An Investigation on LTE Mobility Management

An Investigation on LTE Mobility Management

Ren-Huang Liou, Yi-Bing Lin, Fellow, IEEE, and Shang-Chih Tsai

Abstract—Mobility management in Long Term Evolution (LTE) is different from that in the third generation mobile telecom networks. In LTE, the Mobility Management Entity (MME) is responsible for the mobility management function. The MME is connected to a large number of evolved Node Bs (cells) that are grouped into the Tracking Areas (TAs). The TAs are further grouped into TA Lists (TALs). When a User Equipment (UE) moves out of the current TAL, it reports its new location to the MME. If the LTE network attempts to connect to the UE, the MME asks the cells in the TAL to page the UE. In LTE paging, the MME may sequentially page a cell, the TA of the cell, and/or the TAL of the cell. This paper investigates the performance of LTE paging, and provides the guidelines for the best paging sequence of cells.

Index Terms—Location update, long term evolution (LTE), mobility management, paging

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1

I

I

Equipments (UEs) are tracked so that incoming calls can be delivered to the UEs. Typical mobility management procedures include location update and paging. When a UE moves from one location to another location, the UE reports its new location to the network through the location update procedure. When an incoming call to the UE arrives, the network identifies the location of the UE via the paging procedure.

In Long Term Evolution (LTE), the Mobility Management Entity (MME; Fig. 1a) is responsible for the mobility management function [1], [2], which is connected to a group of evolved Node Bs (eNBs; the LTE term for base stations; see Fig. 1b). The radio coverage of an eNB (or a sector of the eNB) is called a cell (see the dashed squares; Fig. 1c). Every cell has a unique cell identity. The cells are grouped into the Tracking Areas (TAs; e.g., TA 1 contains Cell 1 and Cell 2 in Fig. 1d). Every TA has a unique TA identity (TAI). The TAs are further grouped into TA Lists (TALs) [1]. In Fig. 1, TAL 1 consists of TA 2, TA 3, and TA 4 (Fig. 1e).

A UE stores the TAL that includes the TA where the UE resides. In Fig. 1(1), the UE is covered by Cell 5, and the TAL it stores is TAL 1 ¼ fTA2; TA3; TA4g. If the LTE network attempts to connect to the UE, it asks the cells in the TAL (e.g., Cell 3-Cell 8) to page the UE. Every eNB periodically broadcasts its TAI. The UE listens to the broadcast TAI and checks if the received TAI is in its TAL. If so, it means that the UE does not move out of the current location. In Fig. 1, when the UE moves from Cell 5 to Cell 7, it receives the TA

4 identity broadcast from eNB 7. Since TA 4 is included in TAL 1, the UE still resides in the same location. When the UE moves to Cell 9 (Fig. 1(2)), the received TA 5 identity (broadcast from eNB 9) is not found in TAL 1, which means that the UE has moved out of the current location. In this case, the UE executes the location update procedure to inform the MME that it has left TAL 1. The MME then assigns a new TAL to the UE. In Fig. 1, the new TAL is TAL 2¼ fTA4; TA5; TA6g. Note that the TAL is assigned on a per-user basis (i.e., TALs for different UEs may have different sizes and shapes), and the newly assigned TAL may be overlapped with the previously assigned TAL (e.g., TAL 2 is overlapped with TAL 1 in Fig. 1). We consider the central policy [1] that assigns a new TAL whose central TA includes the cell where the UE currently resides. In Fig. 1(2), the UE resides in TA 5, and TAL 2 ¼ fTA4; TA5; TA6g is centered at TA 5. In the central policy, the TALs may be overlapped. For example, TA 4 is included in both TAL 1 and TAL 2.

When an incoming call to the UE arrives, it may incur large paging traffic if all cells in the TAL page the UE simultaneously. To resolve this issue, we implement three paging schemes in LTE. In this paper, an “interacted cell” refers to a cell where the UE is paged, makes calls, or performs location update. In other words, the interacted cell is the cell through which the UE had the interaction with the network.

. Scheme CT (Cell-TAL). When an incoming call arrives, the MME first asks the last interacted cell to page the UE. If fails, all cells in the TAL are asked to page the UE.

. Scheme TT (TA-TAL). When an incoming call arrives, the TA of the last interacted cell is asked to page the UE. If fails, all cells in the TAL are asked to page the UE.

. Scheme CTT (Cell-TA-TAL).When an incoming call arrives, the MME first asks the last interacted cell to page the UE. If fails, the TA of the last interacted cell is asked to page the UE. If fails again, all cells in the TAL are asked to page the UE.

