无线网关对自相似数据流影响的研究
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摘要
由于网络流量的自相似对网络设计、网络协议等具有重要影响,研究人员认为现在的无线网络数据流同样具有自相似性,其原因有以下几个方面:首先,近年来无线网络技术比如IEEE802.11、Bluetooth、GPRS、WiMAX等飞速发展,无线通信与无线网络用户在接入Internet时能和有线用户一样获得相同的带宽,这也就意味着无线网络的网络流量有可能与有线网络中的网络流量一样存在自相似性。其次,有线网络中TCP协议的重传会造成网络数据的自相似,由于无线网络本身的不稳定性,TCP协议更高的重传同样会造成无线网的数据流具有自相似性。最后,有线网络数据流的自相似性可能经无线网关转发传播到无线网络中。
考虑到无线网络本身功率有限、无线信道快速变化等特征,当有线网络中的自相似数据流经无线网关转发后,无线网关输入、输出数据流的自相似性变化规律是本文的主要研究内容。为了便于数学分析,本文简化了无线网关模型,它主要完成数据流的缓存、重新封装、转发功能,而且其工作模式也仅仅考虑两种理想情况:“实时转发”与“功率控制”模式。在研究了参考文献的结论的基础上,本文给出了自相似数据流经无线网关转发到无线网络时其自相似性的变化规律的理论分析,进一步的MATLAB软件仿真结果表明:
1.无线网关工作在“功率控制”模式、网关缓冲区与无线信道容量相等时,网关输入、输出为ON/OFF随机过程,输出数据流ON状态持续时间的拖尾系数不变,OFF状态持续时间的拖尾系数是输入数据流两状态持续时间拖尾系数的最小值,网关输入、输出数据流的自相似性程度不变。
2.无线网关工作在“功率控制”模式、网关缓冲区远大于无线信道容量时,网关输出数据流ON状态持续时间的拖尾系数增加1,OFF状态持续时间的拖尾系数不变,数据流的自相似性有不同程度增大。
3.无线网关工作在“实时转发”模式时,无论网关缓冲区与无线信道容量之间的关系如何,其输入、输出数据流的自相似性程度不会发生变化。
本文另一项研究内容是自相似数据流经无线网关转发时,网关缓冲区内数据的分布情况,理论分析及MATLAB软件仿真结果表明:无线网关缓冲内数据服从Pareto分布,而且分布函数的参数满足α=min(α_A,α_1)-1。
Due to the important consequences of traffic self-similarity in network design and network protocol, some studies have assumed that wireless traffic is also self-similar by follow reasons. First of all, it is true that recent advances in wireless networks such as IEEE802.11, Bluetooth, GPRS and WiMAX can enable high-speed communication and that high-speed wireless users tend to have the same bandwidth requirements as wired users when accessing the Internet. Second, one plausible justification of self-similarity in wireless traffic could be TCP effects. The loss rate here is higher than that of cable traffic, thus, TCP could generate self-similarity in the wireless traffic even more so as it does in the cable case. Last, the self-similarity of cable traffic may be propagated to wireless network when cable traffic is fed to the wireless network via a wireless gateway.
However, due to factors such as power limitations and the wireless channel, the change of the self-similarity is the main research in this thesis as cable self-similar traffic is passed to the wireless network through a wireless gateway. In order to facilitate the mathematical analysis, this thesis simplifys the wireless gateway with data cache, re-package and forward, and it operates under "instant transfer" and "power control" mode. On the basis of the reference one, this thesis provides an analytical study of the propagation of traffic characteristics as cable traffic is passed to the wireless network through a gateway. The MATLAB software simulation results show that:
1. When the gateway operates under "power control" mode with its buffer equaled to wireless channel capacity, the incoming traffic and the outgoing traffic of the wireless gateway will be ON/OFF stochastic process, and the tail index of the ON states durations of the outgoing traffic will be the same as in the incoming traffic, while the tail index of the OFF states durations will be the little one of two states durations of the incoming traffic. The self-similarity of outgoing traffic will be the same as incoming traffic.
2. When the gateway operates under "power control" mode with large buffer, the tail index of the ON states durations of the outgoing traffic will increase by one, while the tail index of the OFF states durations will be the same as in the incoming traffic. The self-similarity of the outgoing traffic will increase.
3. When the gateway operates under "instant transfer" mode, the tail index of states duration of outgoing traffic is the same as the incoming traffic, and the self-similarity of outgoing traffic will not change too.
