## A Study of Traffic Statistics of Assembled Burst Traffic in Optical Burst Switched Networks (2002)

Venue: | In Proceedings of Opticomm |

Citations: | 26 - 1 self |

### BibTeX

@INPROCEEDINGS{Yu02astudy,

author = {Xiang Yu and Yang Chen and Chunming Qiao},

title = {A Study of Traffic Statistics of Assembled Burst Traffic in Optical Burst Switched Networks},

booktitle = {In Proceedings of Opticomm},

year = {2002},

pages = {149--159}

}

### OpenURL

### Abstract

Optical Burst Switching (OBS) is considered as a promising switching technique for building the next generation optical Internet. In OBS networks, one important issue is how the performance will be affected by bursts assembled from packets, which is the basic transmission unit in OBS. In this paper, we study the fundamental statistic properties such as the burst length distribution, inter-arrival time distribution, as well as correlation structure of assembled burst traffic from burst assembly algorithms. From both theoretical and empirical results, it is demonstrated that after the assembly, the traffic will in general approach the Gaussian distribution. In particular, the variance of assembled traffic decreases with the increase in the assembly window size and the traffic load. However, the long range dependence in the input traffic will not change after assembly.

### Citations

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(Show Context)
Citation Context ...input traffic will also approach Gaussian because of the packet independence property in a short time period. To determine the long range dependence property, we can examine the correlation structure =-=[8, 16] o-=-f the assembled traffic. If we divide the time axis into K blocks and each block contains m sub-blocks. Suppose the traffic load 1 = arriving in the ith sub-block of kth block is W (k−1)m+i, andW (m... |

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Citation Context ... (aBµ) n T n i n! (n − 1)! e−aB ]e −µTi (8) To analyze (8), we first give a lower bound and an upper bound (derived in Appendix) as follows: 1 2 e−aB e −µTi+√ aBµTi <P{ti = Ti} <Ce −=-=aB e −µTi+√ aBµTi (9) wh-=-ere C>1 is a constant. From (9), we can see that when Ti is small, the distribution will be larger than exponential because of the additional term √ aBµTi. However, when Ti becomes large, the distr... |

1129 | Self-similarity in World Wide Web traffic: evidence and possible causes
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Citation Context ...m a different angle. If we fix the number of packets in a burst, then the burst inter-arrival time ti can be viewed as the aggregation of a fixed number of packet inter-arrival time, that is, n� ti =-=∼ (10) x-=-m m=1sand also, the number of packet is decided by the distribution of packet size qm. Since we have n ∼ B/q where B is fixed, the distribution of n is decided by distribution of qm and should also ... |

471 |
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Citation Context ...inite link capacity, the transmission time of a packet is negligibly small and accordingly each arrival packet can be treated as a point in the time axis. In other words, Simple P oisson Pointprocess =-=[14]-=- can be used to model the input traffic in the infinite link speed scenario, which assumes that: (1) no packet arrives at exactly the same time; (2) all packet arrivals are independent. For simplicity... |

198 | Terabit burst switching
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Citation Context ...ill approach the constant B. Thus, the burst size has a very limited distribution range. However, the inter-arrival time ti of the bursts is variable of interest in such a case. Similarly to Equation =-=(3), -=-the distribution of inter-arrival time ti is the distribution of the sum of ni = B/q packets’ inter-arrival times, and can be calculated as follows if we use B as an approximation of the burst size:... |

142 | Self-similarity and Heavy Tails: Structural Modeling of Network Traffic
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Citation Context ...load scenario and 100 percentile to present the heavy traffic load scenario. In our simulation, the LRD traffic is generated by multiplexing independent sources with Pareto-distributed ON/OFF periods =-=[17]. I-=-n the ON period, traffic source send packets out back to back while in the OFF periods, no packet comes out from the source. The probability density function of the Pareto distribution are: α · bα ... |

127 | Cankaya: Control architecture in optical burst switched WDM networks
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Citation Context ...fect of the assembled traffic on the performance enhancement in OBS networks, we provide simulation result for a single OBS core node with 8 output wavelengths, first-fit scheduling with void filling =-=[7]-=-. The input to the scheduling algorithm is either unassembled (raw) Poisson packet traffic or burst traffic assembled from the same Poisson packet traffic using burst assembly Algorithm II, both under... |

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Citation Context ...ribution at different traffic load To study the long range dependence in the assembled traffic, we use an input LRD traffic with its Hurst parameter equals to 0.75. Figure 6 illustrates the R/S plots =-=[18,19]-=- for the input packet traffic and the assembled traffic respectively. The slope of the R/S plot represents the Hurst parameter associated with the corresponding traffic. It can be seen that the Hurst ... |

