机器类通信的队列模型与过载控制研究
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摘要
机器类通信（MTC, Machine Type Communications）①定义为通过蜂窝网络进行数据传输的机器与机器（M2M, Machine-to-Machine）通信；与人与人（H2H,Human to Human）通信相比，具有应用类型繁多、业务模式多样、终端数量巨大、小数据通信、上行占优、定时通信、较低移动性等典型特征。MTC通信的大量引入与快速推广将给参照H2H通信业务特性设计的蜂窝网络带来巨大挑战。
当海量MTC终端同步入网时，其瞬时突发性将造成承载网络严重的流量过载或网络拥塞。为评估海量MTC终端的入网性能并提出相应的过载控制机制，有必要建立MTC通信专属的流量模型，即建立能表征海量MTC终端瞬时突发性的统计模型，以期为蜂窝网络的优化设计提供解决思路。为话音通信和分组交换网建立的经典Markov队列模型，因其独立增量特性和无后效性，被长期用于随机流量建模；但由于它们均蕴含到达过程服从泊松过程的假设，将不再适用于MTC通信的流量估计与建模。引入具有非泊松或非Markov特性的统计模型成为必然。3GPP（the3rdGeneration Partnership Project）建议采用Beta分布模拟海量MTC终端短时间内同步入网的瞬时突发特性。Beta分布是具有有限支撑区间的双参数概率密度函数，可等效为有限区间内随机抽取的n个点的第r小点的概率密度函数，将其作为MTC通信到达时间间隔的概率密度函数，比以负指数分布作为到达时间间隔的泊松过程更能刻画MTC通信的瞬时突发特性。基于该提案与MTC通信的典型应用特征，本文为MTC通信建立了四类小区流量预测模型和两类基于Beta分布的队列模型，并提出了四类MTC通信专属的过载控制机制，含工程可实现的MTC通信专属的退避机制。相关工作可为海量终端入网性能分析和过载控制提供参考。
论文的主要研究内容和成果包括：
①为满足基于MTC基本特征与特定网络模型的性能评价需要，本文以小区为单位，为MTC通信的不同应用场景建立了四类总流量预测模型，分别是静止模型、扩展静止模型、随机游走模型和移动模型，从宏观上给出了本地小区突发数据及信令开销的计算办法。分析表明：海量MTC终端接入时将使本地小区出现严重的流量和信令过载，预成簇或布置网关节点可以通过“瞬时大数据”换取“较少的信令开销”进而缓解网络的承载压力。
②鉴于经典Markov队列模型难以刻画海量MTC终端同步入网的瞬时突发特性，基于3GPP参考流量模型，本文首先求解了以Beta分布作为到达时间间隔的更新过程的t时刻之前的平均更新次数，即给定时间间隔内的平均更新个数，分析了MTC通信到达过程的接入强度等基本特性。接着基于G/M/1队列模型，为纯MTC业务建立Beta/M/1队列模型，为混合MTC业务和H2H业务建立Beta+M/M/1队列模型，分析了海量MTC终端的入网性能及其对H2H通信的影响。通过推导参数为任意正整数的第一类合流超几何函数的有限级数表示，给出了参数为任意正整数的Beta分布的概率生成函数的有限级数表示，该有限级数形式由指数函数和低阶幂函数的有限次加法和乘法运算构成，为到达时间间隔为Beta分布的更新过程和队列模型的求解提供了解决思路。数值仿真表明：当MTC通信的到达时间间隔服从Beta分布时，其到达过程的接入强度、队列系统的平均等待时间和平均逗留时间均远远大于由泊松过程模拟的H2H通信，验证了业界熟知的由MTC带来的网络拥塞问题，相关结论也为过载控制机制的设计提供了理论依据。所建队列模型与所给求解办法不仅适用于3GPP参考模型，还可推广到其他具有瞬时突发性的应用场景。
③为解决海量MTC接入时承载网络面临的过载问题，结合上述队列模型，本文提出了四类MTC通信专属的过载控制机制，分别是组间聚类、可任意调整到达时间间隔的纯数学方案、MTC专属的ACB机制以及工程可实现的MTC专属的退避机制。融入MTC通信流量特性的过载控制机制具有更强的针对性。通过蒙特卡洛仿真验证了“MTC专属的退避机制-分段均匀随机退避算法”的性能情况，数值仿真表明：当MTC与H2H混合接入时，该算法可有效降低随机接入过程的冲突概率和退避次数、保障H2H的通信质量，将系统有效吞吐量提高2%~5%，代价是MTC业务的接入时延增加100~200个包时延，然而该时延对于具有时延容忍性的MTC应用是可接受的。
Machine type communications (MTC) is defined as machine to machine (M2M)communications over cellular mobile networks. It is a subclass of M2Mcommunications which are automatic applications involving machines or devicescommunicating through a network without human intervention. In contrast to human tohuman (H2H) communications, MTC applications are essentially characterized byvarious application types, diverse business models, huge number of terminals,infrequent small amount data transmission, time controlled transmission, time tolerantquality of service (QoS), terminals with low mobility and etc... The typical MTCapplications include smart grid, Internet of vehicles, smart home, telemetering, wirelesssensor network and etc... These applications are the integral part of future ubiquitousnetwork, which have broad application prospects and market potentials. Conventionalcellular mobile networks have been optimally designed for H2H communications. Toaccommodate the new challenges brought by MTC and guarantee the QoS of both MTCand H2H communications, it should be further developed and re-optimized.