. R.-H. Liou and S.-C. Tsai are with the Department of Computer Science, National Chiao Tung University, No. 1001, University Road, Hsinchu City, Taiwan 300, R.O.C. E-mail: {rhliou, tsaisc}@cs.nctu.edu.tw. . Y.-B. Lin is with the Department of Computer Science, National Chiao

Tung University, No. 1001, University Road, Hsinchu City, Taiwan 300, R.O.C., the Institute of Information Science and the Research Center for Information Technology Innovation, Academia Sinica, Nankang, Taipei, Taiwan, R.O.C., and King Saud University. E-mail: [email protected]. Manuscript received 8 Aug. 2011; revised 2 Oct. 2011; accepted 11 Nov. 2011; published online 28 Nov. 2011.

For information on obtaining reprints of this article, please send e-mail to: [email protected], and reference IEEECS Log Number TMC-2011-08-0447. Digital Object Identifier no. 10.1109/TMC.2011.255.

Basically, the central policy and the three paging schemes we described for LTE mobility management partially implement the movement-based and the distance-based location updates [3], [4], [5] with the Shortest-Distance-First (SDF) paging [4], [6]. Although these schemes have been intensively studied in the literature, they have not been exercised in any commercial mobile telecom network because their implementations are not feasible. Specifically, in the distance-based location update, the UE is required to have the cell topology information (i.e., the distance relation-ship between cells) [3], [7], [8], which can not be practically implemented in a real network. In the SDF paging, it is difficult to dynamically define the neighboring cells (when the radio coverage changes, the “adjacent cells” may also change). Through the predefined TA configuration, LTE can partially implement the distance-based scheme with the SDF paging for commercial operation. In this paper, we show that LTE mobility management outperforms third-generation (3G) mobility management by capturing the advantages of the distance-based scheme with the SDF paging. We propose an analytic model to evaluate the performance of the TAL-based location update with the above three paging schemes. This paper is organized as follows: Section 2 introduces the TAL-based location update. Section 3 proposes an analytic model for modeling the TAL-based scheme. Section 4 investigates the performance of the TAL-based scheme by numerical examples, and the conclusions are given in Section 5.

2

TAL-B

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This section describes the TAL-based location update by considering one-dimensional (1D) random walk model for the UE movement. This configuration significantly simplifies the description and provides better demonstration. Also, 1D

configuration does exist in real environment [9]. We will extend the 1D model to a 2D model through simulation.

Fig. 2 illustrates the TAL configuration where a rectan-gular represents a cell. In this configuration, a TAL contains NT TAs and each TA covers NCcells. In a TAL, the TAs are sequentially labeled from 1 to NT, and the cells are sequentially labeled from 1 to NCNT. To simplify our discussion on the central policy mentioned in Section 1, we assume that NT is an odd number. Following the central policy, the TAL is overlapped with each of its adjacent TALs by NCbNT=2c cells. Therefore, when the UE leaves the current TAL from Cell NCNT, the entrance cell of the newly assigned TAL is Cell NCbNT=2c þ 1. Similarly, if the UE leaves the current TAL from Cell 1, the entrance cell of the newly assigned TAL is Cell NCð Nb T=2c þ 1Þ.

In most commercial 3G mobile telecom networks, the base stations are grouped into Location Areas (LAs) [10]. When the UE moves from old LA to new LA, a location update is performed. When an incoming call arrives, all cells in the LA of the UE will page the UE. The 3G mobility management scheme is a special case of the TAL-based location update with the TT paging where the size of an LA is the size of a TAL, and NT ¼ 1.

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This section models the TAL-based location update and the paging schemes. We first describe the input parameters and output measures.

Fig. 3 illustrates the timing diagram for the cell crossings and the incoming call arrivals. In this figure, we assume that the intercall arrival interval tc¼ 2 1is an exponen-tial random variable with the mean 1=c. Let tm;i¼ tiþ1 ti be the cell residence time between the ði  1Þth cell crossing and the ith cell crossing. Assume that tm;i is independent

and identically distributed random variable with the mean 1=m, the variance V , and the Laplace transform fmðsÞ. When the UE makes cell crossing, the UE moves to the right-hand side neighboring cell with routing probability p, and moves to the left-hand side neighboring cell with probability 1  p. We consider the following three output measures:

. Cu: the expected number of location updates during tc . Cp;x: the expected number of cells that page the UE when an incoming call arrives, where x 2 fCT ; T T ; CT Tg

. Cd;x: the expected number of polling cycles [6] before the UE is found, where x 2 fCT ; T T ; CT T g. Note that the maximum number of polling cycles for the CT, the TT, and the CTT schemes are 2, 2, and 3, respectively.

It is clear that the smaller the above output measures, the better the performance of the location update and paging schemes.