Another study of this thesis is the buffer content distribution of the wireless gateway. Theoretical analysis and MATLAB software simulation results show that: the buffer content of the wireless gateway will be Pareto distribution, and its parameters satisfy: a = min(a_A, a_1)-1.
考虑到无线网络本身功率有限、无线信道快速变化等特征,当有线网络中的自相似数据流经无线网关转发后,无线网关输入、输出数据流的自相似性变化规律是本文的主要研究内容。为了便于数学分析,本文简化了无线网关模型,它主要完成数据流的缓存、重新封装、转发功能,而且其工作模式也仅仅考虑两种理想情况:“实时转发”与“功率控制”模式。在研究了参考文献的结论的基础上,本文给出了自相似数据流经无线网关转发到无线网络时其自相似性的变化规律的理论分析,进一步的MATLAB软件仿真结果表明:
1.无线网关工作在“功率控制”模式、网关缓冲区与无线信道容量相等时,网关输入、输出为ON/OFF随机过程,输出数据流ON状态持续时间的拖尾系数不变,OFF状态持续时间的拖尾系数是输入数据流两状态持续时间拖尾系数的最小值,网关输入、输出数据流的自相似性程度不变。
2.无线网关工作在“功率控制”模式、网关缓冲区远大于无线信道容量时,网关输出数据流ON状态持续时间的拖尾系数增加1,OFF状态持续时间的拖尾系数不变,数据流的自相似性有不同程度增大。
3.无线网关工作在“实时转发”模式时,无论网关缓冲区与无线信道容量之间的关系如何,其输入、输出数据流的自相似性程度不会发生变化。
本文另一项研究内容是自相似数据流经无线网关转发时,网关缓冲区内数据的分布情况,理论分析及MATLAB软件仿真结果表明:无线网关缓冲内数据服从Pareto分布,而且分布函数的参数满足α=min(α_A,α_1)-1。
Due to the important consequences of traffic self-similarity in network design and network protocol, some studies have assumed that wireless traffic is also self-similar by follow reasons. First of all, it is true that recent advances in wireless networks such as IEEE802.11, Bluetooth, GPRS and WiMAX can enable high-speed communication and that high-speed wireless users tend to have the same bandwidth requirements as wired users when accessing the Internet. Second, one plausible justification of self-similarity in wireless traffic could be TCP effects. The loss rate here is higher than that of cable traffic, thus, TCP could generate self-similarity in the wireless traffic even more so as it does in the cable case. Last, the self-similarity of cable traffic may be propagated to wireless network when cable traffic is fed to the wireless network via a wireless gateway.
However, due to factors such as power limitations and the wireless channel, the change of the self-similarity is the main research in this thesis as cable self-similar traffic is passed to the wireless network through a wireless gateway. In order to facilitate the mathematical analysis, this thesis simplifys the wireless gateway with data cache, re-package and forward, and it operates under "instant transfer" and "power control" mode. On the basis of the reference one, this thesis provides an analytical study of the propagation of traffic characteristics as cable traffic is passed to the wireless network through a gateway. The MATLAB software simulation results show that:
1. When the gateway operates under "power control" mode with its buffer equaled to wireless channel capacity, the incoming traffic and the outgoing traffic of the wireless gateway will be ON/OFF stochastic process, and the tail index of the ON states durations of the outgoing traffic will be the same as in the incoming traffic, while the tail index of the OFF states durations will be the little one of two states durations of the incoming traffic. The self-similarity of outgoing traffic will be the same as incoming traffic.
2. When the gateway operates under "power control" mode with large buffer, the tail index of the ON states durations of the outgoing traffic will increase by one, while the tail index of the OFF states durations will be the same as in the incoming traffic. The self-similarity of the outgoing traffic will increase.
3. When the gateway operates under "instant transfer" mode, the tail index of states duration of outgoing traffic is the same as the incoming traffic, and the self-similarity of outgoing traffic will not change too.
Another study of this thesis is the buffer content distribution of the wireless gateway. Theoretical analysis and MATLAB software simulation results show that: the buffer content of the wireless gateway will be Pareto distribution, and its parameters satisfy: a = min(a_A, a_1)-1.
引文
[1]Yu J,PETROPULU P.Study of the Effect of the Wireless Gateway on Incoming Self-Similar Traffic.IEEE TRANS.ON SIGNAL PROCESSING,2006,.54(10):3741-3758.
[2]HARPANTIDOU Z,PATERAKIS M.Random multiple access of broadcast channels with Pareto distributed packet inter-arrival times.1EEE wireless Communications,1998,5(2):48-55.