Prior to any technology enhancement for MTC, an appropriate traffic modelenabling preliminary performance evaluation is of prime important. Classic Markovianqueue models under the assumption of Poisson arrival have been long-term used forstochastic traffic modeling in telecommunications, as Poisson process can model thenumber of occurrences of a rare event in a very large population. However, thepossibility of massive MTC devices generating their access attempts in a short timeperiod makes the arrival pattern of MTC more bursty. The burstiness of MTC trafficinvalidates the commonly-used Markovian models under the assumption of Poissonarrival which is characterized by the negative exponentially distributed inter-arrival time(IAT). In case of this, a non-Markovian statistical traffic model may be more appropriate.Beta distribution is a distribution with two shape parameters and limited support rangewhich has the flexibility to model a lot of MTC devices starting their access in a shorttime period. It has been proposed by the3rdGeneration Partnership Project (3GPP) tomodel the IAT of MTC.
On the basis of this, this dissertation builds four traffic prediction models for localcellular, two queue models for MTC and presents some insights to access control forMTC, which serves as a preliminary study on traffic modeling and network performance evaluation and management for MTC by the use of queue theory andrenewal theory. The main contributions are as follows:
①According to the main application scenarios and the typical features of MTCdescribed in3GPP TS22.368, this paper establishes four traffic prediction models forlocal celluar in the context of massive MTC access, namely the no-mobility model,extended no-mobility model, low mobility model, full mobility model, in which themethod to calculate the volume of burst data and signaling overhead is given out.
②By the useage of order statistics, the differences between Beta distribution andexponential distribution which is the inter-arrival time distribution of Poisson processare elaborated as well as the reason why Beta distribution is more suitable for MTC. Tocarry out the performance analysis of MTC under Beta arrival, the moment generationfunctions (MGFs) of Beta distributions with integral paramerters, which are theconfluent hyper-geometric functions of first kind, are given out analytically. By theuseage of renewal theory and Volterra integral equation of the second kind withdifference kernel, the methodology to deduce the access intensity of MTC that isdefined as the mean number of renewals by time t, is presented. Numerical results arepresented by useage of numerical Laurent series expansion and then present the maincharacteristics of the arrival process of MTC. Two queue models are built for MTC.One is about pure MTC traffic, namely, Beta/M/1model. The other is about blendingH2H and MTC traffic, namely, Beta+M/M/1model. These two models associated withBeta distribution are special cases of G/M/1model. With the MGFs of Betadistributions deduced above, they can be solved by the standard method of G/M/1model. Numerical results show that as the burstiness of MTC is extremely larger thanthat of H2H communications, it could potentially increase the mean sojourn time andthe mean waiting time of queueing syetems and degrade the performance of networkand decrease the QoS of H2H communications. These works provide researchers andengineers a basis to appropriately choose traffic models for different MTC applicationsand promptly judge the effectiveness of newly designed control measures.
③To enhance radio access network overload control, the underlying mathematicalmeanings of3GPP proposals are firstly elaborated. On the basis of aforementioned queuemodels, four overload control measures are proposed. They are inter-class grouping,IAT shaping, ACB scheme dedicated to Beta distribution and MTC specific back-offmechanism. Among them, only the last one has the potential to put into practice. MonteCarlo simulations show that MTC specific back-off mechanism can effectively reduce the collision probability of random access process of network in context of MTC andimprove the throughput by2%-5%with additional100-200packets access delay whichis tolerable for most of the MTC applications.