We first derive Cu. Let E½M be the expected number of cell crossings before the UE leaves the current TAL (i.e., the expected number of cell crossings between two consecutive location updates). Then, Cucan be computed as

Cu¼ E½tc E½ME½tm;i ¼ m cE½M : ð1Þ

In [11], we have derived E½M with the following final formats. If p ¼ 0:5, E½M ¼ NC NT 2   þ 1   NC NT 2   þ 1   : ð2Þ If p 6¼ 0:5, E½M ¼ A 1þ A  B   _N CNTþ 1 B NC N₂T  1 2p 1 " # þ 1 B 1þ A  B   _N CNTþ 1 A NC N₂T þ 1 2p 1 " # ; ð3Þ where A¼1 1p p NCðbNT2cþ1Þ 11p_p NCNTþ1 and B¼ 11p_p NCbNT2cþ1 11p_p NCNTþ1: ð4Þ

Now we derive Cp;CT, Cp;T T, and Cp;CT T. Fig. 4 illustrates the state-transition diagram for the TAL-based location update. In this figure, state j represents that the UE resides in Cell j of the TAL, where 1  j  NCNT. For 2  j  NCNT 1, the UE moves from state j to state j þ 1 with probability p, and moves from state j to state j  1 with probability 1  p.

The state transition from state 1 to state NCðbNT=2c þ 1Þ represents that the UE leaves the current TAL from Cell 1 and enters Cell NCðbNT=2c þ 1Þ of the newly assigned TAL. Similarly, the transition from state NCNT to state NCbNT=2c þ 1 represents that the UE leaves the current TAL from Cell NCNT and enters Cell NCbNT=2c þ 1 of the newly assigned TAL. Let i be the steady-state probability that the UE resides in Cell i. From Fig. 4, we obtain the following balance equations:

i¼

ð1  pÞiþ1; for i¼ 1 pi1þ ð1  pÞiþ1; for 2 i  NC

NT 2   ; NC NT 2   þ 2  i  NC NT 2   þ 1    1 and NC NT 2   þ 1   þ 1  i  NCNT 1 pi1þ ð1  pÞiþ1 þ pNCNT; for i¼ NC NT 2  þ 1 pi1þ ð1  pÞiþ1 þ ð1  pÞ1; for i¼ NC NT 2   þ 1   pi1; for i¼ NCNT: 8 > > > > > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > > > > > : ð5Þ

By rearranging (5), if p ¼ 0:5, i can be rewritten as i¼ i1; for 1 i  Nc NT 2   þ 1 NC NT 2   þ 1   1; for Nc NT 2   þ 1 < i  Nc NT 2   þ 1    NCNT i þ 1 1; for Nc NT 2   þ 1   < i  NCNT: 8 > > > > > > > > > > > > > > < > > > > > > > > > > > > > > : ð6Þ If p 6¼ 0:5 and NT ¼ 1, i is rewritten as i¼ 1; for 1 i  NC: ð7Þ If p 6¼ 0:5 and NT 6¼ 1, i is rewritten as i¼ 1 1 p   1þ p 2 2p 1   _p 1 p  i2 1 " # ( ) 1; for 2 i  NC NT 2   þ 1 1 1 p   1þ p 2 2p 1   _p 1 p  i2 1 " # ( ) 1  p 1 p  iNC NT2  1 1 2 4 3 5 p 2p 1   NCNT; for NC NT 2   þ 1 < i  NC NT 2   þ 1   1þ ð1  pÞ 2 1 2p " # 1 p p  NCNTi1 1 " # ( )  NCNT p   ; for NC NT 2   þ 1    i  NCNT 1; 8 > > > > > > > > > > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > > > > > > > > > > : ð8Þ and NCNT ¼ 1 1 p   1þ p 2 2p 1   p 1 p  NC NT2  þNC2 1 2 4 3 5 8 < : 9 = ; p 1 p  NC1 1 " #  p 2p 1   þ1 pþ ð1  pÞ2 pð1  2pÞ " # ( 1 p p  NC NT2  1 1 2 4 3 5 9 = ; 1 1: ð9Þ Probability i can be solved by usingPN_i¼1CNTi¼ 1 and (6)-(9).

Let qðkÞ_i;j be the probability that the UE moves from Cell i to Cell j after k cell crossings without any location update (it is possible that Cell j is revisited several times during these k cell crossings). Let q_i;0ðkÞ and qðkÞ_i;N

CNTþ1 be the

probabilities that the UE initially stays in Cell i and moves out of the current TAL from Cell 1 and Cell NCNT at the kth cell crossing, respectively. Probabilities qðkÞi;j, q

ðkÞ i;0, and qðkÞ_i;NCNTþ1 are derived as follows. To compute the probability that the UE leaves the current TAL at the kth cell crossing (i.e., qðkÞ_i;0 and qðkÞ_i;N

