多速率可变比特率业务背景下数据业务的服务质量研究
|
摘要
当今社会发展所催生的新业务使得通信网络的通信信息量飞速增加。由于通信量和新业务的增长速度太快,网络性能方面的研究跟不上网络业务的发展,导致网络优化工作的艰难及规划的不合理。因此,加强宽带综合业务网络的性能研究,有效利用既定的网络条件为各种业务服务至关重要。
随着现代通信网络的发展,宽带网络承载的业务不断丰富,除了尽力而为数据业务之外,还包括各种实时业务。多速率实时业务的丢包率和尽力而为业务的平均延时是体现宽带综合业务网络性能的重要参数,是决定用户服务质量的重要环节,对其进行研究具有重要意义。
长期以来研究实时业务采用恒定比特率(CBR,constant bit rate)业务模型。而实践证明,诸如话音、视频等实时业务传输过程中的速率是可变的,传统CBR业务模型不足以精确地表示速率可变的实时业务,不能有效地利用网络有限的带宽资源。因此,速率可变的实时业务应采用可变比特率(VBR,variable bit rate)业务模型。本文采用了流行的ON-OFF模型简单有效地描述实时VBR业务的统计特性,对多速率实时VBR业务与尽力而为业务复用系统的性能进行了研究,在优先处理实时VBR业务分组的基础上,利用系统瞬时剩余容量处理尽力而为业务。通过对该综合业务排队系统的分析,推导出系统平均剩余容量、实时VBR业务丢包率及尽力而为业务平均延时的定量解析式,并利用离散事件的时间步长仿真法进行系统仿真,验证了理论公式的正确性。通过对仿真结果的观察进一步分析了系统负荷的变化对丢包率的影响,得出了丢包率并非随负荷增加而单调增加的新结论。在研究宽带综合业务系统性能上迈出了新的一步。
短消息业务作为典型的尽力而为业务之一,其应用非常广泛。而现有的GSM网络不能很好解决其延时问题。本文探讨了短消息的传输机制,分析其延时原因,结合GPRS网络提出短消息传输流程的改善方案。
Today, new services like data and video spurred by social development have been making the rapid increase of the traffic in the communication network. Because of the traffic and new service growing too fast, the study on performance of the broadband network can not follow the development of the network service, it is hard to optimize the broadband network and find a reasonable programming project. So it is quite important to strengthen the performance research and effectively utilize the existing network condition to support integrated services.
The modern communication network can bear various services including best effort services and real time services. The cell loss probability of the multi-rate real time service and the average delay of the best effort service are the most important performance parameters and they can determine the quality of service in broadband integrated networks. So it is significant to study these parameters.
Generally, the CBR(Constant Bit Rate) service model has been used to study real time services. However, it is proved that the transmission rate of many real time services like voice and video is variable; the CBR model can not describe them accurately and can not utilize the limited network bandwidth effectively. So the real time service with variable rate should be described as the VBR(Variable Bit Rate) service model. The paper has chosen the typical ON-OFF model to describe the statistical characteristics of real time VBR services, studied the performance on the multiplex system of multi-rate real time VBR services and best effort service. At any moment, real time cells have the advantage over best effort data packets, and these data packets can be buffered and transmitted by utilizing the moment residual capacity. Through comprehensive analysis of the integrated service queuing, this paper has educed computation formulas of the average residual capacity, cell loss probability and average packet delay. By discrete interval simulation, it is proved that the formulas are correct. And through the analysis on the relation between the cell loss probability and the system load, a new conclusion that the cell loss probability is not a monotonic function of the call level load is obtained. These researches have made a new progress in the performance study of broadband integrated service system.
As one of typical best effort services, the application of short message service is very extensive. However, the delay problem can not be well solved in GSM. This paper has discussed the transmission mechanism of short message service, analyzed the delay reasons and suggested an improved transmission strategy utilizing GPRS.