62 | On the nonstationarity of Internet traffic
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Citation Context ...kets contained in the previous k − 1blocksandqNk−1+idenotes the (Nk−1 + i)th packet in the arrived traffic load. So, when m →∞we also have n →∞, and (12) is rewritten as r (m) (k) ∼ k =-=2(H−1) as n →∞. (13) I-=-f the sub-block time is large enough compared with assembly window size, we can approximate W ′ (m) k ,the local average workload in assembled burst traffic in time block k, with the average summati... |

56 | Tamil, “On optical burst switching and self-similar traffic
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(Show Context)
Citation Context ...cketsarrivals goes up or the assembled burst size goes up. In addition, as more and more packets are aggregated in a burst, the burst length in Algorithm I will approach its mean value: pi → ¯p = q=-= T (5) µ a-=-nd the inter-arrival time in Algorithm II will also approach its mean value: ti → ¯t = µ B (6) q In other words, the assembled burst traffic from both Algorithm I and II will become Gaussian distr... |

55 |
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(Show Context)
Citation Context ...ribution at different traffic load To study the long range dependence in the assembled traffic, we use an input LRD traffic with its Hurst parameter equals to 0.75. Figure 6 illustrates the R/S plots =-=[18,19]-=- for the input packet traffic and the assembled traffic respectively. The slope of the R/S plot represents the Hurst parameter associated with the corresponding traffic. It can be seen that the Hurst ... |

53 |
Traffic Theory and the Internet
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(Show Context)
Citation Context ...del can be used to analyze the assembled according to the above discussion, with more packets aggregated in a burst, the inter-arrival time distribution ti will approach its mean value: ti → ¯t →=-= µ B (11)-=- a Similarly, the burst size distribution of the assembled traffic from Burst Assembly Algorithm I will also has the same distribution as (8). And the assembled burst traffic will also approach Gaussi... |

36 | Just-enougth-time(JET): A High Speed Protocol for Bursty Traffic
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(Show Context)
Citation Context ...al packet can be treated as a point in the time axis. In other words, Simple P oisson Pointprocess [14] can be used to model the input traffic in the infinite link speed scenario, which assumes that: =-=(1)-=- no packet arrives at exactly the same time; (2) all packet arrivals are independent. For simplicity, we assume fixed packet size first. 1. Poisson Traffic with Fixed Packet SizesSuppose all the packe... |

31 | On burst assembly in optical burst switching networks—A performance evaluation of just-enough-time
- Dolzer, Gauger
(Show Context)
Citation Context ...re aggregated in a burst, the burst length in Algorithm I will approach its mean value: pi → ¯p = q T (5) µ and the inter-arrival time in Algorithm II will also approach its mean value: ti → ¯t=-= = µ B (6)-=- q In other words, the assembled burst traffic from both Algorithm I and II will become Gaussian distribution of zero variance, i.e., constant rate traffic. 2. Poisson Traffic with Variable Packet Siz... |

28 | Broadband Traffic Modeling: Simple Solutions to Hard Problems
- Addie, Zukerman, et al.
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(Show Context)
Citation Context ...input traffic will also approach Gaussian because of the packet independence property in a short time period. To determine the long range dependence property, we can examine the correlation structure =-=[8, 16] o-=-f the assembled traffic. If we divide the time axis into K blocks and each block contains m sub-blocks. Suppose the traffic load 1 = arriving in the ith sub-block of kth block is W (k−1)m+i, andW (m... |

11 | The effect of statistical multiplexing on the long range dependence of Internet packet traffic. Bell Labs
- Cao, Cleveland, et al.
(Show Context)
Citation Context ...−1) is called local average workload. Let r (m) (k) denote the correlation with lag k of the original long range dependent input packet traffic, and r (m) (k) satisfies: r (m) (k) ∼ k 2(H−1) as =-=m →∞. (12) Suppo-=-se there are n packets contained in the time block k, then the local average workload can be rewritten as W (m) 1 k = m {qNk−1+1 + ... + qNk−1+n}, where Nk−1 is the total number of packets conta... |

7 |
Optical burst switching(OBS)-a new paradigm for an optical
- Qiao, Yoo
- 1999
(Show Context)
Citation Context ...axis. In other words, Simple P oisson Pointprocess [14] can be used to model the input traffic in the infinite link speed scenario, which assumes that: (1) no packet arrives at exactly the same time; =-=(2)-=- all packet arrivals are independent. For simplicity, we assume fixed packet size first. 1. Poisson Traffic with Fixed Packet SizesSuppose all the packets have a size equal to a constant q, and the in... |

2 |
A comparative study of
- Xin, Qiao
- 2001
(Show Context)
Citation Context ...-arrival times, and can be calculated as follows if we use B as an approximation of the burst size: ni � P {ti = Ti} = P { xm = Ti} m=1 B/q � = P { = (µTi) B/q−1 m=1 xm = Ti} (2) (3) (B/q − 1=-=)! e−µTi (4)-=- In short, Burst Assembly Algorithm I shapes the Poisson traffic to an assembled burst traffic with a constant inter-arrival time (T ) and a burst size distribution satisfying (3). On the other hand, ... |