CNTþ1), Fig. 5 modifies Fig. 4 by

adding two absorbing states 0 and NCNTþ 1 and removing the transitions from state 1 to state NCðbNT=2c þ 1Þ and from NCNT to NCbNT=2c þ 1. Let qi;j be the one-step transition probability from state i to state j. Fig. 5 illustrates the state-transition diagram, where the transition probabil-ity matrix Q ¼ ðqi;jÞ of the random walk is

Q¼ 1 0 0 0    0 0 0 1p 0 p 0    0 0 0 0 1p 0 p    0 0 0 .. . .. . .. . .. . . . . .. . .. . .. . 0 0 0 0    0 p 0 0 0 0 0    1p 0 p 0 0 0 0    0 0 1 0 B B B B B B B B B @ 1 C C C C C C C C C A ðNCNTþ2ÞðNCNTþ2Þ: ð10Þ Let QðkÞ_{¼ ðq}ðkÞ

i;jÞ be the transition matrix. From (10), QðkÞ is computed by the matrix multiplication QðkÞ_¼Qk

i¼1Q. Based on qi;jðkÞ, q

ðkÞ i;0 and q

ðkÞ

i;NCNTþ1 are computed as

Fig. 4. State-transition diagram for TAL-based location update.

Fig. 5. State-transition diagram for 1D random walk model with two absorbing states.

Fig. 3. Timing diagram for the cell crossings and the incoming call arrivals.



qðkÞ_i;0 ¼ qi;0; for k¼ 1 qðkÞ_i;0  qðk1Þ_i;0 ; for k > 1 

ð11Þ and



qðkÞ_i;NCNTþ1¼ qi;NCNTþ1; for k¼ 1

qðkÞ_i;NCNTþ1 qðk1Þ_i;NCNTþ1; for k > 1: (

ð12Þ Given that the UE resides in Cell i when the previous incoming call arrives (i.e., Cell i is an “interacted cell”; see 1 in Fig. 3), let ðk;nÞi be the probability that after k cell crossings and n location updates, the UE moves back to the last interacted cell. If n ¼ 0, then the last interacted cell is Cell i. If n  1, the last interacted cell is the cell where the UE performs the nth location update. From (11) and (12), ðk;nÞi is computed as

ðk;nÞ_i ¼

1; for k¼ 0 and n ¼ 0

q_i;iðkÞ; for k > 0 and n¼ 0 Xk j¼1 ðkj;n1Þ NC NT2  þ1q ðjÞ i;NCNTþ1  þ ðkj;n1Þ NC NT2  þ1  qðjÞ i;0 ; for k n  1 0; for k < n: 8 > > > > > > > > > < > > > > > > > > > : ð13Þ

In (13), for k ¼ 0 and n ¼ 0, the UE does not make any cell crossing (i.e., the UE still stays in Cell i), and ð0;0Þ_i ¼ 1. For k > 0 and n ¼ 0, the last interacted cell is Cell i, and the probability that the UE moves from Cell i back to Cell i after k cell crossings without any location update is qðkÞi;i. For k n  1, two cases are considered. First, if the UE moves out of the current TAL from Cell NCNT at the jth cell crossing (with probability q_i;NðjÞ_CNTþ1), the last interacted cell is Cell NCbNT=2c þ 1 of the newly assigned TAL, and the numbers of the remaining cell crossings and location updates are k  j and n  1, respectively. Second, if the UE moves out of the current TAL from Cell 1 at the jth cell crossing (with probability q_i;0ðjÞ), the last interacted cell is Cell NCðbNT=2cþ1Þ of the newly assigned TAL, and the numbers of the remaining cell crossings and location updates are k  j and n  1, respectively. For k < n, it is impossible that the number of cell crossings is smaller than that of location updates. Therefore, ðk;nÞi ¼ 0 for k < n.

Let ðkÞ be the probability that the UE makes k cell crossings during tc. From our previous work [6], ðkÞ is derived as ðkÞ ¼ 1 m c   1 f mðcÞ   ; for k¼ 0 m c   1 f mðcÞ  2 f_mðcÞ  k1 ; for k > 0: 8 < : ð14Þ

Assume that tm;i is a Gamma random variable with the mean 1=m, the variance V , and the Laplace transform

f_mðsÞ ¼ 1 V msþ 1

  1

V 2_m

: ð15Þ

We consider the Gamma distribution because it has been shown that the distribution of any positive random variable can be approximated by a mixture of Gamma distributions [12]. The Gamma distribution was used to model UE movement in many studies [5], [6], [9] and is used in this

paper to investigate the impact of variance for cell residence times. From (15), (14) is rewritten as

ðkÞ ¼ 1 m c   1 1 V mcþ1   1 V 2_m   ; for k¼ 0 m c   1 _{1V } mcþ1   1 V 2_m  2 1 V mcþ1  k1 V 2_m ; for k > 0: 8 > > < > > : ð16Þ Let C be the probability that the UE resides in the last interacted cell when an incoming call arrives. From (6)-(9), (13) and (16), C is expressed as C¼ X1 k¼0 ðkÞ X NCNT i¼1 i Xk n¼0 ðk;nÞ_i : ð17Þ In the right-hand side of (17), the UE makes k cell crossings during tc with probability ðkÞ (0  k  1) and resides in Cell i with probability i(1  i  NCNT) when the previous incoming call arrives. Therefore, Cis the summation of the product ðkÞiðk;nÞi over all possible ðk; i; nÞ pairs (i.e., 0  n k  1 and 1  i  NCNT).

