Published online 2 April 2013 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/wcm.2371
RESEARCH ARTICLE
A dynamic paging scheme for long-term evolution
mobility management
Yi-Bing Lin, Ren-Huang Liou*and Chun-Ting Chang
Department of Computer Science, National Chiao Tung University, Taiwan
ABSTRACT
In long-term evolution, the service area is partitioned into several tracking areas (TAs), which comprise one or more cells (the radio coverages of base stations). The TAs are grouped into TA list (TAL). When an incoming call arrives, the net-work attempts to connect to the user equipment (UE) by paging the cells in the UE’s TAL, which may incur large paging traffic that significantly consumes the limited radio resources. To resolve this issue, this paper proposes a dynamic paging scheme that determines the paging sequence of cells in real time according to the UE movement and call behavior. We compare the performance of the dynamic paging with that of the previously proposed Cell-TA-TAL (CTT) paging. Our study indicates that the dynamic paging outperforms the CTT paging when movement pattern is regular and the UE moves frequently. Copyright © 2013 John Wiley & Sons, Ltd.
KEYWORDS
dynamic paging; long-term evolution (LTE); mobility management *Correspondence
Ren-Huang Liou, Department of Computer Science, National Chiao Tung University, Taiwan. E-mail: rhliou@cs.nctu.edu.tw
1. INTRODUCTION
Mobility management of mobile telecom networks [1–4] tracks the user equipment (UE) through the location update and the paging procedures. The location update proce-dure is executed when the UE moves from one location to another location. When the network attempts to connect to the UE (e.g., when an incoming call arrives), the network executes the paging procedure by broadcasting the pag-ing messages to the base stations where the UE probably resides.
In long-term evolution (LTE), the mobility management entity (MME; Figure 1 (a)) is responsible for tracking the locations of the UEs [5–7]. The MME is connected to a group of base stations (evolved Node B). The radio cov-erages of the base stations are called cells (Figure 1 (b)). These cells are grouped into non-overlapped tracking areas (TAs) [5,6]. For example, in Figure 1 (c), TA 1 includes Cells 1 and 2. Every TA has a unique TA identity (TAI). The TAs are further grouped into the TA lists (TALs). The MME allocates the TAL to the UE via the location update procedure. For example, if the UE (Figure 1 (1)) updates its location in Cell 4, the MME allocates TAL 1 (Figure 1 (d)) to the UE, where TAL 1 D fTA 1; TA 2; TA 3g. Every base station periodically broadcasts its TAI. The UE detects that
it has left the current TAL by searching the TAL for the TAI received from the the base station. If the received TAI is found in the TAL, it means that the UE does not leave the current TAL. Otherwise, the UE executes the location update procedure to inform the MME of its new location. Then, the MME allocates a new TAL to the UE. In Figure 1, when the UE moves from Cell 4 to Cell 7 (Figure 1 (2)), the received TA 4 identity is not found in TAL 1. Therefore, the UE performs the location update procedure, and the MME allocates TAL 2 to the UE. For the TAL allocation, we consider the central policy [5] that allocates the TAL whose central TA is the TA where the UE currently resides. In the central policy, the allocated TALs may be overlapped. For example, in Figure 1, both TALs 1 and 2 include TA 3.
When an incoming call arrives, the MME sends the pag-ing messages to the cells in the UE’s TAL to search the UE, which may incur large traffic that significantly con-sumes the limited radio resources. To resolve this issue, we propose a dynamic paging scheme exercised at the MME to reduce the paging traffic.
This paper is organized as follows. Section 2 proposes the dynamic paging scheme. Section 3 describes a sim-ulation model for this scheme. Section 4 investigates the performance of the dynamic paging scheme by numerical
UE UE TA 1 TAL 1 1 2 c d MME Cell 1 Cell 2 Cell 3 Cell 4 Cell 5 Cell 6 Cell 7 Cell 8 Cell 9 Cell 10 TA 2 TA 3 TA 4 TA 5 TAL 2 b a
Figure 1. Long-term evolution mobility management architecture.
Table I. The acronym list.
3G Third-generation
CTT Cell-TA-TAL
LTE Long-term evolution MME Mobility management entity
TA Tracking area
TAI Tracking area identity TAL Tracking area list
TT TA-TAL
UE User equipment
examples, and the conclusions are given in Section 5. The acronyms used in the paper are listed in Table I.
