for Time-Shared Systems with Bulk Arrivals, Networks Journal,1,1-13 - Kleinrock, Muntz, et al. - 1971 |

7 | Batch arrival processorsharing with application to multi-level processor-sharing scheduling
- Avrachenkov, Ayesta, et al.
- 2005
(Show Context)
Citation Context ...2(1 − ρθ)). The remaining term α(x − θ)/(1 − ρθ) is the time spent in the low priority queue. To find α(x) we can use the interpretation of the lower priority queue as a PS system with batch arrivals =-=[4, 14]-=-. As was shown in [12], α ′ (x) = dα/dx is the solution of the following integral equation α ′ � ∞ (x) = λn α ′ � x (y)B(x + y)dy + λn α ′ (y)B(x − y)dy + bB(x) + 1. (7) 0 0 Here n = F (θ)/(1 − ρθ) is... |

6 |
Batch processor sharing with hyper-exponential service time
- Osipova
(Show Context)
Citation Context ...2(1 − ρθ)). The remaining term α(x − θ)/(1 − ρθ) is the time spent in the low priority queue. To find α(x) we can use the interpretation of the lower priority queue as a PS system with batch arrivals =-=[4, 14]-=-. As was shown in [12], α ′ (x) = dα/dx is the solution of the following integral equation α ′ � ∞ (x) = λn α ′ � x (y)B(x + y)dy + λn α ′ (y)B(x − y)dy + bB(x) + 1. (7) 0 0 Here n = F (θ)/(1 − ρθ) is... |

4 |
Two-level processor sharing scheduling disciplines: mean delay analysis
- Aalto, Ayesta, et al.
- 2004
(Show Context)
Citation Context ...ρ < 1) and is in steady state. Since the hyper-exponential distribution has a decreasing hazard rate, there exists a value of the threshold that minimizes the expected sojourn time in the TLPS system =-=[1, 2]-=-. The main goal of the present work is to determine this optimal value of the threshold. 2 The expected sojourn time in TLPS system Let us denote by Xn θ = ∫ θ d 0 yn dy F (y) dy + θn (1 − F (θ)) the ... |

2 |
A stochastic model for the rate of non-persistent TCP flows
- Baccelli, McDonald
- 2006
(Show Context)
Citation Context ...ten could be modeled with a heavy-tailed distributions. It is known, that the heavy-tailed distribution could be approximated with a hyper-exponential distribution with a significant number of phases =-=[5, 8]-=-. Also in [7], it was shown that the hyper-exponential distribution models well the file size distribution in the Internet. Therefore, in the present work we analyze the TLPS system with hyper-exponen... |