Similar to ðk;nÞi , let  ðk;nÞ

i be the probability that after kcell crossings and n location updates, the UE moves back to the TA of the last interacted cell given that the UE resides in Cell i when the previous incoming call arrives. From (11) and (12), ðk;nÞi is derived as

ðk;nÞi ¼ 1; for k¼ 0 and n ¼ 0 PNC _NCi l m j¼NC _NCi l m NCþ1

qðkÞi;j; for k > 0 and n¼ 0 Pk j¼1  kj;n1 ð Þ NC NT2  þ1q ðjÞ i;NCNTþ1  þ ðkj;n1Þ NC NT2  þ1  qðjÞ i;0 ; for k n  1 0; for k < n: 8 > > > > > > > > > > > > < > > > > > > > > > > > > : ð18Þ The explanation of (18) is similar to that of (13), and the details are omitted.

Let Tbe the probability that the UE resides in the TA of the last interacted cell when an incoming call arrives. Similar to (17), from (6)-(9), (16) and (18), Tis expressed as

T ¼ X1 k¼0 ðkÞ X NCNT i¼1 i Xk n¼0 ðk;nÞ_i : ð19Þ From (17) and (19), Cp;x is computed as

Cp;CT ¼ Cþ1 C 1þ NCNT ð20Þ Cp;T T¼ TNCþ  1 T  NCþ NCNT ; ð21Þ and Cp;CT T¼ Cp;CT; for NC¼ 1 Cþ ðT CÞð1 þ NCÞ þ ð1  TÞð1 þ NCþ NCNTÞ; for NC6¼ 1: 8 < : ð22Þ

Similar to the derivations for Cp;x, Cd;x is computed as Cd;CT ¼ Cþ 2ð1  CÞ ¼ 2  C; ð23Þ Cd;T T¼ Tþ 2ð1  TÞ ¼ 2  T; ð24Þ and Cd;CT T ¼ Cd;CT; for NC ¼ 1 Cþ 2ðT CÞ þ 3ð1  TÞ; ¼ 3  C T; for NC 6¼ 1: 8 < : ð25Þ

The major differences between our analytic model and the previous models for the movement-based and the distance-based schemes [5], [6] are described as follows:

. In the movement-based and the distance-based schemes, a location update or an incoming call resets the center cell of the residing area [6] to be the last interacted cell. On the other hand, the TAL-based location update resets the central TA of the TAL to be the TA of the last interacted cell (i.e., the last interacted cell may not be the center cell of the TAL). Therefore, our analytic model is more compli-cated than those for the movement-based and the distance-based location updates.

. In the SDF paging, the last interacted cell is the center cell of the subareas (i.e., the TA) [6]. In the TT and the

CTT schemes, the last interacted cell may not be the center cell of the TA.

. The previous analytic models [5], [6] assume that the UE moves from a cell to one of the neighboring cells with the same probability. In our model, the UE can move to each of its neighboring cells with different probabilities.

Our analytic model is used to validate the discrete event simulation model (reviewers, please see the supplementary document, which can be found on the Computer Society Digital Library at http://doi.ieeecomputersociety.org/ 10.1109/TMC.2011.255). Simulation experiments show that the discrepancies between the analytic (i.e., (1), (20)-(25)) and simulation results are within 1 percent. After the simulation of 1D cell configuration has been validated by the analytic model, the validated simulation flowchart is extended to accommodate the 2D mesh cell configuration (i.e., Manhat-tan-street layout).

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This section investigates the performance of the TAL-based location update and paging schemes. We first point out that the performance results for the 1D configuration are consistent with those for the 2D configuration. For x 2 fCT ; T T ; CT T g, Fig. 6a plots Cp;x for the 1D configuration,

and Fig. 6b plots Cp;x for the 2D configuration. Figs. 6c and 6d plot Cu and Cd;x for both the 1D and the 2D configurations, respectively. In the 1D configuration, we consider the TAL size NCNT ¼ 45 and p ¼ 0:5. In the 2D mesh configuration, we consider a 45  45 cell structure, and the UE moves to one of the four neighboring cells with the same routing probabilities 0.25. This figure shows that the trends of Cp;x, Cu, and Cd;xare similar for both the 1D and the 2D models. Therefore, our observations on the 1D model are also valid for the 2D model. For other input parameter setups, same results are observed, and the details are omitted.

