Mobility management with the central-based location area policy
Ren-Huang Liou, Yi-Bing Lin
⇑Department of Computer Science, National Chiao Tung University, 1001 University Road, Hsinchu, Taiwan 300, ROC
a r t i c l e
i n f o
Article history:
Received 5 November 2011
Received in revised form 7 September 2012 Accepted 6 November 2012
Available online 16 November 2012 Keywords:
Location update Mobility management Paging
a b s t r a c t
In Long Term Evolution (LTE), the cells (the radio coverages of base stations) are grouped into the Tracking Areas (TAs), and the TAs are further grouped into the TA List (TAL). The location of the User Equipment (UE) is tracked at the TAL level. To better capture the ‘‘move-ment locality’’ of the UE, when the UE leaves the current TAL, the UE is assigned a new TAL whose central TA is the TA where the UE currently resides. This paper investigates the per-formance of the central-based LTE mobility management scheme, and compares this scheme with the previously proposed central-based mobility management schemes: the movement-based and the distance-based schemes. Our study indicates that under some traffic/mobility patterns, the LTE scheme yields the best performance.
Ó 2012 Elsevier B.V. All rights reserved.
1. Introduction
In most commercial third-generation (3G) mobile telecom networks, the cells (the radio coverages of base stations) are grouped into Location Areas (LAs)[1]. When the User Equipment (UE) moves from an old LA to a new LA, the UE executes the location update procedure to in-form the network of its new location. When an incoming call arrives, the network searches the UE by broadcasting the paging messages to all cells in the LA simultaneously.
The 3G LA-based mobility management scheme has sev-eral disadvantages[2,3]. First, the UE may perform many location updates when the UE resides in the boundary cell of the LA and frequently moves back and forth between two LAs (i.e., the ping–pong effect[4]). Second, when an incoming call arrives, if the LA contains a large number of cells, it may incur large paging traffic to search the UE.
The disadvantages of the LA-based scheme can be avoided in Long Term Evolution (LTE). We first describe the LTE mobility management and then show how the aforementioned issues of the LA-based scheme can be resolved in LTE. In LTE, the cells (Fig. 1a) are partitioned
into non-overlapped Tracking Areas (TAs; Fig. 1b) [5,6]. Every TA has a unique TA Identity (TAI). The TAs are further grouped into TA Lists (TALs). InFig. 1c, TAL 1 includes TA 1, TA 2 and TA 3. The Mobility Management Entity (MME; Fig. 1d) is responsible for assigning the TAL to the UE through the location update procedure. To mitigate the ping-pong effect, we consider the central policy[5]that as-signs the TAL where the UE resides in the central TA of this TAL. InFig. 1(1), when the UE performs the location update in TA 2, the MME assigns TAL 1 to the UE, where TAL 1 = {TA 1, TA 2, TA 3} centered at TA 2. Every base station periodically broadcasts its TAI. The UE detects the location change by searching its TAL for the broadcast TAI. If the broadcast TAI is found in its TAL, it means that the UE still resides in its TAL. Otherwise, the UE executes the location update procedure to inform the MME that it has left the current TAL. In Fig. 1, when the UE moves from Cell 4 (Fig. 1(1)) to Cell 7 (Fig. 1(2)), the broadcast TA 4 identity is not found in TAL 1, and the UE executes the location up-date procedure to inform the MME that the UE has moved out of TAL 1. Then the MME allocates a new TAL to the UE. In Fig. 1, the allocated TAL is TAL 2 = {TA 3, TA 4, TA 5}. Note that the TAL is assigned on a per-user basis (i.e., the different UEs may have different TALs), and the newly as-signed TAL may overlap with the previously asas-signed TAL. InFig. 1, TA 3 is included in both TAL 1 and TAL 2.
1389-1286/$ - see front matter Ó 2012 Elsevier B.V. All rights reserved.
http://dx.doi.org/10.1016/j.comnet.2012.11.003
⇑Corresponding author. Tel.: +886 3 573 1842; fax: +886 3 572 4176. E-mail addresses: [email protected] (R.-H. Liou), [email protected]. edu.tw(Y.-B. Lin).
