无线通信网络中一种改进的基于运动的位置.doc

精品论文无线通信网络中一种改进的基于运动的位置管理方案的建模及开销分析王献1，蒋伟1, 袁伟娜21 西南交通大学信息科学与技术学院，成都6100312 华东理工大学信息科学与工程学院，上海200237 摘要：在原始的基于运动的位置更新（original movement-based location update，OMBLU） 方案中，当穿越的小区数达到运动门限时，执行一次位置更新。 MBLU方案易受乒乓效应的影 响。 此处乒乓效应指移动设备（user eqipment，UE）在相邻小区间来来回回往返运动。 为了 应对此问题，文献提出一种改进的基于运动的位置更新（improved movement-based location update，IMBLU）方案。 在IMBLU中，当访问的不同的小区数达到运动门限时，执行一次位 置更新。 要在无线通信网络中实施IMBLU方案，首先需要确定能使位置更新开和寻呼开销最 小的最佳运动门限。 因此，需要一个全面的数学模型。 提出一个这样的模型来分析IMBLU方 案的信令开销。 采用一维随机走动模型描述UE的移动性。 推导得到IMBLU方案的信令开销的 闭合解析公式。 基于上述公式，开展数值分析，以评估相关参数对信令开销的影响。 数值分析 发现，信令开销是运动门限的向下凸函数；当乒乓效应较强时，IMBLU方案相对于OMBLU方 案的优越性更明显；仅在低移动性的情况下，小区驻留时间的方差才对信令开销产生显着影 响。 提出的模型和所得的结果对于在无线通信网络中实施IMBLU方案具有指导意义。 关键词：无线通信技术；基于运动的位置更新；乒乓效应；建模；信令开销中图分类号： TN929.5Modeling and Cost Analysis of an Improved Movement-Based Location Update Scheme in Wireless Communication NetworksWANG Xian1, JIANG Wei1, YUAN Wei-Na21 School of Information Science and Technology, Southwest Jiaotong University, Chengdu610031, China2 School of Information Science and Engineering, East China University of Science andTechnology, Shanghai 200237, ChinaAbstract: An improved movement-based location update (IMBLU) scheme was proposed in the literature to tackle the vulnerability of the original movement-based location update基金项目： Specialized Research Fund for the Doctoral Program of Higher Education of China (20090184120020)作者简介： WANG Xian (1979-), male, associate professor, major research direction: mobility management and performance modeling for personal communications service network, as well as queueing system.E-mail: drwangxiangmail.com- 13 -(OMBLU) scheme, which performs a location update (LU) when the number of cells crossed reaches a movement threshold, to the ping-pong effect, a synonym for the phenomenon that a user equipment (UE) moves back-and-forth between adjacent cells. In the IMBLU scheme the criterion for performing an LU is that the number of different cells visited reaches the movement threshold. Prior to implementing the IMBLU scheme in wireless communication networks, first we need to determine the optimal movement threshold that minimizes the signaling cost of the IMBLU scheme incurred by LUs and paging. Therefore, a comprehensive mathematical model is required. This paper devotes to this requirement by developing such a model to analyze the signaling cost of the IMBLU scheme. We characterize UE mobility by a one-dimensional random walk model and derive closed-form analytical formula for the signaling cost of the IMBLU scheme, based on which we carry out a numerical to investigate the influence of relevant parameters on the signaling cost. It is observed that the signaling cost is a downward convex function with respect to the movement threshold, that the superiority of the IMBLU scheme over the OMBLU scheme is proportional to the intensity of the ping-pong effect, as well as that the variance of cell residence time exerts noticeable influence on the signaling cost only in the scenario of low mobility. This paper can guide the implementation of the IMBLU scheme in wireless communication networks.Key words: wireless communication technology; movement-based location update;ping-pong effect; modeling; signaling cost0 IntroductionIn wireless communication networks for the successful delivery of incoming calls, a network must keep track of user equipments (UEs) than roam within its coverage. UE tracking is realized through a mechanism called location management. There are two basic operations in location management, namely, location update (LU) and paging. LU is the process through which a UE updates its registration of location in location databases residing in core network, while paging is the process through which upon the arrival of an incoming call the network pinpoints the cell where the UE is currently camping on by broadcasting polling signals in an area called paging area (PA), which consists of cells adjacent to the cell where the last LU before the call arrival occurs. Both LUs and paging incur signaling cost. An LU scheme must try to minimize the overall signaling cost due to LUs and paging.Existing LU schemes can be classified into two groups, namely, static and dynamic schemes. In static LU schemes, such as IS-41 1 and GSM MAP 2 , the coverage of a network is parti- tioned into location areas (LAs) (sometimes called registration areas), each of which comprises a number of cells, and an LU is