[3]SOWDEN B,SOWERBY K.The impact of long-range dependent traffic in a CDMA system supporting real-time services.IEEE Global Telecommunications Conf.(IEEE GLOBECOM),2001,6,:3509-3513.
[4]Stanford H.Rowe,Marsha L.Schuh.Computer Networking.PEASON Prentice Hall.
[5]YANG X,PETROPULU P,the Extended Alternating Fractal Renewal Process for Modeling Traffic in High-Speed Communication Networks.IEEE TRANSACTIONS ON SIGNAL PROCESSING,2001,49(7):1349-1363.
[6]J.G.Kim,M.M.Krunz.Bandwidth alloeation in wireless networks with guaranteed packet-loss performance.IEEE/ACM Trans.Netw.2000,8(3):337-349.
[7]Allen B.Downey.The Structural cause of file size distributions.
[8]ARMOLD B,Pareto Distributions.Baltimore,MD:International,1983.
[9]李海芬.P areto分布的统计分析.[硕士学位论文],华东师范大学,2004.
[10]南新艳.广义Pareto分布.[硕士学位论文],华东师范大学,2005.
[11]李海芬,茆诗松.Pareto分布的校验.徐州师范大学学报,2004.
[12]WILL E,MURAD S.On the self-similar nature of ethernet traffic(extended version).IEEE/ACM Transactions on Networking,1994,2(2):1-15.
[13]PAXSON V,FLOYD S.Wide area traffic:the failure of possion modeling.IEEE/ACM Transactions on Networking,1995,3(3):226-244.
[14]LIKHANOV N,TSYBAKOV B,GEORGANAS N.Analysis of an ATM buffer with self-similar("fractal") input traffic.INFOCOM'95.Boston,MA,USA,1995:985-992.
[15]TSYBOKO B,GEORGANAS N.On self-similar traffic in ATM queues:definitions,overflow probability bound,and cell delay distribution.IEEE/ACM Transactions on Networking,1997,5(3):397-409.
[16]COX D.Long-Range Dependence:A Review.IA:Iowa State Univ Press,1984:55-74.
[17]吴援明,宁正容,梁恩志.网络自相似业务模型发展通信学报2004,25(3):97-104.
[18]Junshan Zhang,Ming Hu,Ness B.Shroff.Bursty Data Over CDMA:MAI Self Similarity.Rate Control and Admission Control,2002.
[19]P.Abry,P.Flandrin,M.S.Taqqe and D.Veitch:Wavelets for the analysis,estimation and synthesis of scaling data.
[20]YU J,PETROPULU P,SETHU H.Rate-Limited EAFRP—A New Improved Model for High-Speed Network Traffic.IEEE TRANSACTIONS ON SIGNAL PROCESSING,2005,53(2):505-522.
[21]W.Willinger,M.S.Taqqu,R.Sherman,and D.V.Wilson,Self-similarity through high-variability:statistical analysis of Ethernet LAN traffic at the source level,IEEE/ACM Trans.Netw.,1997,5(1):71-86.
[22]W.Leland,M.Taqqu,W.Willinger,and D.Wilson,On the self-similar nature of Ethernet traffic (extended version),IEEE/ACM Trans.Netw.,1994,2(1):1-15.
[23]秦元勋等.计算物理学.成都:四川科学技术出版社,1984.
[24]孙亮,高云峰,张桂芝任意分布随机数发生器的一种构造方法,聊城师院学报(自然科学版),2000,13(1):43-45.
[25]J.G.Kim and M.M.Krunz,Bandwidth allocation in wireless networks with guaranteed packet-loss performance,IEEE/ACM Trans.Netw.,2000,8(3):337-349.
[26]J.G.Proakis,Digital Communications,4th ed.New York:McGraw-Hill,2000.
[27]N.H.Bingham,C.M.Goldie,and J.L.Teugels,Regular Variabtion.Cambridge,U.K.:Cambridge Univ.Press,1987.
[28]P.Embrechts,C.M.Goldie,and N.Veraverbeke,Subexponentiality and infinite divisibility,Z.Wahr.verw.Gebiete.,1979,49:335-347.
[29]J.W.Cohen,Some results on regular variation for distributions in queueing and fluctuation theory,J.Appl.Probab.,1973,10:343-353.
[30]O.Kella and W.Whitt,A storage model with a two-state random environment,Oper.Res.,1992,40(2):257-262.