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Computer Networks
We also note that the 3G LA-based location update is a spe-cial case of the LTE TAL-based location update when the size of an LA is equal to that of a TAL and the TAL only con-tains one TA. When an incoming call arrives, the cells of the UE’s TAL will page the UE. In most commercial 3G mobile networks, all cells in the LA of the UE will execute the pag-ing procedure simultaneously. To reduce the pagpag-ing traffic, we consider a LTE paging scheme[7]where the MME re-cords the cell where the UE has interacted with the net-work (e.g., makes call, receives call, or performs location update). This cell is referred to as the interacted cell. When an incoming call arrives, the MME conducts the TAL paging procedure as follows:
Step 1.1. The MME sends the paging message to the last interacted cell. If the MME receives the paging response from the UE, the MME establishes the connection to the UE to deliver the incom-ing call, and the pagincom-ing procedure is termi-nated. Otherwise (i.e., the MME does not receive the response within a timeout period), Step 1.2 is executed.
Step 1.2. The MME sends the paging messages to the TA of the last interacted cell. If the MME receives the paging response, the connection is estab-lished, and the paging procedure is terminated. Otherwise, Step 1.3 is executed.
Step 1.3. The MME sends the paging messages to all cells in the TAL to search the UE. After the UE sends the paging response to the MME, the incoming call is delivered to the UE.
We define a polling cycle as a period between when the MME sends the paging messages to the cells and when the MME receives the paging response or a timeout occurs. Let Npbe the maximum number of the polling cycles before the UE is found. Steps 1.1–1.3 indicate that Np= 3 in the TAL paging scheme.
Our previous work has proposed an analytic model to compare the performance between the central-based LTE mobility management and the 3G mobility management, which shows that the LTE mobility management outper-forms the 3G mobility management [7]. This paper describes a simulation model for the TAL-based scheme,
and compares the TAL-based scheme with the
move-ment-based [2,8] and the distance-based [8–10,13]
schemes with the Shortest-Distance-First (SDF) paging [2,10]. Note that the movement-based and the distance-based schemes with the SDF paging were intensively stud-ied in the literature. However, these schemes have not been exercised in any commercial mobile telecom network because their implementations are not feasible (to be elab-orated). The central policy and the TAL paging scheme we described for the LTE mobility management partially implement the distance-based scheme with the SDF pag-ing, and we will show that our approach can capture the advantages of the distance-based scheme with the SDF paging.
This paper is organized as follows. Section2introduces the TAL-based, the movement-based, and the distance-based location updates. Then we describe the SDF paging scheme. Section3proposes a simulation model for these location update and paging schemes. Section 4compares the performance of the TAL-based, the movement-based, and the distance-based schemes by numerical examples, and the conclusions are given in Section5.
2. Location update and paging schemes
This section describes the TAL-based, the movement-based, and the distance-based location update schemes. For the description purpose, we consider a two-dimensional (2-D) mesh cell configuration (i.e., Manhattan-street lay-out) as illustrated inFig. 2, where a rectangular represents a cell. In this configuration, each cell has eight neighboring cells. Many previous studies assume that the UE moves to one of the neighboring cells with the same routing proba-bility[2,8,10]. We relax this assumption to accommodate heterogeneous routing patterns. In our random walk mod-el, the UE moves to the right-hand side neighboring cell with routing probability p, and moves to one of other neighboring cells with the same probability (1 p)/7. If p = 0.125, then the routing pattern is homogeneous (i.e., the UE movement exhibits locality; e.g., a pedestrian or a vehicle in local roads), which is the same as those in [2,8,10]. If p = 1, the UE moves to one direction (e.g., a vehi-cle in highways). Note that in[7], we used the 1-D model to represent the UE movement in highways. On the other hand, this paper uses 2-D model for city layout. We have showed that the effects of the input parameters in 1-D and 2-D models are similar[7]. Based on the 2-D cell con-figuration, we describe the location updates and the
Short-est-Distance-First (SDF) paging in the following
subsections.
Fig. 1. LTE mobility management architecture.