2. DYNAMIC PAGING SCHEME
On the basis of the TA/TAL architecture described in Section 1, we have considered three paging schemes for LTE mobility management in [8]. The details are re-iterated here for the reader’s benefit. In these schemes, an interacted cell refers to a cell where the UE has inter-acted with the network (e.g., receives a call or performs a location update).
Scheme Cell-TA-TAL (CTT). When an incoming call arrives, the MME first sends the paging message to the last interacted cell to alert the UE. If the MME does not receive the response within a timeout period, the MME sends the paging messages to the TA of the last interacted cell. If the MME still receives no response
from the UE, the MME sends the paging messages to all cells in the TAL.
Scheme TA-TAL (TT). When an incoming call arrives, the MME sends the paging messages to the TA of the last interacted cell. If the MME does not receive the response within a timeout period, the MME sends the paging messages to all cells in the TAL.
Scheme 3G (traditional third-generation approach). When an incoming call arrives, the MME sends the paging messages to all cells in the TAL simultaneously. This scheme is used in the existing 3G mobile networks [1]. We define a polling cycle [9] as the period between when the MME sends a paging message to alert the UE and when the MME receives the paging response or a timeout occurs. Let Np be the maximum number of polling cycles before
the UE is found. The numbers Npof the CTT, the TT, and
the 3G schemes are 3, 2, and 1, respectively.
In [8], the performance of the three schemes was evalu-ated. The study indicated that depending on the UE move-ment patterns and call activities, one paging scheme may outperform the other two. This paper proposes a dynamic paging scheme that automatically selects the ‘best’ paging scheme in real time according to the UE movement and call behavior.
Ideally, the dynamic paging selects the paging scheme with the smallest number of paged cells. Practically, the selection decision for a UE is made on the basis of the UE’s recent ‘behavior history’. Specifically, for the UE, the MME computes the average number of paged cells for the CTT, TT, and 3G schemes in the m most recent incom-ing call arrivals. When the i th incomincom-ing call arrives, we define Cp;s.i / as the average number of paged cells for
the s scheme in the mD mi nfi 1; mg most recent call arrivals, where s 2 fC T T ; T T ; 3Gg. When i D 1, we do not have any history datum, and Cp;s.1/ D 0 for all
s 2 fC T T ; T T ; 3Gg. To compute Cp;s.i / with i 2,
we first introduce three scenarios when an incoming call arrives. In this paper, we denote NC and NT as the
num-ber of cells in a TA and the numnum-ber of TAs in a TAL, respectively.
Scenario 1. The UE resides in the last interacted cell. In this scenario, the number of cells that page the UE for CTT, TT, and 3G schemes are 1; NC, and NCNT,
respectively. In Figure 1, suppose that the last inter-acted cell is Cell 4. In this scenario, Cell 4 will page the UE for CTT. On the other hand, Cells 3 and 4 (TA 2) will page the UE for TT, and Cells 1-6 (TAL 1) will page the UE for 3G.
Scenario 2. The UE resides in the TA of the last interacted cell but is not in the last interacted cell. In this sce-nario, the number of cells that page the UE for CTT, TT, and 3G schemes are 1 C NC; NC, and NCNT,
respectively. In Figure 1, suppose that the last inter-acted cell is Cell 4. For CTT paging, Cell 4 will page the UE, and then Cells 3 and 4 (TA 2) will page the UE. For TT paging, Cells 3 and 4 (TA 2) will page
the UE. For 3G paging, Cells 1-6 (TAL 1) will page the UE.
