Reducing Signaling Overhead for
Femtocell/Macrocell Networks
Huai-Lei Fu, Student Member, IEEE,
Phone Lin, Senior Member, IEEE, and Yi-Bing Lin, Fellow, IEEE
Abstract—Femtocell technology has been proposed to offload user data traffic from the macrocell to the femtocell and extend the limited coverage of the macrocell in mobile communications networks. In existing commercial femtocell/macrocell networks, a widely accepted solution to configure the location areas (LAs) is to partition the femtocells overlapped with a macrocell into small groups and to assign each group with a unique LA ID different from that of the macrocell. Such configuration can reduce the paging cost in the mobility management, but increases registration signaling overhead due to discontinuous coverage of femtocells. To reduce signaling overhead in the femtocell/macrocell network, we propose a delay registration (DR) algorithm that postpones the registration until the delay timer expires when the mobile station (MS) moves into the overlapped femtocell. Analytical models and simulation experiments are proposed to investigate the performance of the DR algorithm. Our analytical models are generally enough to accommodate various MS mobility behaviors. Our study can provide guidelines for the operators to set up a delay timer to reduce signaling overhead while sustaining the traffic offloading capability of the femtocell.
Index Terms—Femtocell, macrocell, mobile communications networks, mobility management
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1
I
NTRODUCTIONI
Na mobile communications network (MCN), the servicearea is populated with base stations (BSs). The radio coverage of a BS (or a sector of the BS) is called a cell. In an outdoor environment, network operators deploy macro-cells with radio coverage area of 0.5 to 2 kilometer-radius. The fast growing population of mobile users leads to an exponential increase in user data traffic demand for the MCN, but the capacity of outdoor macrocells are not sufficient to satisfy such demand.
The femtocell [1], [2], [3] (also called home BS) with low deployment cost was proposed to offload the user data traffic to the macrocell and extend the limited coverage of the macrocell. A femtocell is the radio coverage of a short-range, low-cost, and low-power wireless BS, typically covering an area with the radius of 5 to 20 meters [2]. Femtocells operate in the same licensed spectrum as a macrocell. In femtocell and macrocell deployment environ-ment planned by some mobile network operators, hundreds to thousands of femtocells are overlapped with a macrocell. In the viewpoint of mobile network operators, traffic offloading is one of the major reasons for femtocell deploy-ment. When a mobile station (MS) resides in a femtocell overlapped with a macrocell, as long as the MS has the
authority to access the femtocell, the MS prefers to connect to the femtocell so as to offload traffic to the macrocell.
We name the MCNs with femtocells and macrocells as femtocell/macrocell networks. Fig. 1 depicts an example of the femtocell/macrocell network based on the universal mobile telecommunications system [4]. In this figure, the macrocell Cell (see the solid circle) overlays with the femtocells cell1; . . . ; cell5(see the dashed circles). The
macro-cell connects to the core network (CN; Fig. 1a) through the radio network controller (RNC; Fig. 1b). The femtocells connect to the CN through the femto gateway (Femto GW; Fig. 1c) and a broadband Internet network [5] (Fig. 1d). The Femto GW plays the role of an RNC. Importantly, the service area of femtocells may be discontinued. For example, in Fig. 1, cell1; . . . ; cell5can be treated as “islands” that do not
overlap with each other.
The cells in the femtocell/macrocell network are grouped into location areas (LAs). Each LA is assigned with a unique LA ID (LAI). The LAs are used for mobility management. The mobility management consists of “registration” and “call termination.” Each macrocell or femtocell uses a wireless broadcast channel to broadcast its individually corresponding LAI. The MS listens to the wireless broadcast channel to identify in which LA it resides. When the MS moves from one LA to another (that is, the LAI stored in the MS storage is different from the received LAI), the MS initiates a “registration” to report the LAI of the cell in which it resides to the location database in the CN. This process is also known as “location update.” “Call termination” refers to the process of routing an incoming call to an MS. In this process, the CN obtains the LA of the MS by querying the location database, instructs all cells in the LA to “page” the MS, and then sets up the call to the MS through the cell in which the MS responds to the “page.” Details of registration and call termination can be found in [6].
. H.-L. Fu and P. Lin are with the Department of Computer Science and Information Engineering, National Taiwan University, No. 1, Sec. 4, Roosevelt Rd., Taipei, Taiwan 106, R.O.C.
E-mail: vicfu@pcs.csie.ntu.edu.tw, plin@csie.ntu.edu.tw.
. Y.-B. Lin is with Department of Computer Science and Information Engineering, National Chiao Tung University, Engineering Building C, Kuang-Fu Campus, 1001 University Rd., Hsinchu, Taiwan 300, R.O.C. E-mail: liny@csie.nctu.edu.tw.
Manuscript received 7 Dec. 2011; revised 23 Mar. 2012; accepted 11 May 2012; published online 31 May 2012.
For information on obtaining reprints of this article, please send e-mail to: tmc@computer.org, and reference IEEECS Log Number TMC-2011-12-0659. Digital Object Identifier no. 10.1109/TMC.2012.132.