2.1. TAL-based location update
Let NCbe the number of cells in a TA and NTbe the num-ber of TAs in a TAL.Fig. 3illustrates a TAL configuration, where NC= NT= 9. In the TAL, a cell is labelled as hx, yi, where x is the column label, y is the row label, and 1 6 x; y 6 ffiffiffiffiffiffiffiffiffiffiffiffiNCNT
p
. Similarly, a TA is labelled as hX,Yi, where 1 6 X; Y 6 ffiffiffiffiffiffiNT
p
. TA hX,Yi includes cells hx, yi where ðX 1Þ ffiffiffiffiffiffiNC p þ 1 6 x 6 X ffiffiffiffiffiffiNC p and ðY 1Þ ffiffiffiffiffiffiNC p þ 1 6y 6 YpffiffiffiffiffiffiNC. To simplify our discussion on the central pol-icy mentioned in Section1, we assume that ffiffiffiffiffiffiNT
p
is an odd number. Due to the central policy, when the UE moves out of the current TAL (i.e., the UE moves to Cell hx,yi where x = 0 or ffiffiffiffiffiffiffiffiffiffiffiffiNCNT
p
þ 1, or y = 0 or ffiffiffiffiffiffiffiffiffiffiffiffiNCNT p
þ 1), the entrance TA is reset to the central TA (i.e., TA h ffiffiffiffiffiffiNT
p =2 ; ffiffiffiffiffiffiNT p =2 i), and the entrance cell is reset to the cell in TA h ffiffiffiffiffiffiNT p =2 ; ffiffiffiffiffiffiNT p =2
iat the same relative position. For example, inFig. 3, when the UE moves from Cell h9,5i to Cell h10,5i, Cell h10, 5i is reset to Cell h4,5i. Cell h10, 5i in TA h4, 2i is at the same relative position as Cell h4, 5i in TA h2, 2i. 2.2. Movement-based and distance-based location updates
In the movement-based location update, the UE
maintains a counter to record the number of cell boundary crossings since the last interaction with the network
(location update or incoming call). When the counter value reaches the predefined threshold K, the UE updates its new location and resets the counter value to zero. Also, when an incoming call is delivered to the UE, the counter value is re-set to zero[2].
In the distance-based location update, the UE updates its location when the distance (in terms of the number of cells) between the last interacted cell and the current cell of the UE is K. Note that in the distance-based location up-date, the UE is required to have the knowledge of the cell topology information (i.e., the distance relationship be-tween cells)[3,8,11], which cannot be practically imple-mented in a real network. Therefore, the distance-based location update is an idealized mechanism, and is consid-ered in this paper for comparison purpose.
The movement-based and the distance-based location updates ensure that the maximum distance between the last interacted cell and the cell where the UE resides is K 1[2]. Define the residing area of the UE as the area which is within the maximum distance K 1 from the last inter-acted cell.Fig. 4illustrates a residing area with K = 5. If the last interacted cell is Cell hK, Ki (i.e., Cell h5, 5i), then the residing area of the UE ranges from Cell h1, 1i to Cell h2K 1, 2K 1i (i.e., from Cell h1, 1i to Cell h9, 9i). To make a fair comparison with the TAL-based location update, we assume that the size of the residing area of the
based and the distance-based location updates is NCNT(i.e., (2K 1)2= N
CNT).
In the movement-based and the distance-based
schemes, when the UE updates its location or an incoming call is delivered to the UE, the cell where the UE currently resides is reset to Cell hK, Ki (i.e., the center cell of the resid-ing area). On the other hand, the TAL-based location up-date resets the central TA of the TAL to the TA of the last interacted cell (note that the last interacted cell may not be the center cell of the TAL). We also note that an incom-ing call in the TAL-based scheme does not reset the central TA to the TA of the last interacted cell.
2.3. Shortest-Distance-First (SDF) paging
The Shortest-Distance-First (SDF) paging proposed in[2] is described as follows. The residing area of the UE (i.e., Cell h1, 1i to Cell h2K 1, 2K 1i) is partitioned into NT= min (K, Np) subareas. Let Ajbe the subarea j where 0 6 j 6 NT - 1. Subarea Ajincludes Cells hx,yi where lj6x, y 6 rj. The boundary values ljand rjare computed as
lj¼ K Kðj þ 1Þ NT þ 1 and rj¼ K þ Kðj þ 1Þ NT 1 ð1Þ
When an incoming call arrives, the network first partitions the residing area of the UE into the subareas according to
(1). Then the network searches the subareas
A0, A1, . . . , ANT1sequentially until the UE is found (where
A0#A1# # ANT1).
Fig. 4shows an SDF partitioning example where K = 5 and Np= 3. In this figure, NT= min (K, Np) = 3, l0= r0= 5, l1= 3, r1= 7, l2= 1, and r2= 9. Suppose that the UE resides in Cell h4, 5i. When an incoming call arrives, the network identifies the UE’s location after searching A0 and A1. Therefore, the total number of searched cells is 26 (one cell in A0and 25 cells in A1).