Scenario 3. The UE resides in the TAL but is not in the TA of the last interacted cell. In this scenario, the num-ber of cells that page the UE for CTT, TT, and 3G schemes are 1 C NC C NCNT; NC C NCNT and
NCNT, respectively. In Figure 1, suppose that the
last interacted cell is Cell 4. For CTT paging, Cell 4 will page the UE, then Cells 3 and 4 (TA 2) will page the UE, and finally Cells 1–6 (TAL 1) will page the UE. For TT paging, Cells 3 and 4 (TA 2) will page the UE, and then Cells 1–6 (TAL 1) will page the UE. For 3G paging, Cells 1–6 (TAL 1) will page the UE. In our approach, the MME records the scenario type of each call arrival. Let nI.i / be the number of scenarios I
that occurred between the .i m/th call arrival and the .i 1/th call arrival where I 2 f1; 2; 3g. On the basis of nI.i /, NC, and NT, Cp;s.i / is computed as Cp;C T T.i / D 8 ˆ ˆ < ˆ ˆ : n1.i / m C n 3.i / m .NCNT C 1/; for NCD 1 n1.i / m C n 2.i / m .1 C NC/ C n 3.i / m .1 C NCC NCNT/; for NC¤ 1 (1) Cp;T T.i / D n 1.i / C n2.i / m NC C n 3.i / m .NCC NCNT/ (2) and Cp;3G.i / D NCNT (3)
In (1), for NC D 1 (i.e., the TA only contains one cell,
and scenario 2 never occurs), if the UE is not found in the last interacted cell, all cells in the TAL will page the UE for the CTT paging. Therefore, for the CTT paging with NC D 1, the number of cells that page the UE in
scenario 3 is NCNT C 1. For CTT with NC ¤ 1, the
numbers of cells that page the UE are 1, 1 C NC, and
1 C NC C NCNT for scenarios 1, 2, and 3, respectively
(as previously mentioned). In (1)–(3), nI.i / is affected by
the movement patterns and call activities of a user. When the i th incoming call arrives, the MME selects the paging scheme with the smallest Cp;s.i / among the CTT, TT, and
3G schemes. We note that if two or more schemes have the smallest Cp;s.i /, the MME selects the one with the
smallest Npto reduce the paging delay.
3. SIMULATION MODEL
This section proposes a discrete-event simulation model (Monte Carlo simulation) to study the performance of the dynamic paging scheme. Note that our previous work indi-cated that the CTT scheme outperforms both the TT and
the 3G schemes with most input parameter setups [8]. Therefore, it suffices to compare the performance of the dynamic paging scheme with that of the CTT scheme. For the dynamic paging (denoted as s D D) and the CTT pag-ing (denoted as s D C T T ), we consider two performance measures as follows:
Cd ;s: the expected number of polling cycles before
the UE is found.
Cp;s: the expected number of paged cells when an
incoming call arrives.
It is clear that the smaller the aforementioned performance measures, the better the paging scheme.
For the demonstration purpose, we consider a two-dimensional (2D) mesh cell configuration (i.e., Manhattan-street-like layout) [10–15]. Figure 2 illustrates the mesh cell configuration, where a cycle represents a cell, and each cell has eight neighboring cells. Various movement
patterns can be investigated in our study. To highlight the effect of ‘movement locality’, we considered the scenario where a UE moves to one direction with a probability different from other directions [15]. In this paper, we extend the previous work by considering the following movement pattern: The UE moves to one of the upper-right, the upper-right, and the lower-right neighboring cells with the routing probability p and moves to one of the other neighboring cells with the probability .1 3p/=5. It is clear that the movement pattern has the best locality when p D 0:125.
On the basis of the mesh cell configuration, Figure 3 shows a TAL configuration, where NC D NT D 9. In the
TAL, the cells are labeled as hx; yi, where x is the column label, y is the row label, and 1 x; y pNCNT. The
1 - 3p
5
1 - 3p
5
1 - 3p
5
1 - 3p
5
1 - 3p
5
p
p
p
1,9 2,9 3,9 1,8 2,8 3,8 1,7 2,7 3,7 TA 1,3 6,9 5,9 4,9 6,8 5,8 4,8 6,7 5,7 4,7 TA 2,3 9,9 8,9 7,9 9,8 8,8 7,8 9,7 8,7 7,7 TA 3,3 1,6 2,6 3,6 1,5 2,5 3,5 1,4 2,4 3,4 TA 1,2 6,6 5,6 4,6 6,5 5,5 4,5 6,4 5,4 4,4 TA 2,2 9,6 8,6 7,6 9,5 8,5 7,5 9,4 8,4 7,4 TA 3,2 1,3 2,3 3,3 3,2 2,2 1,2 3,1 2,1 1,1 TA 1,1 5,2 4,2 6,3 5,3 4,3 6,2 6,1 5,1 4,1 TA 2,1 9,3 8,3 7,3 9,2 8,2 7,2 9,1 8,1 7,1 TA 3,1
Figure 3. An example of the tracking area (TA) list configuration .NCD NTD 9/.