[2]HARPANTIDOU Z,PATERAKIS M.Random multiple access of broadcast channels with Pareto distributed packet inter-arrival times.1EEE wireless Communications,1998,5(2):48-55.
[3]SOWDEN B,SOWERBY K.The impact of long-range dependent traffic in a CDMA system supporting real-time services.IEEE Global Telecommunications Conf.(IEEE GLOBECOM),2001,6,:3509-3513.
[4]Stanford H.Rowe,Marsha L.Schuh.Computer Networking.PEASON Prentice Hall.
[5]YANG X,PETROPULU P,the Extended Alternating Fractal Renewal Process for Modeling Traffic in High-Speed Communication Networks.IEEE TRANSACTIONS ON SIGNAL PROCESSING,2001,49(7):1349-1363.
[6]J.G.Kim,M.M.Krunz.Bandwidth alloeation in wireless networks with guaranteed packet-loss performance.IEEE/ACM Trans.Netw.2000,8(3):337-349.
[7]Allen B.Downey.The Structural cause of file size distributions.
[8]ARMOLD B,Pareto Distributions.Baltimore,MD:International,1983.
[9]李海芬.P areto分布的统计分析.[硕士学位论文],华东师范大学,2004.
[10]南新艳.广义Pareto分布.[硕士学位论文],华东师范大学,2005.
[11]李海芬,茆诗松.Pareto分布的校验.徐州师范大学学报,2004.
[12]WILL E,MURAD S.On the self-similar nature of ethernet traffic(extended version).IEEE/ACM Transactions on Networking,1994,2(2):1-15.
[13]PAXSON V,FLOYD S.Wide area traffic:the failure of possion modeling.IEEE/ACM Transactions on Networking,1995,3(3):226-244.
[14]LIKHANOV N,TSYBAKOV B,GEORGANAS N.Analysis of an ATM buffer with self-similar("fractal") input traffic.INFOCOM'95.Boston,MA,USA,1995:985-992.
[15]TSYBOKO B,GEORGANAS N.On self-similar traffic in ATM queues:definitions,overflow probability bound,and cell delay distribution.IEEE/ACM Transactions on Networking,1997,5(3):397-409.
[16]COX D.Long-Range Dependence:A Review.IA:Iowa State Univ Press,1984:55-74.
[17]吴援明,宁正容,梁恩志.网络自相似业务模型发展通信学报2004,25(3):97-104.
[18]Junshan Zhang,Ming Hu,Ness B.Shroff.Bursty Data Over CDMA:MAI Self Similarity.Rate Control and Admission Control,2002.
[19]P.Abry,P.Flandrin,M.S.Taqqe and D.Veitch:Wavelets for the analysis,estimation and synthesis of scaling data.
[20]YU J,PETROPULU P,SETHU H.Rate-Limited EAFRP—A New Improved Model for High-Speed Network Traffic.IEEE TRANSACTIONS ON SIGNAL PROCESSING,2005,53(2):505-522.
[21]W.Willinger,M.S.Taqqu,R.Sherman,and D.V.Wilson,Self-similarity through high-variability:statistical analysis of Ethernet LAN traffic at the source level,IEEE/ACM Trans.Netw.,1997,5(1):71-86.
[22]W.Leland,M.Taqqu,W.Willinger,and D.Wilson,On the self-similar nature of Ethernet traffic (extended version),IEEE/ACM Trans.Netw.,1994,2(1):1-15.
[23]秦元勋等.计算物理学.成都:四川科学技术出版社,1984.
[24]孙亮,高云峰,张桂芝任意分布随机数发生器的一种构造方法,聊城师院学报(自然科学版),2000,13(1):43-45.
[25]J.G.Kim and M.M.Krunz,Bandwidth allocation in wireless networks with guaranteed packet-loss performance,IEEE/ACM Trans.Netw.,2000,8(3):337-349.
[26]J.G.Proakis,Digital Communications,4th ed.New York:McGraw-Hill,2000.
[27]N.H.Bingham,C.M.Goldie,and J.L.Teugels,Regular Variabtion.Cambridge,U.K.:Cambridge Univ.Press,1987.
[28]P.Embrechts,C.M.Goldie,and N.Veraverbeke,Subexponentiality and infinite divisibility,Z.Wahr.verw.Gebiete.,1979,49:335-347.
[29]J.W.Cohen,Some results on regular variation for distributions in queueing and fluctuation theory,J.Appl.Probab.,1973,10:343-353.
[30]O.Kella and W.Whitt,A storage model with a two-state random environment,Oper.Res.,1992,40(2):257-262.