随着现代通信网络的发展,宽带网络承载的业务不断丰富,除了尽力而为数据业务之外,还包括各种实时业务。多速率实时业务的丢包率和尽力而为业务的平均延时是体现宽带综合业务网络性能的重要参数,是决定用户服务质量的重要环节,对其进行研究具有重要意义。
长期以来研究实时业务采用恒定比特率(CBR,constant bit rate)业务模型。而实践证明,诸如话音、视频等实时业务传输过程中的速率是可变的,传统CBR业务模型不足以精确地表示速率可变的实时业务,不能有效地利用网络有限的带宽资源。因此,速率可变的实时业务应采用可变比特率(VBR,variable bit rate)业务模型。本文采用了流行的ON-OFF模型简单有效地描述实时VBR业务的统计特性,对多速率实时VBR业务与尽力而为业务复用系统的性能进行了研究,在优先处理实时VBR业务分组的基础上,利用系统瞬时剩余容量处理尽力而为业务。通过对该综合业务排队系统的分析,推导出系统平均剩余容量、实时VBR业务丢包率及尽力而为业务平均延时的定量解析式,并利用离散事件的时间步长仿真法进行系统仿真,验证了理论公式的正确性。通过对仿真结果的观察进一步分析了系统负荷的变化对丢包率的影响,得出了丢包率并非随负荷增加而单调增加的新结论。在研究宽带综合业务系统性能上迈出了新的一步。
短消息业务作为典型的尽力而为业务之一,其应用非常广泛。而现有的GSM网络不能很好解决其延时问题。本文探讨了短消息的传输机制,分析其延时原因,结合GPRS网络提出短消息传输流程的改善方案。
Today, new services like data and video spurred by social development have been making the rapid increase of the traffic in the communication network. Because of the traffic and new service growing too fast, the study on performance of the broadband network can not follow the development of the network service, it is hard to optimize the broadband network and find a reasonable programming project. So it is quite important to strengthen the performance research and effectively utilize the existing network condition to support integrated services.
The modern communication network can bear various services including best effort services and real time services. The cell loss probability of the multi-rate real time service and the average delay of the best effort service are the most important performance parameters and they can determine the quality of service in broadband integrated networks. So it is significant to study these parameters.
Generally, the CBR(Constant Bit Rate) service model has been used to study real time services. However, it is proved that the transmission rate of many real time services like voice and video is variable; the CBR model can not describe them accurately and can not utilize the limited network bandwidth effectively. So the real time service with variable rate should be described as the VBR(Variable Bit Rate) service model. The paper has chosen the typical ON-OFF model to describe the statistical characteristics of real time VBR services, studied the performance on the multiplex system of multi-rate real time VBR services and best effort service. At any moment, real time cells have the advantage over best effort data packets, and these data packets can be buffered and transmitted by utilizing the moment residual capacity. Through comprehensive analysis of the integrated service queuing, this paper has educed computation formulas of the average residual capacity, cell loss probability and average packet delay. By discrete interval simulation, it is proved that the formulas are correct. And through the analysis on the relation between the cell loss probability and the system load, a new conclusion that the cell loss probability is not a monotonic function of the call level load is obtained. These researches have made a new progress in the performance study of broadband integrated service system.
As one of typical best effort services, the application of short message service is very extensive. However, the delay problem can not be well solved in GSM. This paper has discussed the transmission mechanism of short message service, analyzed the delay reasons and suggested an improved transmission strategy utilizing GPRS.
引文
[1]Paxson V,Mahdavi G J,Mathis M.Frame work for IP Performance Metrics.RFC2330,May 1998.
[2]杨雅辉,李小东.IP网络性能指标体系的研究.通信学报,2002,23(11):1-7.
[3]Mathis M,Allman M.A Framework for Defining Empirical Bulk Transfer Capacity Metrics.RFC3148,July 2001.
[4]Almes G,Kalidindi S,Zekauskas M.A One-way Packet Loss Metric for IP PM.RFC 2680,September 1999.
[5]Mahdavi J,Paxson V.IP PM Metrics for Measuring Connectivity.RFC 2678,September 1999.
[6]Jain R,Kalyanaraman S,Fahmy S,et al.Out-of-Rate RM Cell Issues and Inconsistencies in the End System Behavior and Pseudocode.ATM Forum/95-0973,August 1995.
[7]Jain R,Fahmy S,Kalyanaraman S,et al.More Strawvote Comments:TBE vs Queue Sizes.ATM Forum/95-1661,December 1995.
[8]Kalyanaraman S,Jain R,Fahmy S,et al.Performance of TCP/IP over ABR Service on ATM Networks.In:Proceedings of GLOBECOM'96[C].London,UK:IEEE,1996,1:468-475.
[9]Paxson V,Floyd S.Wide Area Traffic:The Failure of Poisson Modeling[J].IEEE/ACM Transactions on Networking,1995,3(3):226-244.