TAs are labeled as hX ; Y i, where 1 X ; Y pNT. TA
hX ; Y i consists of cells hx; yi where .X 1/pNCC 1
x XpNCand .Y 1/
p
NCC1 y Y
p
NC. To
sim-plify the discussions on the central policy, we assume that p
NT is an odd number. Because the central policy is
exer-cised, when the UE leaves the current TAL, the entrance TA is reset to the central TA of the ‘next’ TAL, and the entrance cell is reset to the cell in the central TA at the same relative position. For example, in Figure 3, when the UE in Cell h9; 1i moves to the right-hand side neighboring cell, the entrance cell is reset to Cell h4; 4i. In the simulation, an event e has two attributes as follows:
The type attribute indicates one of the two event types. A Call event represents a call arrival. When the
Call event occurs, the MME searches the UE through
the paging procedure. A Move event represents that the UE crosses the cell boundary to a neighboring cell. The t s attribute indicates the timestamp when the
event occurs.
The inter-call arrival time tc is a random number drawn
from an exponential generator GC with the mean 1=c.
The residence time tmthat the UE stays in a cell is a
ran-dom number drawn from a Gamma generator GMwith the
mean 1=mand the variance V . We consider the Gamma
distribution because this distribution is widely used in tele-com modeling [8,9,15–18]. Other distributions such as Weibull and truncated Normal show similar results and will not be presented here. Let U be a uniform random num-ber between 0 and 1 drawn from a generator GD. In this
simulation, the last interacted cell is labeled as h Nx; Nyi, and the cell where the UE currently resides is represented by hx; yi. Three counters are used to measure the output statistics as follows:
i : the number of incoming calls. nd: the number of polling cycles.
np: the number of paged cells.
From the aforementioned counters, we compute
Cd ;sD
nd
i and Cp;sD np
i (4)
The details of the simulation procedure are given in Appendix A.
We validate the simulation model of the dynamic pag-ing by two analytic models as follows. Our previous work [8] proposed the analytic models to derive the paging costs of the CTT and TT schemes for the one-dimensional (1D) TAL configuration. The validation procedure is described with the following steps:
Step 1.1. For some input parameter setups (e.g., m=cD
0:01, V D 1=2m, NC D 3, NT D 15, p D 0:5,
and m D 50), the dynamic paging will select the CTT scheme to search the UE in most incoming calls (more than 99%). In this case, we compare the paging cost of the dynamic paging with that of the CTT scheme derived in [8]. Our study indicates that the analytic and simulation results are consistent (the discrepancies are within 1%), and the details are omitted.
Step 1.2. Similar to Step 1.1, when m=c D 10, V D
1=2m, NC D 3, NT D 15, p D 0:9, and m D 50,
the dynamic paging will select the TT scheme in most incoming calls. Our study also shows that the analytic and simulation results are consistent (the discrepancies are within 1%).
Step 1.3. For other input parameter setups, the dynamic paging may not always select the same paging scheme. We modify the simulation program to record the percentages of calls where the CTT, TT, and 3G schemes are exercised. From the percentages and the paging costs derived in [8], we compute the expected paging cost of the dynamic paging scheme and com-pare the expected paging cost with the simulation results. Our study indicates that the discrepancies are within 1%, and the analytic analysis is consistent with the simulation results.
4. NUMERICAL EXAMPLES
This section compares the performance of the dynamic paging scheme and the CTT paging scheme by numerical examples. We consider the TAL’s size NCNT D 152. For
other NCNT values, the results are similar and are
omit-ted. Our simulation experiments also show that m 10 is appropriate. In this paper, we consider m D 20 and NCD 32.
4.1. Analysis of theCd ;sperformance
This subsection investigates the effects of p, m=c, and
V on the expected number Cd ;s of polling cycles before
the UE is found.
Effects ofp: When p increases, the UE tends to move to the right-hand side neighboring cells, and worse locality is expected. In this case, the UE is more likely to be far away from the last interacted cell. There-fore, both Cd ;Dand Cd ;C T Tincrease as p increases.
Figure 4 (a) shows that Cd ;D=Cd ;C T T increases as
p increases, and the effect of p becomes more signif-icant when m=c increases (to be discussed next).
Clearly, the more the locality, the more the dynamic scheme outperforms the CTT scheme.