There are two alternatives to assign LAs in the femtocell/macrocell network [7], [8]. In the first alternative, all femtocells overlapped with a macrocell are assigned to the same LA as that of the macrocell. If more than hundreds of femtocells are overlapped with the macrocell, all of the femtocells and the macrocell must together page an MS for its incoming call, cumulating high paging cost. In the second alternative, the femtocells overlapped with the macrocell are partitioned into small groups, and each group is assigned with a unique LAI different from that of the macrocell.
Compared with the first alternative, the second alter-native significantly reduces the paging cost [8]. Hence, the second alternative is more often exercised in existing commercial MCNs. However, a potential problem of this second alternative is that registration occurs every time the MS moves between the macrocell and the overlapped femtocell, increasing signaling overhead to the network. Take, for example, the network architecture in Fig. 1, where the LA of the macrocell Cell is Lm, and Lf is the
LA assigned to the overlapped femtocells cell1, cell2; . . . ;
cell5. Since the service area of these femtocells is
discontinuous, when an MS moves from one femtocell to another, it crosses through the macrocell and switches between Lm and Lf, triggering registration. For example,
the MS movement Cell ! cell1! Cell ! cell2! Cell !
cell3! Cell ! cell4! Cell ! cell5! Cell results in as
many as 10 registrations.
In this paper, we focus on the location update issue in the femtocell/macrocell networks. To be more specific, we investigate the mobility management for the second alter-native of LA layout. The major challenge is that the frequent execution of registration due to small and discontinuous femtocell coverage causes high signaling overhead. Note that some mobile network operators exercise the business models such that private home BSs can be purchased by users, and each home BS can only be accessed by a particular user’s mobile devices. In this scenario, not many subsequent registrations will be sent to many femtocells, so the frequent registration issue does not exist.
Following most of location update studies [9], [10], [11], we do not consider channel capacity of femtocells or macrocells, which is an independent issue dealt by admission control. The channel capacity issue is out of the scope of this paper and should be treated separately to investigate original call admission and handoff strategies for femtocell/macrocell networks.
Previous works [12], [13], [14] have addressed the mobility management issue for the macrocell-microcell hierarchical mobile networks. Both [12] and [13] addressed
the mobility management issue for the macrocell-microcell hierarchical mobile networks in which microcell radio coverage is continuous, i.e., when an MS moves from one microcell to another, it does not cross any overlapped macrocell. On the other hand, our work addresses the issue caused by coverage discontinuity of femtocells. In [12], the authors proposed a macro-micro paging scheme (based on the predefined delay constraints) to balance the paging load between the macrocell and overlapped microcell. They did not focus on the signaling overhead reduction for registration (i.e., location update), and therefore, the proposed technique does not reduce regis-tration overhead. In [13], the authors proposed a cross-tier registration and paging scheme. In this scheme, a registra-tion is executed only when an MS crosses the boundary between two LAs in the macrocell tier. Based on the paging load, the CN determines whether to page an MS through the macrocell tier or microcell tier. The proposed scheme requires significant modification on the existing mobility management protocols at the CN side, which is considered impractical in the femtocell/macrocell net-works. Work [14] proposed the integration of high-tier mobile networks and low-tier mobile networks, and these networks operate in separate mobility management proto-cols. Work [14] also proposed intelligent algorithms to determine whether the MS should perform the registration operation when the MS switches tiers. The architecture considered in [14] is more complicated than the femtocell/ macrocell networks, and the performance is not as good as our approach due to an extra layer of mobility manage-ment integration of two networks.
In this paper, we propose the delay registration (DR) algorithm that postpones registration when an MS moves into the overlapped femtocell in the femtocell/macrocell network. Details of the DR algorithm are given in the next section. We propose analytical models and conduct simula-tion experiments to investigate the performance of the DR algorithm. In the proposed analytical models, we assume general distributions for the residence time periods in the overlapped femtocell and in the nonoverlapped areas of the macrocell. Our analytical model is generally enough to accommodate various MS mobility behaviors. The analy-tical model is validated against the simulation experiments. The remaining parts of the paper are organized as follows: Details of the DR algorithm are given in Section 2. In Section 3, we describe the analytical models. In Section 4, we evaluate the performance of the DR algorithm and provide guidelines for the setup of the delay timer. Section 5 concludes this paper.
2
T
HEDR A
LGORITHMThis section proposes the DR algorithm. The DR algorithm is exercised at the MS to determine whether the registration should be performed. No modification is required at the network side.
To simplify our description, we consider the following MS moving behavior: A macrocell overlays with several femtocells. Let Lmbe the LAI assigned to the macrocell and
Lf be the LAI assigned to the overlapped femtocells.
Initially, an MS is in the nonoverlapped area in the
macrocell, and Lm is the LAI stored in the location
database. At time t, the MS moves into the overlapped femtocell (i.e., the MS can also receive Lf) and stays in the
overlapped femtocell for tf. At t þ tf, the MS moves from
the overlapped femtocell into the macrocell, and can no longer receive Lf.