[10]孙海荣,李乐民.ATM网络中的ABR业务在不同ON-OFF业务背景下的性能研究.电子学报,1999,27(1):49-53.
[11]冷晓冰,付立政,王中.自相似VBR业务环境下ABR流量控制算法的性能分析.通信学报,2000,21(7):87-92.
[12]Jelenkovic R R,Melamed B.Automated TES modeling of compressed video.In:Proceedings of INFOCOM'95[C].Boston,MA,USA:IEEE,1995,2:746-752.
[13]李生红,刘泽民.MPEG标准VBR视频业务新模型及其性能研究.电子学报,2000,28(1):42-44.
[14]王中,冷晓冰,付立政.VBR MPEG-2业务统计复用特性的研究.通信学报,2002,23(7):61-69.
[15]Gao J,Rubin I.Multifractal analysis and modeling of VBR video traffic.Electronics Letters,2000,36(3):278-279.
[16]Hong F,Wu Z.Multifractal analysis and model of the MPEG-4 video traffic.In:Proceedings of IEEE 2003 International Performance Computing and Communications Conference.Phoenix,Arizona,USA:IEEE,2003,463-467.
[17]王升辉,裘正定.VBR视频流多重分形建模.电子与信息学报,2006,28(6):1120-1123.
[18]李生红,刘泽民.一种基于扩展自相似过程的VBR视频业务新模型.通信学报,2000,21(4):53-57.
[19]田宁红,周敏,龙昭华.一种改进的无线局域网对尽力而为服务的应用.计算机工程与应用,2006,42(31):120-122.
[20]张鹏飞,黄生叶,赵海琳.宽带综合业务网络中尽力而为业务性能研究.计算机工程,2007,33(9):126-127.
[21]El-Hadidi M T,Elsayed K M,Abdallah M M.Performance analysis and estimation of call admission control parameters in wireless integrated voice and data networks[J].Wireless Networks,2002,11(4):327-343.
[22]Kim J Y,Stuber G L.Performance Analysis of Macrodiversity Voice/Data CDMA Systems[J].IEEE Transactions on Wireless Communications,2006,5(8):2111-2118.
[23]Lei Huang,C.-C.Jay Kuo.Joint Connection-Level and Packet-Level Quality-of-Service Support for VBR Traffic in Wireless Multimedia Networks[J].IEEE Journal on Selected Areas in Communications,2005,23(6):1167-1177.
[24]Bianchi G.Performance analysis of the IEEE 802.11 distributed coordination function[J].IEEE Journal on Selected Areas in Communications,2000,18(3):535-547.
[25]Khurana S,Kahol A,Gupta S K S,et al.Performance evaluation of distributed co-ordination function for IEEE 802.11 wireless LAN protocol in presence of mobile and hidden terminals[A].In:Proceedings of MASCOT'99[C].College Park,MD,USA:IEEE,1999,40-47.
[26]Ho T S,Chen K C.Performance analysis of IEEE 802.11 CSMA/CA medium access control protocol[A].In:Proceedings of PIMRC'96[C].Taipei,Taiwan:IEEE,1996,407-411.
[27]Chuan H F,Zukerman M.Performance evaluation of IEEE 802.11[A].In:Proceedings of Vehicular Technology Conference,2001[C].Rhodes,Greece:IEEE,2001,2:841-845.
[28]Bruno R,Conti M,Gregori E.IEEE 802.11 optimal performances:RTS/CTS mechanism vs.basic access[A].In:Proceedings of Personal,Indoor and Mobile Radio Communications,2002[C].Lisbon,Portugal:IEEE,2002,4:1747-1751.
[29]Veeraraghavan M,Cocker N,Moors T.Support of voice services in IEEE 802.11wireless LANs[A].In:Proceedings of INFOCOM 2001[C].Anchorage,USA:IEEE,2001,1:488-497.
[30]Zahedi A,Pahlavan K.Capacity of a wireless LAN with voice and data services[J].IEEE Transactions on Communications,2000,48(7):1160-1170.
[31]Zahedi A,Pahlavan K.Voice and data integration on TCP/IP wireless networks[A].In:Proceedings of PIMRC'97[C].Helsinki,Finland:IEEE,1997,2:678-682.
[32]Crow B P,Widjaja I,Kim J G,et al.IEEE 802.11 wireless local area networks[J].IEEE Communications Magazine,1997,35(9):116-126.