Effects ofm=c: When m=c increases (i.e., more
cell crossings during tc), the UE may be far away
from the last interacted cells, and higher Cd ;D and
Cd ;C T T are expected. Figure 4 (b) indicates that
Cd ;D=Cd ;C T T decreases as m=c increases. This
phenomenon is explained as follows. When m=c
increases, the dynamic paging is more likely to select the TT or the 3G scheme because the UE may be far away from the last interacted cell. Because the pag-ing delays of the TT and 3G schemes are smaller than that of the CTT scheme, Cd ;D=Cd ;C T Tdecreases as
m=cincreases. The figure shows that the dynamic
Figure 4. Effects ofp and m=conCd;D=Cd;CTT.NCD 32,NTD 52,m D 20, and V D 1=2m/.
Figure 6. Effects of m=c,p, and V on Cp;D=Cp;CTT(NCD 32,NTD 52, andm D 20).
scheme outperforms the CTT scheme in the m=c
range being considered. We have also considered the scenario where m=c changes from time to time,
and similar results are observed, which will not be presented here.
Effects ofV : When V is small (i.e., movement pattern is regular), most tm values are close to 1=m. In this
case, if m=c is small, the UE is more likely to be
found in the last interacted cell, and the dynamic and CTT schemes have similar (and good) Cd ;s
perfor-mance (in Figure 5, for V 1=2m, the values of the ı and curves are close to 1). On the other hand, when m=c is large, dynamic paging outperforms
CTT paging because the dynamic paging scheme is more likely to select the TT or the 3G scheme, which has smaller paging delay (in Figure 5, for V 1=2m, the values of the ˘ curves are smaller than 1). For any mvalue, when V increases, more longer tmperiods
are observed, and the UE does not move in many con-secutive tc periods that fall in these tm. In this case,
the UE is always found in the last interacted cell, and both the dynamic paging and the CTT paging have similar performance (in Figures 5, for V > 102=2m,
the values of all curves are close to 1).
4.2. Analysis of theCp;sperformance
This subsection investigates the expected number Cp;s of
paged cells when an incoming call arrives. The effects of m=c, p, and V on Cp;s are similar to those on Cd ;s
described in Subsection 4.1. However the ‘degrees’ of the effects of these parameters on Cp;sand Cd ;s for the CTT
and the dynamic schemes are different. A nontrivial result is that Cp;D=Cp;C T T 1 for various m=c, p, and V
values (as illustrated in Figure 6). The reason is given as
follows. When m=cis small, it is more likely to find the
UE in the last interacted cell. In this case, dynamic pag-ing selects the CTT scheme to search the UE, and both the dynamic and CTT pagings have similar and good per-formance (in Figure 6, the values of the ı and curves are close to 1). On the other hand, when m=c is large,
the dynamic paging is more likely to select the TT or the 3G scheme. In this case, if p is small, we observe that the dynamic paging likely selects the TT scheme, which has a slightly lower paging cost than the CTT scheme [8]. There-fore, the dynamic paging outperforms the CTT paging (in Figure 6(a), the values of the ˘ curve are smaller than 1). On the other hand, if p is large, because of the high pag-ing cost of the 3G scheme, the pagpag-ing cost of the dynamic scheme is slightly higher than that of the CTT scheme (in Figure 6(b), the values of the ˘ curve are slightly larger than 1). We note that the performance discrepancies of the paging cost between the dynamic and the CTT pagings are within 0:2% for all input parameter setups under our study.
5. CONCLUSIONS
This paper proposed the dynamic paging scheme for LTE mobility management. The performance is measured by the expected number Cd ;sof polling cycles before the UE
is found and the expected number Cp;sof paged cells when
an incoming call arrives. We compare the performance of the dynamic paging with the best static paging scheme called CTT. Our study indicates the following results:
For the Cd ;s performance, when V is small and
m=c is large (i.e., movement pattern is
regu-lar and the UE moves frequently), the dynamic paging outperforms the CTT paging. On the other hand, when V is large or m=c is small, the
dynamic paging and the CTT paging have similar performance.
For the Cp;s performance, the dynamic and CTT
schemes have similar performance for all input parameter setups under our study.
In summary, the dynamic paging scheme is better than the CTT paging scheme.
APPENDIX A: DETAILED
SIMULATION PROCEDURES
This appendix describes the detailed simulation proce-dures for the dynamic and CTT schemes. 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. An array I Œi is maintained to record the sce-nario type of the i th incoming call (e.g., I Œi D 1 means that the UE resides in the last interacted cell when the i th call arrives). Figure A.1 illustrates the simula-tion flow chart for the dynamic paging scheme with the following steps:
Step 1. Set the counters (i.e., i , nd, and np) and
the simulation clock t to 0. Initialize Nx, Ny, x, and y by randomly selecting integers from 1 to p
NCNT.