当海量MTC终端同步入网时，其瞬时突发性将造成承载网络严重的流量过载或网络拥塞。为评估海量MTC终端的入网性能并提出相应的过载控制机制，有必要建立MTC通信专属的流量模型，即建立能表征海量MTC终端瞬时突发性的统计模型，以期为蜂窝网络的优化设计提供解决思路。为话音通信和分组交换网建立的经典Markov队列模型，因其独立增量特性和无后效性，被长期用于随机流量建模；但由于它们均蕴含到达过程服从泊松过程的假设，将不再适用于MTC通信的流量估计与建模。引入具有非泊松或非Markov特性的统计模型成为必然。3GPP（the3rdGeneration Partnership Project）建议采用Beta分布模拟海量MTC终端短时间内同步入网的瞬时突发特性。Beta分布是具有有限支撑区间的双参数概率密度函数，可等效为有限区间内随机抽取的n个点的第r小点的概率密度函数，将其作为MTC通信到达时间间隔的概率密度函数，比以负指数分布作为到达时间间隔的泊松过程更能刻画MTC通信的瞬时突发特性。基于该提案与MTC通信的典型应用特征，本文为MTC通信建立了四类小区流量预测模型和两类基于Beta分布的队列模型，并提出了四类MTC通信专属的过载控制机制，含工程可实现的MTC通信专属的退避机制。相关工作可为海量终端入网性能分析和过载控制提供参考。
论文的主要研究内容和成果包括：
①为满足基于MTC基本特征与特定网络模型的性能评价需要，本文以小区为单位，为MTC通信的不同应用场景建立了四类总流量预测模型，分别是静止模型、扩展静止模型、随机游走模型和移动模型，从宏观上给出了本地小区突发数据及信令开销的计算办法。分析表明：海量MTC终端接入时将使本地小区出现严重的流量和信令过载，预成簇或布置网关节点可以通过“瞬时大数据”换取“较少的信令开销”进而缓解网络的承载压力。
②鉴于经典Markov队列模型难以刻画海量MTC终端同步入网的瞬时突发特性，基于3GPP参考流量模型，本文首先求解了以Beta分布作为到达时间间隔的更新过程的t时刻之前的平均更新次数，即给定时间间隔内的平均更新个数，分析了MTC通信到达过程的接入强度等基本特性。接着基于G/M/1队列模型，为纯MTC业务建立Beta/M/1队列模型，为混合MTC业务和H2H业务建立Beta+M/M/1队列模型，分析了海量MTC终端的入网性能及其对H2H通信的影响。通过推导参数为任意正整数的第一类合流超几何函数的有限级数表示，给出了参数为任意正整数的Beta分布的概率生成函数的有限级数表示，该有限级数形式由指数函数和低阶幂函数的有限次加法和乘法运算构成，为到达时间间隔为Beta分布的更新过程和队列模型的求解提供了解决思路。数值仿真表明：当MTC通信的到达时间间隔服从Beta分布时，其到达过程的接入强度、队列系统的平均等待时间和平均逗留时间均远远大于由泊松过程模拟的H2H通信，验证了业界熟知的由MTC带来的网络拥塞问题，相关结论也为过载控制机制的设计提供了理论依据。所建队列模型与所给求解办法不仅适用于3GPP参考模型，还可推广到其他具有瞬时突发性的应用场景。
③为解决海量MTC接入时承载网络面临的过载问题，结合上述队列模型，本文提出了四类MTC通信专属的过载控制机制，分别是组间聚类、可任意调整到达时间间隔的纯数学方案、MTC专属的ACB机制以及工程可实现的MTC专属的退避机制。融入MTC通信流量特性的过载控制机制具有更强的针对性。通过蒙特卡洛仿真验证了“MTC专属的退避机制-分段均匀随机退避算法”的性能情况，数值仿真表明：当MTC与H2H混合接入时，该算法可有效降低随机接入过程的冲突概率和退避次数、保障H2H的通信质量，将系统有效吞吐量提高2%~5%，代价是MTC业务的接入时延增加100~200个包时延，然而该时延对于具有时延容忍性的MTC应用是可接受的。
Machine type communications (MTC) is defined as machine to machine (M2M)communications over cellular mobile networks. It is a subclass of M2Mcommunications which are automatic applications involving machines or devicescommunicating through a network without human intervention. In contrast to human tohuman (H2H) communications, MTC applications are essentially characterized byvarious application types, diverse business models, huge number of terminals,infrequent small amount data transmission, time controlled transmission, time tolerantquality of service (QoS), terminals with low mobility and etc... The typical MTCapplications include smart grid, Internet of vehicles, smart home, telemetering, wirelesssensor network and etc... These applications are the integral part of future ubiquitousnetwork, which have broad application prospects and market potentials. Conventionalcellular mobile networks have been optimally designed for H2H communications. Toaccommodate the new challenges brought by MTC and guarantee the QoS of both MTCand H2H communications, it should be further developed and re-optimized.