The remainder of this section shows the results for the 1D configuration because several nontrivial observations can be easily explained through the analytic model of this simple configuration.

4.1 Analysis of the CuPerformance

In the 1D configuration, it suffices to consider 0:5  p  1 in our study. In practice, a small p (e.g., p ¼ 0:5; solid lines in Fig. 7) represents the movement of a pedestrian or a vehicle in local roads, which exhibits locality. A large p (e.g., p ¼ 0:85; dashed lines in Fig. 7) represents the movement of a vehicle in highways. When p increases, the UE tends to move to one direction. Therefore, Cu increases as p increases. In Fig. 7, the values of the dashed curves (p ¼ 0:85) are higher than those of the solid curves (p ¼ 0:5).

When m=c increases (i.e., more cell crossings during tc), more location updates are expected (i.e., Cu increases as m=c increases). In Fig. 7, the values of the curves (m=c¼ 50) are higher than those of the curves (m=c¼ 5).

The effect of NCon Cucan be explained as follows. When NC¼ 1, the entrance cell of the UE is the center cell of the new TAL. On the other hand, when NC¼ 45 (i.e., NT ¼ 1 or the TAL only has one TA), the entrance cell of the UE is the

boundary cell of the new TAL. Now consider p ¼ 0:5. If NC¼ 1, then it is unlikely that the UE will move out of the TAL in first few cell crossings. On the other hand, if NC¼ 45, then the UE will move out of the TAL at the first cell crossing with probability 0.5. In other words, for a fixed NCNT value, if p is small, E½M decreases as NC increases. For example, for NCNT ¼ 45 and p ¼ 0:5, (2) indicates that E½M ¼ 529 for NC¼ 1 and E½M ¼ 45 for NC¼ 45. Since Cu is inversely proportional to E½M (see (1)), for a fixed NCNT value, Cuincreases as NCincreases for a small p (the solid curves in Fig. 7).

On the other hand, for a fixed NCNT value, if p is large, E½M increases as NC increases. In the extreme case, when p¼ 1, (3) is rewritten as E½M ¼ NC N₂T

 

. If NCNT ¼ 45, we have E½M ¼ 23 for NC¼ 1 and E½M ¼ 45 for NC¼ 45. Therefore, for a large p, Cudecreases as NC increases (the dashed curves in Fig. 7).

As mentioned in Section 2, the 3G location update is a special case of the TAL-based scheme where NT ¼ 1 (i.e., NC¼ 45; see the 4 symbol in Fig. 7). When p ¼ 0:5, the TAL-based scheme with NT 6¼ 1 can reduce about 90 percent of the 3G location update cost. When p ¼ 0:85, the TAL-based scheme with NT6¼ 1 incurs extra 4-36 percent cost over the 3G location update.

4.2 Analysis of the Cp;x Performance

This section investigates the effects of m=c, p, V , and NC on Cp;x.

. Effects of m=c: For all x 2 fCT ; T T ; CT T g, Fig. 8 indicates that Cp;xincrease as m=cincreases. When m=c increases, it is more likely that the UE is far away from the last interacted cell when an incoming call arrives, and thus higher Cp;xare expected. When m=cis small, the low-mobility UE is more likely to be found in the last interacted cell, and there is no need to page the TA. In this case, we observe that Cp;CT T < Cp;CT < Cp;T T. On the other hand, when

Fig. 8. Effects of m=cand p on Cp;x(NC¼ 9, NT¼ 5 and V ¼ 1=2m).

m=cis large, the UE is unlikely to reside in the last interacted cell, and paging the last interacted cell incurs extra paging cost. Therefore, Cp;CT T is slightly larger than Cp;T T. The effect of m=con Cp;CTis more significant than that on Cp;CT T, and than that on Cp;T T. In summary, for small m=c, Cp;CT T < Cp;CT < Cp;T T. For large m=c, Cp;CT T  Cp;T T < Cp;CT.

. Effects of p: For all x 2 fCT ; T T ; CT T g, Fig. 8 indicates that a large p incurs high paging costs Cp;x because the UE may be far away from the last interacted cell when an incoming call arrives. The effect of p becomes more significant when m=c increases. Fig. 9 shows that the effects of p on Cp;x become insignificant as V increases. In Figs. 8, 9, and 10, for most p values, Cp;CT T are smaller than both Cp;CT and Cp;T T.

. Effects of V: For a fixed m value, we have the following facts about the variance V of the cell residence time tm;i.