Step 2. The first Call event e1and Move event e2are
gen-erated. For event e1, e1:type is Call, and e1:t s D
t C tc where tcis generated from GC. For event e2,
e2:type is Move, and e2:t s D t C tm where tm is
generated from GM. Events e1 and e2 are inserted
into the event list.
Steps 3 and 4. The first event e in the event list is deleted and processed on the basis of its type. The simulation clock t is set to e:t s. If e:type is Call, Step 5 is exe-cuted. If e:type is Move, the simulation proceeds to Step 20.
Steps 5–17 simulate a Call event, which are described as follows.
Step 5. When an incoming call arrives, i is incremented by one.
Step 6. As mentioned in Section 2, if i = 1, we do not have any history datum to estimate the paging cost of each paging scheme. In this case, we select the 3G scheme because the 3G scheme has the smallest paging delay, and Step 15 is executed. Otherwise, the flow goes to Step 7.
Step 7. The MME computes nI.i / based on I Œj where
i m j i 1, and for s 2 fC T T ; T T ; 3Gg, Cp;s.i / are calculated from nI.i / and equations
(1)–(3).
Step 8. As mentioned in Section 2, the MME selects the paging scheme s with the smallest Cp;s.i /. If two or
more schemes have the smallest Cp;s.i /, the one with
the smallest Npis selected.
Step 9. If s D C T T , Step 10 is executed. If s D T T , the simulation proceeds to Step 13. If s D 3G, the flow goes to Step 15.
Steps 10 and 11 (CTT is exercised). The MME sends the paging message to the last interacted cell, and both ndand npare incremented by one. If the UE resides
in the last interacted cell (i.e., xD Nx and yD Ny), then the UE will receive the paging message, and the simulation proceeds to Step 16. Otherwise, Step 12 is executed.
Step 12. If a TA only contains one cell (i.e., NCD 1), the
TA of the last interacted cell has paged the UE in Step 10, and the UE is not found in Step 11. In this case, Step 15 is executed to search the UE in all cells of the TAL. Otherwise, the flow goes to Step 13.
Steps 13 and 14 (TT is exercised). The MME sends the paging messages to the TA of the last interacted cell. Therefore, npis incremented by NC, and ndis
incre-mented by one. If the UE resides in the TA of the last interacted cell (i.e.,˙x=pNCD ˙x=N
p NC
and ˙y=pNC D ˙y=N
p
NC), the UE is found,
and Step 16 is executed. Otherwise, the simulation proceeds to Step 15.
Step 15 (3G paging is exercised). The MME sends the paging messages to all cells in the TAL. Therefore, npis incremented by NCNT, and ndis incremented
by one.
Step 16. The MME records the scenario type I Œi of the i th incoming call as follows:
ifxD Nx and yD Ny then I Œi 1;
else if˙x=pNCD˙x=N p NCand ˙ y=pNCD˙y=N p NCthenI Œi 2; elseI Œi 3.
Then, the MME updates the last interacted cell by setting h Nx; Nyi to hx; yi.
Step 17. The next Call event e1is generated and inserted
into the event list, where e1:t s D t C tc.
Step 18. If 10 million of Call events have been processed, Step 19 is executed. Otherwise, Step 3 is executed. In our experience, 10 million of Call events are enough to produce stable statistics.
Step 19. The performance measures are computed by (4), and the simulation terminates.
Steps 20–24 handle a Move event, which are described as follows.
Step 20. When the UE crosses the cell boundary to a neighboring cell, the movement direction is deter-mined by the uniform random number U generated by GD. From Figure 2, new hx; yi are updated by
Figure A.1. Simulation flow chart for the dynamic paging scheme. hx; yi 8 ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ < ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ ˆ : hx 1; yC 1i; for 0 U <1 3p 5 hx 1; yi; for1 3p 5 U < 2.1 3p/ 5 hx 1; y 1i; for2.1 3p/ 5 U < 3.1 3p/ 5 hx; yC 1i; for3.1 3p/ 5 U < 4.1 3p/ 5 hx; y 1i; for4.1 3p/ 5 U < 1 3p hxC 1; yC 1i; for 1 3p U < 1 2p hxC 1; yi; for 1 2p U < 1 p hxC 1; y 1i; for 1 p U 1 (A.1)
Step 21. If the UE leaves the current TAL (i.e., xp D 0 or NCNTC 1, or yD 0 or
p
NCNTC 1), Step 22 is
executed. Otherwise, Step 24 is executed.