performed when the UE steps into a new LA. In static schemes, LU frequency and PA are the same for all the UEs. Intuitively, for UEs with dense call arrivals,frequent LUs are necessary to curb the paging cost; while for those with sporadic call arrivals, frequent LUs are unnecessary. Therefore, static LU schemes are not cost-effective because they fail to take into account the mobility and traffic characteristics of individual UEs. A cost- effective LU scheme should be a dynamic one and can adapt to diverse mobility and traffic patterns.To tackle the drawback of static LU schemes, three dynamic schemes were proposed, namely, distance-based LU (DBLU), movement-based LU (MBLU), and time-based LU (TBLU) schemes, where an LU is performed when the distance in terms of cells traveled, or the number of cells crossed, or the elapsing time since the last LU reaches a threshold 3 . Among the three dynamic schemes, the DBLM scheme is the most effective and at the same time the most impractical, because it requires the network to provide UEs information about the distance between different cells and existing networks cannot satisfy this requirement. The TBLM scheme is the simplest to implement but also the most ineffective, because it may produce unnecessary LUs. Imagine that a stationary UE for a long time does not need to perform an LU before it moves. The MBLU scheme is the most practical, attributing to its effectiveness and easy-to-implement nature 4, 5 . The extra expense incurred by the MBLU scheme is the introduction of a counter in the UE to tally the number of cells crossed since the last LU. The signaling cost of the MBLU scheme due to LUs and paging depends on the threshold, called the movement threshold, which has relation with factors such as the mobility and traffic patterns, the architecture used for location management, etc. A plethora of studies in the literature have been carried out to investigate the signaling cost as well as other aspects of the MBLU scheme under diverse conditions 419 . The optimal movement threshold that minimizes the signaling cost can be determined based on the results developed in the literature.The MBLU scheme is vulnerable to ping-pong effect, which refers to the phenomenon that the UE moves back-and-forth between neighboring cells. Imagine that with the MBLU scheme, a UE repetitively moving between two cells performs LUs in the same way as in the case of moving directly. It is easily seen that in the case of repetitive movement, LUs should be performed less frequently than in the case of direct movement. In 20 Baek and Ryu proposed an improved MBLU (IMBLU) scheme that performs an LU when the number of different cells visited since the last LU reaches the movement threshold to cope with the ping-pong effect embarrassing the MBLU scheme. To avoid confusion hereafter we refer to the MBLU scheme as the original MBLU (OMBLU) scheme. Apparently, the IMBLU scheme has better performance than the OMBLU scheme when the ping-pong effect exists. A mathematical model for the IMBLU scheme is necessary for determining the optimal movement threshold. Due to the different criteria for initiating an LU in the OMBLU and IMBLU scheme, the results developed in the existing studies for the OMBLU scheme are unavailable to the IMBLU scheme.In this paper we propose a mathematical model to analyze the signaling cost of the IMBLU qqqqi1pppp qqqq01ipppp图 1: Markov chain depicting the one-dimensional random walk modelscheme. We depict UE mobility by a one-dimensional random walk model with a parameter that represents the intensity of the ping-pong effect, and derive closed-form analytical formula for the signaling cost of the IMBLU scheme, based on which a numerical study is conducted to assess the influence of relevant parameters on the signaling cost. It is observed that the signaling cost is a downward convex function with respect to the movement threshold, that the superiority of the IMBLU scheme over the OMBLU scheme is more prepossessing in the case of stronger ping-pong effect, as well as that the variance of cell residence time has perceivable influence on the signaling cost only in the scenario of low mobility. The model proposed and results developed in this paper are conducive to guiding the implementation of the IMBLU scheme in wireless communication networks.The thread followed in the rest of this paper is as follows. Sect. 1 expatiates on the mobility