We note that the SDF paging is never implemented in commercial mobile telecom network because it is difficult to dynamically define the neighboring cells (because the radio coverage may change due to the radio characteristics and the ‘‘adjacent cells’’ also change). Similarly, it is not practical to set NC= 1 in LTE.
3. Simulation model
We use the discrete event simulation to investigate the performance of the location update and paging schemes described in the previous sections. We consider two per-formance measures:
Cu,s: the expected number of location updates between two consecutive incoming calls for the ‘‘s’’ scheme, where s 2 {T, M, D} denoting the TAL-based, the move-ment-based, and the distance-based location updates, respectively
Cp,s: the expected number of cells that page the UE when an incoming call arrives for the TAL paging (s = T), the movement-based scheme with the SDF pag-ing (s = M), and the distance-based scheme with the SDF paging (s = D), respectively
It is clear that the smaller the above performance mea-sures, the better the performance of the location update and paging schemes. In our simulation model, an event e has two attributes:
The type attribute indicates the event type. There are two event types. A Call event represents a call arrival. When this event occurs, the core network establishes the connection to a UE through the paging procedure. A Move event represents that the UE crosses the cell boundary to a neighboring cell.
The ts attribute indicates the timestamp when the event occurs.
The inter-call arrival time tcis a random number drawn from an exponential generator GCwith the mean 1/kc. The inter-move time tmis a random number drawn from a Gam-ma generator GMwith the mean 1/kmand the variance V. 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[2,7,10], and is used in this paper to investi-gate the impact of variance for cell residence times. The direction of each UE movement is determined by a uniform random number U between 0 and 1 drawn from a generator GD. Four labels are used to track a UE’s location:
hx; yi: the column and the row labels of the last inter-acted cell, respectively
hx⁄, y⁄
i: the column and the row labels of the cell where the UE currently resides, respectively
There are three output variables in the simulation model:
Fig. 4. The residing area layout for the movement-based and the distance-based location updates with the SDF paging (K = 5 and Np= 3).
na: the number of call arrivals nu: the number of location updates
np: the number of cells that page the UE when an incoming call arrives
From the above output variables, we compute
Cu;s¼ nu na and Cp;s¼ np na ð2Þ
In the simulation, a clock t is maintained to indicate the simulation progress, which is the timestamp of the event being processed. All events are inserted into the event list, and are deleted/processed from the event list in the non-decreasing timestamp order.Fig. 5illustrates the simula-tion flow chart for the TAL-based locasimula-tion update and pag-ing with the followpag-ing steps:
Step 1. Set all output variables (i.e., na, nuand np) and the simulation clock t to 0. Initialize x; y; x, and y⁄
to an integer randomly selected between 1 and
ffiffiffiffiffiffiffiffiffiffiffiffi NCNT p
.
Step 2. The first Call event e1and Move event e2are gen-erated and are inserted into the event list. For event e1, e1.type is Call and e1.ts = t + tcwhere tc is generated from GC. For event e2,e2.type is Move and e2.ts = t + tmwhere tmis generated from GM.
Step 3. The first event e in the event list is deleted, and is processed based on its type in Step 4. The clock t is set to e.ts.
Step 4. If e.type is Call, then Step 5 is executed. If e.type is Move, the simulation proceeds to Step 15. Step 5. When an incoming call arrives, nais incremented
by one. The last interacted cell pages the UE, and npis incremented by one.
Step 6. If the UE resides in the last interacted cell (i.e., hx;yi ¼ hx; yi), then Step 11 is executed. Other-wise, the simulation proceeds to Step 7. Step 7. If NC= 1 (i.e., the TA only contains one cell), the
TA of the last interacted cell has paged the UE in Step 5, and Step 10 is executed. Otherwise, Step 8 is executed.
Step 8. All cells in the TA of the last interacted cell page the UE, and npis incremented by NC.
Step 9. If the UE resides in the TA of the last interacted cell (i.e., dx= ffiffiffiffiffiffiN C p e ¼ dx= ffiffiffiffiffiffiNC p e and dy= ffiffiffiffiffiffiN C p e ¼ dy= ffiffiffiffiffiffiNC p
e), then Step 11 is executed. Otherwise, the simulation proceeds to Step 10. Step 10. All cells in the TAL page the UE, and npis
incre-mented by NCNT.