[33]Liu H H,Wu J L C.Packet telephony support for the IEEE 802.11 wireless LAN[J].IEEE Communications Letters,2000,4(9):286-288.
[34]Suzuki T,Tasaka S.Performance evaluation of integrated video and data transmission with the IEEE 802.11 standard MAC protocol[A].In:Proceedings of GLOBECOM'99[C].Rio de Janeireo,Brazil:IEEE,1999,1b:580-586.
[35]Visser M A,Zarki M E.Voice and data transmission over an 802.11 wireless network[A].In:Proceedings of PIMRC'95[C].Toronto,Canada:IEEE,1995,2:648-652.
[36]Naor Z.An efficient short messages transmission in cellular networks.In:Proceedings of INFOCOM 2004[C].Hong Kong:IEEE,2004,1:641-649.
[37]Jiang H.Reliability,Costs and Delay Performance of Sending Short Message Service in Wireless Systems.In:Proceedings of IEEE 1998 International Conference on Universal Personal Communications.Florence,Italy:IEEE,1998,2:1073-1077.
[38]张大方,李珩,吕耀兴等.一种基于负载的短信中心性能优化策略.湖南大学学报(自然科学版),2004,31(3):76-80.
[39]Dodd A Z.通信技术导论(第4版).晓波.北京:清华大学出版社,2006,15-196.
[40]McDysan D.IP与ATM网络中的QoS和业务量管理.黄锡伟,黄建伟.北京:清华大学出版社,2004,14-170.
[41]周学泳,石丹.短信息(SMS)与WAP的开发及应用.北京:电子工业出版社,2002-2-66.
[42]Kaufman J S.Blocking in a shared resource environment.IEEE Transactions on Communications,1981,29(10):1474-1481.
[43]李建东.信息网络理论与基础.西安:西安电子科技大学出版社,2001,54-90.
[44]Roberts J W,Virtamo J T.The Superposition of Periodic Cell Arrival Streams in an ATM Multiplexer[J].IEEE Transactions on Communications,1991,39(2):298-303.
[45]刘晏兵,孙世新,唐红.基于IP突发信源模型数据包的定量计算研究.电子学报,2003,31(12A):2187-2189.
[46]Guerin R,Ahmadi H,Naghshineh M.Equivalent Capacity and Its Application to Bandwidth Allocation in High-Speed Networks.IEEE Journal of Selected Areas in Communications,1991,9(7):968-981.
[47]Schwartz M.Broadband Integrated Networks.北京:清华大学出版社,1998,32-130.
[48]Elwalid A,Mitra D,Wentworth H.A New Approach for Allocating Buffers and Bandwidth to Heterogeneous,Regulated Traffic in an ATM Node.IEEE Journal of Selected Areas in Communications,1995,13(6):1115-1127.
[49]Tseng Y H,Wu E H,Chen G H.Scene-change aware dynamic bandwidth allocation for real-time VBR video transmission over IEEE 802.15.3 wireless home networks.IEEE Transactions on Multimedia,2007,9(3):642-654.
[50]黄生叶,叶梧,冯穗力.基于准独立近似的巨型资源共享系统呼叫阻塞概率的快速算法.通信学报,2002,23(11):122-128.
[51]吴新瞻,吴新垣.随机模型与计算机模拟.北京:电子工业出版社,1990,351-360.
[52]钟章队,蒋文怡,李红君.GPRS通用分组无线业务.北京:人民邮电出版社,2001-65-117.
[53]ETSI.Digital Cellular Telecommunications System(Phase 2+).ETSI EN 301 344V7.3.0,February 2000.
[54]杨筱凡,曹鹏,蔡斌等.GPRS骨干网内移动终端间路由的优化方案.通信学报,2003,24(5):72-78.
[2]杨雅辉,李小东.IP网络性能指标体系的研究.通信学报,2002,23(11):1-7.
[3]Mathis M,Allman M.A Framework for Defining Empirical Bulk Transfer Capacity Metrics.RFC3148,July 2001.
[4]Almes G,Kalidindi S,Zekauskas M.A One-way Packet Loss Metric for IP PM.RFC 2680,September 1999.
[5]Mahdavi J,Paxson V.IP PM Metrics for Measuring Connectivity.RFC 2678,September 1999.
[6]Jain R,Kalyanaraman S,Fahmy S,et al.Out-of-Rate RM Cell Issues and Inconsistencies in the End System Behavior and Pseudocode.ATM Forum/95-0973,August 1995.