model. Sect. 2 analyzes the signaling cost of the IMBLU scheme. Sect. 3 presents a numerical study. Finally, Sect. 4 concludes this paper.1 Mobility ModelAssume that a UEs movements between cells follow a one-dimensional random walk model, where a cell has one neighbor cell on both its left- and right-hand sides, referred to respectively as the left and right neighbor cell, and after leaving a cell a UE moves respectively into the left and right neighbor cell with probabilities p and q , 1 p. Denote, respectively, by cell i 1 and i + 1 the left and right neighbor cell of cell i, i = 0, ±1, ±2, . . . Fig. 1 shows a Markov chain that describes the mobility model, where state i represents the status that the UE resides in cell i. Denote by xn , n = 0, 1, . . ., the state of the chain after the nth step, where a step stands for a UE movement between cells.i,jDenote by p(n) the probability that when starting in state i the chain reaches state j in exactly n steps, n = 0, 1, . . . It follows that i,j , n = 0,p(n)i,j = nn+ijn+ijp2 qn+ji2 , n |i j| is non-negative and even,2 0, otherwise,whereDefinei,j ,1, i = j,0, otherwise.f (n)i,j ,f (n)0, n = 0,p(1)i,j , n = 1,Pr(xn = j, xm = j, m = 1, . . . , n 1 | x0 = i), n = 2, 3, . . . .i,j is the probability that when starting in state i in exactly n steps the chain reaches state jfor the first time. By enumerating all disjoint probabilities of reaching state j from state i inexactly n steps, it is easily seen thatp(n)nX (m)(nm)i,j =m=1fi,j pj,j,f (n)(n)n1X(m)(nm)i,j = pi,j m=1fi,j pj,j, (1)for n = 1, 2, . . . Given the transition probabilities p(n) , n = 0, 1, . . ., f (n)can be calculatedrecursively for all n = 1, 2, . . . Define for k = ji,j(i,j)p(n)k;i,j ,i,j , n = 0,p(1)i,j , n = 1,Pr(xn = j, xm = k, m = 1, . . . , n 1 | x0 = i), n = 2, 3, . . . ;f (n)k;i,j ,p(n)0, n = 0,f (1)(i,j) , n = 1,Pr(xn = j, xm = j, xm = k, m = 1, . . . , n 1 | x0 = i), n = 2, 3, . . . .k;i,j is the probability that when starting in state i in exactly n steps the chain reaches statek;i,jj without having passed through state k. f (n)is the probability of a first entrance into state jk;i,jfrom state i in exactly n steps without having passed through state k. Probabilities p(n)andf (n)k;i,j are called taboo probabilities 21 . It follows from 21 thatp(n)(n)n1X(m)(nm)i,j = pk;i,j +m=1fi,k pk,j,p(n)nX (m)(nm)k;i,j =m=1fk;i,j pk;j,j ,previous call next calln图 2: Timing diagram depicting cell boundary crossings during the call inter-arrival timefor n = 1, 2, . . . Following from the latter relations and (1), the taboo probabilities can be calculated. Definef (n) x = j, x= j, xm1= k, m1 = 1, . . . , n1, x= 0 ,m1k;0,k1,j , Pr 0m2 1, . . . , n 1 s.t. xm2 = k 1nk > 0, j < 0, n = 2, 3, . . . ;m1f (n) x = j, x= j, xm2= k, m1 = 1, . . . , n 1, x= 0 ,k;0,k+1,j , Pr 0m2 1, . . . , n 1 s.t. xm2 = k + 1f (n)(n)k < 0, j > 0, n = 2, 3, . . . .k;0,k1,j (fk;0,k+1,j ) is the probability of a first entrance into state j from state 0 via state k 1(k + 1) in exactly n steps without having passed through state k. It follows thatf (n)(n)(n)k;0,k1,j = fk;0,j fk1;0,j ,k > 0, j < 0, and n = 2, 3, . . . ,f (n)(n)(n)k;0,k+1,j = fk;0,j fk+1;0,j ,k < 0, j > 0, and n = 2, 3, . . . .dDenote by p(n) , n = 1, 2, . . ., the probability that the chain moves n steps before the movement counter reaches the movement threshold d. It follows that1 =p(n)1, n = 1,0, othewise;(2)0, d 2, n < d,f+ f(n)(n)d =p(n)1;0,d1;0,d d(3)X hf+k=2(n)+ fk;0,k1,k1d(n) i,k;0,k+1,k+1+dd 2, n d.2 Performance Analysis of the IMBLU SchemeFig. 2 shows a timing diagram depicting cell boundary crossings during the call inter- arrival time, denoted by tc , which is the time between two consecutive call arrivals. Supposethat when the previous call arrives, the UE resides in cell 1; and the UE moves across k cells before receiving the next call in cell k + 1, k = 0, 1, . . . Denote by tj , j = 1, 2, . . ., the residence time in cell j, and by r1 the time from the arrival of the previous call in cell 1 till when the UE moves out of cell 1. Here we consider a homogenous wireless communication network, i.e., the structures of all the cells in the network are statistically identical and hence the residence times t1 , t2 , . . . are independent and identically distributed (i.i.d.). Assume that tc follows an exponential distribution of rate , i.e., the call arrival process is Poisson. Denote by f (t) and fr (t) the density funct