Step 11. The MME updates the last interacted cell by set-ting hx; yi to hx⁄, y⁄i.
Step 12. The next Call event e1 is generated and is inserted into the event list where e1.ts = t + tc. Step 13. If ten million of Call events have been processed,
then Step 14 is executed. Otherwise, the simula-tion proceeds to Step 3. In our experience, ten million of Call events are enough to produce sta-ble statistics.
Step 14. The performance measures are computed
according to (2), and the simulation is
terminated.
Step 15. If e.type is Move in Step 4, then this step is exe-cuted. The movement direction of the UE is determined by the uniform random number U which is generated by GD. As shown in Fig. 2, new hx⁄, y⁄
i are computed using the following routing rules. hx;yi hxþ 1; yþ 1i; for 0 6 U <1p 7 hx;yþ 1i; for 1p 7 6U < 2ð1pÞ 7 hx 1; yþ 1i; for 2ð1pÞ 7 6U < 3ð1pÞ 7 hx 1; yi; for 3ð1pÞ 7 6U < 4ð1pÞ 7 hx 1; y 1i; for 4ð1pÞ 7 6U < 5ð1pÞ 7 hx;y 1i; for 5ð1pÞ 7 6U < 6ð1pÞ 7 hxþ 1; y 1i; for 6ð1pÞ 7 6U < 1 p hxþ 1; yi; for 1 p 6 U 6 1 8 > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > : ð3Þ
Step 16. If the UE leaves the current TAL (i.e., x⁄= 0 or ffiffiffiffiffiffiffiffiffiffiffiffi NCNT p þ 1, or y⁄= 0 or ffiffiffiffiffiffiffiffiffiffiffiffiN CNT p þ 1), Step 17 is executed. Otherwise, the flow jumps to Step 19. Step 17. As mentioned in SubSection 2.1, when the UE leaves the current TAL, the entrance cell is reset to the cell in TA h ffiffiffiffiffiffiNT p =2 ; ffiffiffiffiffiffiNT p =2 i in the new TAL. Therefore, x⁄ and y⁄ are set as x ffiffiffiffiffiffiN C p ffiffiffiffiffiffiNT p 2 x ffiffiffiffiffiffi NC p þ x ð4Þ and y ffiffiffiffiffiffiN C p ffiffiffiffiffiffiNT p 2 y ffiffiffiffiffiffi NC p þ y ð5Þ
Step 18. nuis incremented by one. The MME updates the last interacted cell; i.e., hx; yi is set to hx⁄, y⁄
i. Step 19. The next Move event e2is generated and inserted
into the event list where e2.ts = t + tm. The simu-lation jumps to Step 3.
The differences betweenFig. 5and the simulation flow chart for the movement-based location update with the SDF paging are described as follows. An additional variable nmis needed to record the number of cell crossings after the last interaction with the network, and the labels hx; yi are not needed in the movement-based scheme (because the last interacted cell is always hK, Ki in the movement-based scheme). In Step 1, nmis reset to zero. In Steps 5– 10, if the UE is found in ith polling cycle, npis incremented by the summation of the number of cells in A0, A1, . . . , Ai1. In Step 11, hx⁄, y⁄i are reset to hK, Ki, and n
mis reset to zero.
In Step 15, nmis incremented by one, and hx⁄, y⁄i is updated according to(3). In Step 16, if nm= K, Step 17 is executed. Otherwise, the simulation goes to Step 19. In Step 17, hx⁄
, y⁄
i is reset to hK, Ki, and nmis reset to zero.
The simulation flow chart for the distance-based scheme with the SDF paging is similar to that for the move-ment-based scheme with the SDF paging except that the variable nmis not needed in the distance-based scheme. Besides, in Step 16, if x⁄= 0 or 2K or y⁄= 0 or 2K, Step 17 is executed. Otherwise, Step 19 is executed.
We validate the simulation model by the previously proposed analytic models [2,7,10]. Simulation experi-ments show that the discrepancies between the analytic and simulation results are within 1%, and the details are omitted.