[7]Jain R,Fahmy S,Kalyanaraman S,et al.More Strawvote Comments:TBE vs Queue Sizes.ATM Forum/95-1661,December 1995.
[8]Kalyanaraman S,Jain R,Fahmy S,et al.Performance of TCP/IP over ABR Service on ATM Networks.In:Proceedings of GLOBECOM'96[C].London,UK:IEEE,1996,1:468-475.
[9]Paxson V,Floyd S.Wide Area Traffic:The Failure of Poisson Modeling[J].IEEE/ACM Transactions on Networking,1995,3(3):226-244.
[10]孙海荣,李乐民.ATM网络中的ABR业务在不同ON-OFF业务背景下的性能研究.电子学报,1999,27(1):49-53.
[11]冷晓冰,付立政,王中.自相似VBR业务环境下ABR流量控制算法的性能分析.通信学报,2000,21(7):87-92.
[12]Jelenkovic R R,Melamed B.Automated TES modeling of compressed video.In:Proceedings of INFOCOM'95[C].Boston,MA,USA:IEEE,1995,2:746-752.
[13]李生红,刘泽民.MPEG标准VBR视频业务新模型及其性能研究.电子学报,2000,28(1):42-44.
[14]王中,冷晓冰,付立政.VBR MPEG-2业务统计复用特性的研究.通信学报,2002,23(7):61-69.
[15]Gao J,Rubin I.Multifractal analysis and modeling of VBR video traffic.Electronics Letters,2000,36(3):278-279.
[16]Hong F,Wu Z.Multifractal analysis and model of the MPEG-4 video traffic.In:Proceedings of IEEE 2003 International Performance Computing and Communications Conference.Phoenix,Arizona,USA:IEEE,2003,463-467.
[17]王升辉,裘正定.VBR视频流多重分形建模.电子与信息学报,2006,28(6):1120-1123.
[18]李生红,刘泽民.一种基于扩展自相似过程的VBR视频业务新模型.通信学报,2000,21(4):53-57.
[19]田宁红,周敏,龙昭华.一种改进的无线局域网对尽力而为服务的应用.计算机工程与应用,2006,42(31):120-122.
[20]张鹏飞,黄生叶,赵海琳.宽带综合业务网络中尽力而为业务性能研究.计算机工程,2007,33(9):126-127.
[21]El-Hadidi M T,Elsayed K M,Abdallah M M.Performance analysis and estimation of call admission control parameters in wireless integrated voice and data networks[J].Wireless Networks,2002,11(4):327-343.
[22]Kim J Y,Stuber G L.Performance Analysis of Macrodiversity Voice/Data CDMA Systems[J].IEEE Transactions on Wireless Communications,2006,5(8):2111-2118.
[23]Lei Huang,C.-C.Jay Kuo.Joint Connection-Level and Packet-Level Quality-of-Service Support for VBR Traffic in Wireless Multimedia Networks[J].IEEE Journal on Selected Areas in Communications,2005,23(6):1167-1177.
[24]Bianchi G.Performance analysis of the IEEE 802.11 distributed coordination function[J].IEEE Journal on Selected Areas in Communications,2000,18(3):535-547.
[25]Khurana S,Kahol A,Gupta S K S,et al.Performance evaluation of distributed co-ordination function for IEEE 802.11 wireless LAN protocol in presence of mobile and hidden terminals[A].In:Proceedings of MASCOT'99[C].College Park,MD,USA:IEEE,1999,40-47.
[26]Ho T S,Chen K C.Performance analysis of IEEE 802.11 CSMA/CA medium access control protocol[A].In:Proceedings of PIMRC'96[C].Taipei,Taiwan:IEEE,1996,407-411.
[27]Chuan H F,Zukerman M.Performance evaluation of IEEE 802.11[A].In:Proceedings of Vehicular Technology Conference,2001[C].Rhodes,Greece:IEEE,2001,2:841-845.
[28]Bruno R,Conti M,Gregori E.IEEE 802.11 optimal performances:RTS/CTS mechanism vs.basic access[A].In:Proceedings of Personal,Indoor and Mobile Radio Communications,2002[C].Lisbon,Portugal:IEEE,2002,4:1747-1751.
[29]Veeraraghavan M,Cocker N,Moors T.Support of voice services in IEEE 802.11wireless LANs[A].In:Proceedings of INFOCOM 2001[C].Anchorage,USA:IEEE,2001,1:488-497.