- Fact 1.When V is small (i.e., the user movement pattern is regular), most tm;ihave values around 1=m. In this case, if m=c< 1, the UE is likely to be found in the last interacted cell when an incoming call arrives. On the other hand, if m=c> 1, the UE is unlikely to be found in the last interacted cell.

- Fact 2. For any m value, when V increases (i.e., the user movement pattern becomes irregu-lar), more longer tm;i periods will be observed, and the UE does not move in many consecutive tc periods that fall in these tm;i. In this case, the UE is always found in the last interacted cell, and lower Cp;xare observed for all x 2 fCT ; T T ; CT T g.

Due to Fact 1, when V is small and m=c> 1, the UE is unlikely to be found in the last interacted cell, and Cp;CT > Cp;T T (in Fig. 9a, for V  1=2m, the values of the curves are higher than those of the curves). On the other hand, Cp;CT < Cp;T T for a small m=c (in Fig. 9b, for V  1=2m, the values of the curves are lower than those of the curves). Due to Fact 2, Fig. 9 shows that when V is large, low Cp;x are observed for all x 2 fCT ; T T ; CT T g, and Cp;CT < Cp;T T. Specifically, when V > 30=2m, the values of the curves are lower than those of the curves in Fig. 9a, and the values of the curves are lower than those of the curves for all V values in Fig. 9b. The CTT scheme is a combination of the CT and the TT schemes, which explores the advantages of these two schemes in both large and small V scenarios, and yields the best performance. The effect of V on Cp;CT is more significant than that on Cp;CT T, and than that on Cp;T T. In summary, when V is small, Cp;CT T < Cp;CT < Cp;T T for a small m=c, and Cp;CT T Cp;T T < Cp;CT for a large m=c. When V is large, Cp;CT T < Cp;CT < Cp;T T.

. Effects of NC: Since the CT scheme does not page the TA of the last interacted cell, Cp;CT is not sensitive to the change of NC (see the curves in Fig. 10). Fig. 10a indicates that when V is small and m=c> 1, Cp;T T decreases and then increases as NC increases. In this case, the UE is unlikely to reside in the last interacted cell (Fact 1), and a large NCresults in a higher probability that the UE is found in the TA of the last interacted cell. Therefore, there is no need to page all cells in the TAL; i.e., lower Cp;T T is observed. However, if NC is “too” large, the cost of paging the TA is high, and the benefit of paging the TA becomes insignificant. Therefore, Cp;T T decreases and then increases as NC increases. Fig. 10b

indicates that when V is large and m=c< 1, Cp;T T increases as NC increases. In this case, the UE is more likely to be found in the last interacted cell (Fact 2), and it is a waste to page the TA (same result is observed for large V with m=c> 1). This extra cost becomes significant as the TA size is large (i.e., Cp;T T increases as NC increases). As we previously stated, the CTT scheme takes advantages of the CT and the TT schemes to yield the best performance for all NC values. This figure also indicates that the

lowest Cp;x value can be found in the CTT scheme when 5  NC 15 (or 3  NT  9). Note that when NC¼ 1, Cp;CT ¼ Cp;T T ¼ Cp;CT T because a TA only contains one cell and paging the TA is the same as paging the cell (see (23)). On the other hand, when NC¼ 45 (i.e., NT ¼ 1), a TAL only contains one TA, and Cp;CT ¼ Cp;CT T.

As mentioned in Section 2, the 3G paging is a special case of the TT scheme where NT¼ 1 (i.e., NC ¼ 45; see the 4 symbol in Fig. 10). Fig. 10 indicates that the TAL-based

Fig. 11. Effects of m=c, p, and V on Cd;x( NC¼ 9 and NT¼ 5).

paging in terms of the Cp;xperformance. 4.3 Analysis of the Cd;x Performance

Fig. 11 plots Cd;xagainst m=c, p, and V . The effects of m=c, p, and V on Cd;x are similar to those on Cp;x described in Section 4.2, and the details are omitted. It is clear that Cd;T T  Cd;CT  Cd;CT T. As stated in Section 2, the 3G paging simultaneously asks all cells in the LA to page the UE, and thus the polling cycle is 1. The TAL-based paging schemes incur extra 0.01-1.08 polling cycles over the 3G paging for high mobility (Fig. 11a), and incur extra 0.01-0.21 polling cycle over the 3G paging for low mobility (Fig. 11b).