4. Numerical examples
This section compares the performance of the TAL-based, movement-TAL-based, and the distance-based schemes by numerical examples. We show the results for the TAL (residing area) size NCNT= (2K 1)2= 152. The results for other NCNT values are similar and are omitted. For the SDF paging, Np= 3 is considered for two reasons. First, from the simulation model we conducted, the paging cost for Np= 3 is lowest (or near lowest) for the movement-based and the distance-based schemes (the detailed effect of Np on the paging cost will not be presented here). Second, the TAL paging scheme at most pages three times and can be fairly compared with the SDF paging scheme when Np= 3. For the TA size, we select NC= 52.
4.1. Analysis of the Cu,sperformance
This subsection investigates the effects of p,km/kc, and V on Cu,s.
Effects of p: Fig. 6a plots Cu,s/Cu,T against p. For the movement-based scheme (s = M), Cu,M/ Cu,T decreases as p increases. When p increases, the UE tends to move to one direction, and large Cu,T is expected. On the other hand, p does not affect Cu,M because this scheme determines if a loca-tion update is performed based on ‘‘move-ment count’’, and ‘‘move‘‘move-ment count’’ is not affected by the movement direction p. Therefore, Cu,M/Cu,T decreases as p increases. On the other hand, the effect of p on Cu,Dis similar to that on Cu,T, and
Fig. 6a shows that Cu,D/Cu,Tincreases as p increases.
Effects of km/kc: From the analytic models in [7], Cu;T¼kckE½Mm , which is consistent with the
simulation results that when km/kc increases, more cell crossings occur in tc, and higher Cu,s are expected for all schemes.Fig. 6b shows that Cu,M/Cu,Tand Cu,D/Cu,T increase as km/kc increases. For
the movement-based and the distance-based schemes, we observe the following fact:
Fact 1. When K = 1 or p = 1, the distance-based scheme is the same as the movement-based scheme. For other K and p val-ues, the distance-based scheme always has lower location update cost than the movement-based scheme.
Due toFact 1, the values of the X curves (s = D) are lower than those of the curves (s = M) inFigs. 6 and 7.
Effects of V: Fig. 7 shows that Cu,M/Cu,T increases as V increases. This phenomenon is explained as follows. Consider a long observation period T. Let nCbe the number of the inter-call arri-val interarri-vals tcin T. Let nMbe the number of
the cell crossings in T. We consider two extreme cases of V (i.e., V ? 0 and V ? 1). When V ? 0, tmalmost have the same fixed value, and the number of the cell crossings in every tc is about a fixed number nM/nC. The number of the location updates in every tcfor the movement-based scheme is bnM/(n C-K)c. Therefore, the number of the location updates in T for V ? 0 is nCbnM/(nCK)c. On the other hand, when V ? 1, there is one very long tm, and other tm?0. In this case, all cell crossings occur in a certain tc, and the number of the location updates in T for the movement-based scheme is bnM/Kc. It is clear that nCbnM/(nCK)c 6 bnM/Kc (i.e., Cu,M increases as V increases). On the other hand,
Fig. 6. Effects of p and km/kcon Cu,s(NC¼ 5 2
;NT¼ 3 2
;V ¼ 100=k2
m, and K = 8).
V does not affect Cu,Tbecause the incoming call in the TAL-based scheme does not reset the central TA to the TA of the last interacted cell. Therefore, Cu,M/Cu,T increases as V increases. Similarly, Cu,D/Cu,T increases as V increases.
When p is small, the distance-based scheme
outperforms the TAL-based scheme (in
Fig. 7, the values of the solid X curves are smaller than 1) because the distance-based scheme always resets the center cell of the residing area to the last interacted cell (i.e., when the UE resides in the center cell of the residing area, the UE is unlikely to leave the residing area for a small p, and lower location update cost is expected). On the other hand, when p is large, if km/kcis large, the TAL-based scheme outperforms the dis-tance-based scheme (in Fig. 7a, the values of the dashed X curves are larger than 1). This phenomenon can be explained by an extreme case where p = 1 and km/kc?1. In this case, the distance-based scheme performs location update for every K ¼ ð ffiffiffiffiffiffiffiffiffiffiffiffiNCNT
p
þ 1Þ=2 cell crossings. On the other hand, the TAL-based scheme performs location update for every
ffiffiffiffiffiffi NC p ffiffiffiffiffiffi NT p =2
cell crossings. It is clear that ffiffiffiffiffiffi NC p ffiffiffiffiffiffi NT p =2 Pð ffiffiffiffiffiffiffiffiffiffiffiffiNCNT p þ 1Þ=2. Similarly, when both p and V are large, the TAL-based
scheme outperforms the distance-based
scheme (inFig. 7, for V P 200=k2
mthe values
of the dashed X curves are larger than 1). When both km/kcand V are small, only a small number of cell crossings occur in tc(e.g., less than K), which is unlikely to incur location update for the distance-based scheme. In this case, the distance-based scheme outperforms the TAL-based scheme (in Fig. 7b, for V 6 100=k2m, the values of the X curves are smaller than 1).