[30]Zahedi A,Pahlavan K.Capacity of a wireless LAN with voice and data services[J].IEEE Transactions on Communications,2000,48(7):1160-1170.
[31]Zahedi A,Pahlavan K.Voice and data integration on TCP/IP wireless networks[A].In:Proceedings of PIMRC'97[C].Helsinki,Finland:IEEE,1997,2:678-682.
[32]Crow B P,Widjaja I,Kim J G,et al.IEEE 802.11 wireless local area networks[J].IEEE Communications Magazine,1997,35(9):116-126.
[33]Liu H H,Wu J L C.Packet telephony support for the IEEE 802.11 wireless LAN[J].IEEE Communications Letters,2000,4(9):286-288.
[34]Suzuki T,Tasaka S.Performance evaluation of integrated video and data transmission with the IEEE 802.11 standard MAC protocol[A].In:Proceedings of GLOBECOM'99[C].Rio de Janeireo,Brazil:IEEE,1999,1b:580-586.
[35]Visser M A,Zarki M E.Voice and data transmission over an 802.11 wireless network[A].In:Proceedings of PIMRC'95[C].Toronto,Canada:IEEE,1995,2:648-652.
[36]Naor Z.An efficient short messages transmission in cellular networks.In:Proceedings of INFOCOM 2004[C].Hong Kong:IEEE,2004,1:641-649.
[37]Jiang H.Reliability,Costs and Delay Performance of Sending Short Message Service in Wireless Systems.In:Proceedings of IEEE 1998 International Conference on Universal Personal Communications.Florence,Italy:IEEE,1998,2:1073-1077.
[38]张大方,李珩,吕耀兴等.一种基于负载的短信中心性能优化策略.湖南大学学报(自然科学版),2004,31(3):76-80.
[39]Dodd A Z.通信技术导论(第4版).晓波.北京:清华大学出版社,2006,15-196.
[40]McDysan D.IP与ATM网络中的QoS和业务量管理.黄锡伟,黄建伟.北京:清华大学出版社,2004,14-170.
[41]周学泳,石丹.短信息(SMS)与WAP的开发及应用.北京:电子工业出版社,2002-2-66.
[42]Kaufman J S.Blocking in a shared resource environment.IEEE Transactions on Communications,1981,29(10):1474-1481.
[43]李建东.信息网络理论与基础.西安:西安电子科技大学出版社,2001,54-90.
[44]Roberts J W,Virtamo J T.The Superposition of Periodic Cell Arrival Streams in an ATM Multiplexer[J].IEEE Transactions on Communications,1991,39(2):298-303.
[45]刘晏兵,孙世新,唐红.基于IP突发信源模型数据包的定量计算研究.电子学报,2003,31(12A):2187-2189.
[46]Guerin R,Ahmadi H,Naghshineh M.Equivalent Capacity and Its Application to Bandwidth Allocation in High-Speed Networks.IEEE Journal of Selected Areas in Communications,1991,9(7):968-981.
[47]Schwartz M.Broadband Integrated Networks.北京:清华大学出版社,1998,32-130.
[48]Elwalid A,Mitra D,Wentworth H.A New Approach for Allocating Buffers and Bandwidth to Heterogeneous,Regulated Traffic in an ATM Node.IEEE Journal of Selected Areas in Communications,1995,13(6):1115-1127.
[49]Tseng Y H,Wu E H,Chen G H.Scene-change aware dynamic bandwidth allocation for real-time VBR video transmission over IEEE 802.15.3 wireless home networks.IEEE Transactions on Multimedia,2007,9(3):642-654.
[50]黄生叶,叶梧,冯穗力.基于准独立近似的巨型资源共享系统呼叫阻塞概率的快速算法.通信学报,2002,23(11):122-128.
[51]吴新瞻,吴新垣.随机模型与计算机模拟.北京:电子工业出版社,1990,351-360.
[52]钟章队,蒋文怡,李红君.GPRS通用分组无线业务.北京:人民邮电出版社,2001-65-117.
[53]ETSI.Digital Cellular Telecommunications System(Phase 2+).ETSI EN 301 344V7.3.0,February 2000.
[54]杨筱凡,曹鹏,蔡斌等.GPRS骨干网内移动终端间路由的优化方案.通信学报,2003,24(5):72-78.