5

C

This paper investigated the performance of LTE mobility management. We considered the central policy for location update and three paging schemes based on the concept of TA and TAL. Our study indicates the following results:

. The central-based LTE location update outperforms the 3G location update by 90 percent for p ¼ 0:5 (i.e., when the user movement exhibits locality). On the other hand, the LTE scheme incurs extra 4-36 percent cost over the 3G location update for p ¼ 0:85 (i.e., when the user tends to move to one direction). We note that when p  0:75, the TAL-based scheme always outperforms the 3G location update. . The TAL-based paging schemes outperform the 3G

paging by 21-97 percent in terms of the number of paged cells. Among the TAL-based paging schemes, the TT scheme outperforms the CT scheme when the variance V of the cell residence time is small (i.e., the user movement pattern is regular) and the UE moves frequently (i.e., m=c is large). The CT scheme outperforms the TT scheme when V is large or m=c is small. The CTT scheme takes advantages of both the CT and the TT schemes, which has the best performance in most input parameter setups under our study.

. For the number of polling cycles, the TAL-based paging schemes incur extra 0.01-1.08 polling cycles over the 3G paging. Among the TAL-based paging schemes, the TT scheme outperforms the CT and the CTT schemes.

In summary, if network signaling costs for location update and paging are major concern, then the CTT scheme should be selected. If the number of polling cycles is major concern, then the existing 3G mobility management should be selected for the users with high mobility and regular movement patterns (i.e., with small V ). For low mobility users, the extra overheads incurred by the LTE paging can be ignored. Finally, the central-based LTE mobility manage-ment creates several interesting research issues. In the future, we will investigate the MME failure restoration based on dynamic TAL assignment [13], power saving [14], mobility management for mesh-mode LTE [15], handoff in hetero-geneous network [16], and so on.

Corporation, ICL/ITRI, Nokia Siemens Networks, and the MoE ATU plan.

R

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[7] V.W.-S. Wong and V.C.M. Leung, “Location Management for Next-Generation Personal Communications Networks,” IEEE Network, vol. 14, no. 5, pp. 18-24, Sept./Oct. 2000.

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[9] Y.-B. Lin and Y.-C. Lin, “WiMAX Location Update for Vehicle Applications,” Mobile Networks and Applications, vol. 15, no. 1, pp. 148-159, Feb. 2010.

[10] Y.-B. Lin and A.-C. Pang, Wireless and Mobile All-IP Networks. John Wiley & Sons., 2005.

[11] S.-R. Yang, Y.-C. Lin, and Y.-B. Lin, “Performance of Mobile Telecommunications Network with Overlapping Location Area Configuration,” IEEE Trans. Vehicular Technology, vol. 57, no. 2, pp. 1285-1292, Mar. 2008.

[12] F.P. Kelly, Reversibility and Stochastic Networks. Wiley, 1979. [13] Y.-B. Lin, “Per-User Checkpointing for Mobility Database Failure

Restoration,” IEEE Trans. Mobile Computing, vol. 4, no. 2, pp. 189-194, Mar./Apr. 2005.

[14] S.-R. Yang, S.-Y. Yan, and H.-N. Hung, “Modeling UMTS Power Saving with Bursty Packet Data Traffic,” IEEE Trans. Mobile Computing, vol. 6, no. 12, pp. 1398-1409, Dec. 2007.

[15] D.-W. Huang, P. Lin, and C.-H. Gan, “Design and Performance Study for a Mobility Management Mechanism (WMM) Using Location Cache for Wireless Mesh Networks,” IEEE Trans. Mobile Computing, vol. 7, no. 5, pp. 546-556, May 2008.

[16] N. Nasser, A. Hasswa, and H. Hassanein, “Handoffs in Fourth Generation Heterogeneous Networks,” IEEE Comm. Magazine, vol. 44, no. 10, pp. 96-103, Oct. 2006.

Ren-Huang Liou received the BS and MS degrees in computer science from National Chiao Tung University (NCTU), Hsinchu, Tai-wan, R.O.C., in 2007 and 2009, respectively. He is currently working toward the PhD degree at NCTU. His current research interests include Voice over Internet Protocol (VoIP), mobile computing, and performance modeling.

Yi-Bing Lin is a vice president and life chair professor in the College of Computer Science, National Chiao Tung University (NCTU), and a visiting professor of King Saud University. He is also with the Institute of Information Science and the Research Center for Information Technology Innovation, Academia Sinica, Nankang, Taipei, Taiwan, R.O.C. He is the author of the books Wireless and Mobile Network Architecture (Wi-ley, 2001), Wireless and Mobile All-IP Networks (John Wiley, 2005), and Charging for Mobile All-IP Telecommunications (Wiley, 2008). He has received numerous research awards including the 2005 NSC distinguished researcher award and the 2006 Academic Award of the Ministry of Education. He is a fellow of the IEEE, ACM, AAAS, and IET.

Shang-Chih Tsai received the BSCS degree from National Chiao Tung University (NCTU), Hsinchu, Taiwan, R.O.C., in 2008. He is currently working toward the MSCS degree at NCTU. His current research interests include design and analysis of a personal communications services network and performance modeling.

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