Prior to any technology enhancement for MTC, an appropriate traffic modelenabling preliminary performance evaluation is of prime important. Classic Markovianqueue models under the assumption of Poisson arrival have been long-term used forstochastic traffic modeling in telecommunications, as Poisson process can model thenumber of occurrences of a rare event in a very large population. However, thepossibility of massive MTC devices generating their access attempts in a short timeperiod makes the arrival pattern of MTC more bursty. The burstiness of MTC trafficinvalidates the commonly-used Markovian models under the assumption of Poissonarrival which is characterized by the negative exponentially distributed inter-arrival time(IAT). In case of this, a non-Markovian statistical traffic model may be more appropriate.Beta distribution is a distribution with two shape parameters and limited support rangewhich has the flexibility to model a lot of MTC devices starting their access in a shorttime period. It has been proposed by the3rdGeneration Partnership Project (3GPP) tomodel the IAT of MTC.
On the basis of this, this dissertation builds four traffic prediction models for localcellular, two queue models for MTC and presents some insights to access control forMTC, which serves as a preliminary study on traffic modeling and network performance evaluation and management for MTC by the use of queue theory andrenewal theory. The main contributions are as follows:
①According to the main application scenarios and the typical features of MTCdescribed in3GPP TS22.368, this paper establishes four traffic prediction models forlocal celluar in the context of massive MTC access, namely the no-mobility model,extended no-mobility model, low mobility model, full mobility model, in which themethod to calculate the volume of burst data and signaling overhead is given out.
②By the useage of order statistics, the differences between Beta distribution andexponential distribution which is the inter-arrival time distribution of Poisson processare elaborated as well as the reason why Beta distribution is more suitable for MTC. Tocarry out the performance analysis of MTC under Beta arrival, the moment generationfunctions (MGFs) of Beta distributions with integral paramerters, which are theconfluent hyper-geometric functions of first kind, are given out analytically. By theuseage of renewal theory and Volterra integral equation of the second kind withdifference kernel, the methodology to deduce the access intensity of MTC that isdefined as the mean number of renewals by time t, is presented. Numerical results arepresented by useage of numerical Laurent series expansion and then present the maincharacteristics of the arrival process of MTC. Two queue models are built for MTC.One is about pure MTC traffic, namely, Beta/M/1model. The other is about blendingH2H and MTC traffic, namely, Beta+M/M/1model. These two models associated withBeta distribution are special cases of G/M/1model. With the MGFs of Betadistributions deduced above, they can be solved by the standard method of G/M/1model. Numerical results show that as the burstiness of MTC is extremely larger thanthat of H2H communications, it could potentially increase the mean sojourn time andthe mean waiting time of queueing syetems and degrade the performance of networkand decrease the QoS of H2H communications. These works provide researchers andengineers a basis to appropriately choose traffic models for different MTC applicationsand promptly judge the effectiveness of newly designed control measures.
③To enhance radio access network overload control, the underlying mathematicalmeanings of3GPP proposals are firstly elaborated. On the basis of aforementioned queuemodels, four overload control measures are proposed. They are inter-class grouping,IAT shaping, ACB scheme dedicated to Beta distribution and MTC specific back-offmechanism. Among them, only the last one has the potential to put into practice. MonteCarlo simulations show that MTC specific back-off mechanism can effectively reduce the collision probability of random access process of network in context of MTC andimprove the throughput by2%-5%with additional100-200packets access delay whichis tolerable for most of the MTC applications.
引文
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