From the above discussions,Table 1lists the mobility management scheme with the lowest location update cost under different input parameter setups. In this table, the TAL-based scheme outperforms the other schemes when (1)km/kcand p are large or(2)V and p are large.
4.2. Analysis of the Cp,sperformance
This subsection investigates the effects of p, km/kc, and V on Cp,s.
Effects of p: It is clear that the paging cost increases as p increases for all schemes.Fig. 8a indicates that Cp,M/Cp,T and Cp,D/Cp,T increase as p increases.
Effects of km/kc: When km/kc increases, the UE is more likely to be far away from the last interacted cell when the next call arrives, and higher Cp,s are expected for all s 2 {T, M, D}. Fig. 8b shows that Cp,M/Cp,T and Cp,D/Cp,T decrease as
Table 1
The mobility management scheme with the lowest location update cost under different km/kc, V, and p values.
Small km/kc Large km/kc
Small V Large V Small V Large V
Small p Large p Small p Large p Small p Large p Small p Large p
Distance Distance Distance TAL Distance TAL Distance TAL
km/kc increases. Because the move-ment-based scheme performs more location updates than the distance-based scheme (Fact 1), the UE is more likely to be found in the last inter-acted cell for the movement-based
scheme, and the movement-based
scheme with the SDF paging has lower paging cost than the distance-based scheme with the SDF paging. InFigs. 8 and 9, the values of the curves (s = M) are lower than those of the X curves (s = D).
Effects of V: When V is small, most tmhave values about 1/km. In this case, if km/kcis large, the movement-based scheme with the SDF paging outperforms the TAL paging (inFig. 9a, for V 6 10=k2
m, the values of the curves are smaller than 1) because the subareas in the SDF paging are sym-metric to the last interacted cell (see Fig. 4), and the SDF paging is more likely to find the UE before searching all cells in the residing area. On the other hand, if km/kcis small, the TAL paging outper-forms the movement-based scheme with the SDF paging (in Fig. 9b, for V 6 10=k2
m, the values of the curves are larger than 1) because the
low-mobility UE is more likely to be found in the last interacted cell, and it is a waste to page all cells in the subarea A0. For any kmvalue, when V increases,
more longer tm periods will be
observed, and the UE does not move in many consecutive tcperiods that fall in these tm. In this case, the UE is always found in the last interacted cell, and we observe that Cp,T< Cp,M< Cp,D (in
Fig. 9a and b, for V P 2000=k2m; Cp;T<Cp;M<Cp;D).
From the above discussions,Table 2lists the mobility management scheme with the lowest paging cost under different input parameter setups. This table shows that the TAL-based scheme outperforms the other schemes when km/kcis small or V is large.
5. Conclusions
This paper studied the LTE TAL-based mobility manage-ment scheme by measuring the expected number Cu of location updates during the inter-call arrival time and the expected number Cp of cells that page the UE when an incoming call arrives. The TAL-based scheme is com-pared with the movement-based and the distance-based schemes with the SDF paging. We note that the
distance-Fig. 9. Effects of V and p on Cp,s(NC= 52, NT= 32,Np= 3, and K = 8).
Table 2
The mobility management scheme with the lowest paging cost under different km/kc, V, and p values.
Small km/kc Large km/kc
Small V Large V Small V Large V
Small p Large p Small p Large p Small p Large p Small p Large p
based scheme and the SDF paging cannot be practically implemented, while the TAL-based scheme is a partial implementation of the distance-based scheme with the SDF paging, which can be actually realized. Therefore, the distance-based and the SDF paging schemes are considered as the ‘‘optimal performance bounds’’ for the TAL-based scheme. Surprisingly, our study indicates that in many sce-narios, the TAL-based scheme outperforms the other two schemes, and the details are described as follows.