Step 22. As mentioned before, when the UE leaves the cur-rent TAL, the entrance cell is reset to the cell in the central TA. Therefore, xand yare set as
x pNC p NT 2 x p NC C x (A.2) and y pNC pN T 2 y p NC C y (A.3) Step 23. The MME updates the last interacted cell by
setting h Nx; Nyi to hx; yi.
Step 24. The next Move event e2is generated and inserted
into the event list, where e2:t s D t Ctm. The simulation
jumps to Step 3.
The simulation flow chart for the CTT scheme is sim-ilar to that in Figure A.1 except that Steps 6–9 and the array I Œi in Step 16 are not needed in the CTT simu-lation. Moreover, after the execution of Step 5, the CTT simulation goes to Step 10.
APPENDIX B: NOTATION
The notation used in this paper is listed in the succeeding text.
p: the probability that the UE moves to one of the upper-right, right, and lower-right neighboring cells. hx; yi: the label of an arbitrary cell in a TAL
(x: column label; y: row label).
h Nx; Nyi: the label of the last interacted cell ( Nx: column label; Ny: row label).
hx; yi: the label of the cell where the UE currently resides (x: column label; y: row label).
hX ; Y i: the label of an arbitrary TA in a TAL (X : column label; Y : row label).
Cd ;s: the expected number of polling cycles before
the UE is found for the dynamic paging .s D D/ and the CTT paging .s D C T T /, respectively.
Cp;s: the expected number of paged cells when an
incoming call arrives for the dynamic paging .s D D/ and the CTT paging .s D C T T /, respectively. Cp;s.i /: the average number of paged cells for the s
scheme between the .i m/th call arrival and the .i 1/th call arrival, where s 2 fC T T ; T T ; 3Gg. t : the simulation clock.
tc: the inter-call arrival time.
tm: the cell residence time.
1=cD EŒtc: the mean inter-call arrival time.
1=mD EŒtm: the mean cell residence time.
V : the variance for the tmdistribution.
m: the number of the most recent incoming call arrivals.
m: the smaller of i 1 and m. NC: the number of cells in a TA.
NT: the number of TAs in a TAL.
Np: the maximum number of polling cycles before
the UE is found.
nI.i /: the number of scenarios I occurred between
the .i m/th call arrival and the .i 1/th call arrival where I 2 f1; 2; 3g.
i : the number of incoming calls. nd: the number of polling cycles.
np: the number of paged cells.
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.
I Œi : the scenario type of the i th incoming call arrival. s: the paging scheme (s D D for dynamic paging, s D C T T for Cell-TA-TAL paging, s D T T for TA-TAL paging, and s D 3G for third generation paging).
ACKNOWLEDGEMENTS
Y.-B. Lin’s work was supported in part by the NSC 100-2221-E-009-070 and 101-2221-E-009-032, Academia Sinica AS-102-TP-A06, Chunghwa Telecom, IBM, Arcadyan Technology Corporation, the ITRI/NCTU JRC Research Project, the ICL/ITRI Project, Nokia Siemens Networks, Department of Industrial Technology (DoIT) Academic Technology Development Program 100-EC-17-A-03-S1-193, and the MoE ATU plan. R.-H. Liou’s work was supported by the MediaTek Fellowship.
REFERENCES
1. Lin Y-B, Pang A-C. Wireless and Mobile All-IP Net-works. John Wiley & Sons, Inc.: Indianapolis, Indiana, 2005.
2. Pan Y-N, Chen W-E. Enhanced secure SIP/IMS mobility in integrated UMTS-WLAN networks, In Smart Mobility, Nice, France, 2011.
3. Yang S-R, Lin Y-B. Performance evaluation of loca-tion management in UMTS. IEEE Transacloca-tions on Vehicular Technology 2003; 52(6): 1603–1615. 4. Lin Y-B, Pang A-C, Rao Herman C-H. Impact of
mobility on mobile telecommunications networks. Wireless Communications and Mobile Computing 2005; 5(7): 713–732.