For the Cuperformance, the distance-based scheme out-performs the TAL-based and the movement-based schemes when (1) p is small (i.e., the UE movement exhibits locality) or(2)km/kcand V are small (i.e., the UE moves infrequently and the movement pattern is regular). On the other hand, the TAL-based scheme has the lowest location update cost when (1) km/kc and p are large or(2)V and p are large.
For the Cpperformance, the movement-based scheme with the SDF paging outperforms the other schemes when km/kcis large and V is small. For other scenarios (i.e., when km/kcis small or V is large), the TAL paging outperforms the SDF paging.
As a final remark, the LTE mobility management raises many research issues. In the future, we will study load dis-tribution over multipath network[14], power saving[15], and so on.
Acknowledgements
R.-H. Liou’s work was supported by the MediaTek Fel-lowship. Y.-B. Lin’s work was supported in part by NSC 100-2221-E-009-070 and 101-2221-E-009-032, Academia Sinica AS-102-TP-A06, Chunghwa Telecom, IBM, Arcadyan
Technology Corporation, ICL/ITRI project under
B301EA3300, B301AR2R10, and B352BW1100, Nokia Sie-mens Networks, Department of Industrial Technology (DoIT) Academic Technology Development Program 100-EC-17-A-03-S1-193, and the MoE ATU plan.
Appendix A. Notation
The notation used in this paper is listed below. p: the probability that the UE moves to the right-hand
side neighboring cell
hx, yi: the column and the row labels of an arbitrary cell in a TAL, respectively
hx; yi: the column and the row labels of the last inter-acted cell, respectively
hx⁄, y⁄
i: the column and the row labels of the cell where the UE currently resides, respectively
hX, Yi: the column and the row labels of an arbitrary TA in a TAL, respectively
K: the location update threshold for the movement-based and the distance-movement-based schemes
Aj: the subarea j in the SDF paging lj: the left-hand side boundary value of Aj
rj: the right-hand side boundary value of Aj
Cu,s: the expected number of location updates between two consecutive incoming calls for the ‘‘s’’ scheme, where s 2 {T, M, D} denoting the TAL-based, the move-ment-based, and the distance-based location updates, respectively
Cp,s: the expected number of cells that page the UE when an incoming call arrives for the TAL paging (s = T), the movement-based scheme with the SDF pag-ing (s = M), and the distance-based scheme with the SDF paging (s = D), respectively
T: a long observation period t: the simulation clock tc: the inter-call arrival time
tm: the inter-move time (i.e., the cell residence time) 1/kc= E[tc]: the mean inter-call arrival time
1/km= E[tm]: the mean inter-move time V: the variance for the tmdistribution NC: the number of cells in a TA NT: the number of TAs in a TAL
Np: the maximum number of the polling cycles before the UE is found
na: the number of call arrivals nu: the number of location updates
np: the number of cells that page the UE when an incoming call arrives
nC: the number of the inter-call arrival intervals tcin T nM: the number of the cell crossings in T
nm: the number of cell crossings after the last interac-tion with the network
GC: the exponential random number generator GM: the Gamma random number generator GD: the uniform random number generator e,e1,e2: the events in the simulation
U: the uniform random number drawn from GD
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Ren-Huang Liou received the B.S. and the M.S. degrees in Computer Science from National Chiao Tung University (NCTU), Hsinchu, Taiwan, ROC, in 2007 and 2009, respectively. He is currently working toward the Ph.D. degree at NCTU. His current research interests include Voice over Internet Protocol (VoIP), mobile computing, and performance modeling.
Yi-Bing Lin is Vice President and Life Chair professor of College of Computer Science, National Chiao Tung University (NCTU), and a Visiting professor of King Saud University. He is also with Institute of Information Science and the Research Center for Information Technology Innovation, Academia Sinica, Nankang, Taipei, Taiwan, ROC. Lin is the authors of the books Wireless and Mobile Net-work Architecture (Wiley, 2001), Wireless and Mobile All-IP Networks (John Wiley, 2005), and Charging for Mobile All-IP Telecommunica-tions(Wiley, 2008). Lin received numerous research awards including 2005 NSC Distinguished Researcher and 2006 Academic Award of Min-istry of Education. Lin is an ACM Fellow, an AAAS Fellow, an IEEE Fellow and an IET Fellow.