5. 3rd Generation Partnership Project; Technical Spec-ification Group Services and System Aspects; Gen-eral Packet Radio Service (GPRS) enhancements for
Evolved Universal Terrestrial Radio Access Network (E-UTRAN) access, 3GPP. Technical Specification 3G TS 23.401 version 10.0.0 (2010-06), 2010.
6. 3GPP. 3rd Generation Partnership Project; Technical Specification Group Radio Access Network; Evolved Universal Terrestrial Radio Access (E-UTRA) and Evolved Universal Terrestrial Radio Access Network (E-UTRAN); Overall description; Stage 2. Technical Specification 3G TS 36.300 version 10.1.0 (2010-09), 2010.
7. Punz G. Evolution of 3G Networks: The Concept, Architecture and Realization of Mobile Networks Beyond UMTS. Springer: New York, 2010.
8. Liou R-H, Lin Y-B, Tsai S-C. An investigation on LTE mobility management. IEEE Transactions on Mobile Computing 2013; 12(1): 166–176.
9. Akyildiz I, Ho J, Lin Y-B. Movement-based loca-tion update and selective paging for PCS networks. IEEE/ACM Transactions on Networking 1996; 4(4): 629–638.
10. Maxemchuk N. Routing in the Manhattan street net-work. IEEE Transactions on Communications 1987;
35(5): 503–512.
11. Meyer H, Trullols-Cruces O, Hess A, Hummel K, Barcelo-Ordinas J, Casetti C, Karlsson G. VANET mobility modeling challenged by feedback loops, In 2011 the 10th IFIP Annual Mediterranean Ad Hoc Networking Workshop (Med-Hoc-Net), Sicily, Italy, 2011; 95–102.
12. Kraaier J, Killat U. The influence of user mobility on vehicular internet access via IEEE 802.11 access points, In IEEE International Conference on Wireless and Mobile Computing, Networking and Communica-tions, Montreal, Canada, 2006; 335–342.
13. Tchakountio F, Ramanathan R. Tracking highly mobile endpoints, In Proceedings of the 4th ACM International Workshop on Wireless Mobile Multimedia, Rome, Italy, 2001; 83–94.
14. Moustafa M, Habib I, Naghshineh M. Efficient radio resource control for Manhattan street environments. IEEE International Conference on Communications 2002; 5: 3377–3381.
15. Liou R-H, Lin Y-B. Mobility management with the central-based location area policy. Computer Networks 2012. DOI: 10.1016/j.comnet.2012.11.003.
16. Lai Y-C, Lin P, Cheng S-M. Performance modeling for application-level integration of heterogeneous wireless networks. IEEE Transactions on Vehicular Technology 2009; 58(5): 2426–2434.
17. Sou S-I, Jeng J-Y, Lin P. Improving session conti-nuity through user mobility tracking for EPS inter-serving gateway handover. Wireless Communications and Mobile Computing 2012; 12(12): 1077–1090. 18. Pang A-C, Chen Y-K. A multicast mechanism
for mobile multimedia messaging service. IEEE Transactions on Vehicular Technology 2004; 53(6): 1891–1902.
AUTHORS’ BIOGRAPHIES
Yi-Bing Lin is the vice president and
life chair professor of the College of Computer Science, National Chiao Tung University (NCTU) and a visit-ing professor of Kvisit-ing Saud University. He is also with the Institute of Informa-tion Science and the Research Center for Information Technology Innova-tion, Academia Sinica, Nankang, Taipei, Taiwan. Lin is the author of the books Wireless and Mobile Network Archi-tecture (Wiley, 2001), Wireless and Mobile All-IP Net-works (John Wiley, 2005), and Charging for Mobile All-IP Telecommunications (Wiley, 2008). Lin received numer-ous research awards including the 2005 NSC Distinguished Researcher and the 2006 Academic Award of Ministry of Education. Lin is a fellow of ACM, AAAS, IEEE, and IET.
Ren-Huang Liou received his BS and
MS degrees in Computer Science from the National Chiao Tung University (NCTU), Hsinchu, Taiwan, in 2007 and 2009, respectively. He is currently working toward his PhD degree at NCTU. His current research interests include Voice over Internet Protocol (VoIP), mobile computing, and performance modeling.
Chun-Ting Chang received his BS
degree in Computer Science from the National Chiao Tung University (NCTU), Hsinchu, Taiwan, in 2012. She is currently working toward her MS degree at NCTU. Her current research interests include design and analysis of personal communications services net-work and mobile augmented reality.