In the standard 3GPP algorithms for mobility manage-ment, at t one registration is executed to change Lmto Lf
in the location database, and at t þ tf another registration
is performed to change Lf to Lm. Here, two registrations
are performed. Note that if the MS just passes by the femtocell, that is, tf is as short as only a few seconds, we
describe the MS movement as transient. If transient occurs, it is most likely that no call behavior (call origination/ termination) will take place during ½t; t þ tf. Thus, these
two registrations during the transient period may be avoided without significantly affecting traffic offloading capability of the femtocell. To avoid registrations during the transient period, we propose the DR algorithm that introduces a delay timer to postpone the registration until the timer expires.
At t, the DR algorithm suspends the registration and starts the delay timer with length td. Two cases are considered:
. If td< tf, as the delay timer expires at t þ td, the MS
is still in the overlapped femtocell. The MS stops the delay timer and initiates the registration to change Lmto Lf.
. Otherwise (i.e., td tf), the MS stops the delay timer
at t þ tf, and no registration occurs during ½t; t þ tf.
During the period ½t; t þ minðtd; tfÞ, if a call requests
arrives, the request is potentially handled through the macrocell instead of through the overlapped femtocell, and the traffic may not be offloaded from the macrocell to the femtocell. Clearly, the longer the delay timer, the more signaling overhead (caused by registration) avoided. But meanwhile, it is more likely that the traffic to the macrocell cannot be offloaded. In the next section, we propose analytical models to study the tradeoff between signaling overhead reduction and traffic offloading capability.
To summarize, in Table 1, we compare the signaling overhead and traffic offloading capability of the MCN without femtocells, femtocell/macrocell networks with the standard 3GPP algorithms, and femtocell/macrocell net-works with the DR algorithm. The MCN without femtocells does not have traffic offloading capability nor the signaling overhead. The standard 3GPP has the high signaling overhead and high traffic offloading capability. On the other hand, the DR algorithm has the low signaling overhead, but medium to high traffic offloading capability.
The impacts of the DR algorithm on user experience, device energy consumption, and mobile network operators
are discussed as follows: With the DR algorithm, by properly setting the delay timer, the signaling overhead is reduced, and the traffic offloading capability of femtocells can still be achieved. In the femtocell/macrocell networks, more bandwidth is available, and the user will have better experience in call admission. For energy consumption, the DR algorithm reduces the number of registrations executed by an MS, thus saves the MS power consumption. For mobile network operators (or carriers), with the DR algorithm, less registrations (i.e., location database updates) will save more network bandwidth and switch capacity. Note that in most designs of CNs, as indicated in [15], 15 percent of computing power is allocated for location update. Intensive registration due to switching among femtocells and macrocells may exceed 15 percent of computing power and degrade the performance for the CN. Our DR algorithm reduces significant registration overhead in femtocell/macrocell networks.
3
A
NALYTICALM
ODELSIn this section, we propose analytical models to study the impacts of the setup of the delay timer on performance tradeoff between the signaling overhead and traffic off-loading capability. Our study provides guidelines for selecting an appropriate tdsuch that the signaling overhead
decreases, and the traffic offloading capability can still be achieved. The performance metrics derived in our analy-tical model includes two output measures signaling over-head ratio rðtdÞ and potential offload traffic ratio ðtdÞ.
Signaling overhead ratio rðtdÞ: Define a “crossing” as the
event when the MS moves from the macrocell to the overlapped femtocell or vice versa. Consider the intercall arrival time tcbetween two consecutive call request arrivals
to the MS. Let Nc be the number of crossings the MS has
during tc, and Nr be the number of registrations executed
by the MS during tc. Obviously, Nc Nr. If td¼ 0 (i.e., the
standard 3GPP algorithms are exercised), then Nr¼ Nc. We
denote E½NrðtdÞjNc 1 for the DR algorithm with delay td,
and E½Nrð0ÞjNc 1 for the 3GPP algorithms. We define
rðtdÞ as rðtdÞ ¼ E½NrðtdÞjNc 1 E½Nrð0ÞjNc 1 ¼E½NrðtdÞ= Pr½Nc 1 E½Nrð0Þ= Pr½Nc 1 ¼E½NrðtdÞ E½Nrð0Þ ; ð1Þ where 0 < rðtdÞ 1. A smaller rðtdÞ implies that more
signaling overhead for the DR algorithm is reduced. Potential offload traffic ratio ðtdÞ: Let pðtdÞ and pð0Þ denote
the probabilities that a call request arrives when the MS registers to the femtocell (i.e., the location information for the MS is the LAI of a femtocell) for the DR algorithm (with
TABLE 1
delay period td) and for the 3GPP algorithms, respectively.
With the DR algorithm, the traffic offloading capability degrades due to the delay timer, i.e., less call request arrivals when the MS registers to the femtocell than that with the 3GPP algorithms. Hence, we have pðtdÞ pð0Þ.
Define ðtdÞ as
ðtdÞ ¼
pðtdÞ
pð0Þ; ð2Þ
where 0 < ðtdÞ 1. A larger ðtdÞ implies that the DR
algorithm causes less degradation for the traffic offloading capability of the femtocell.
We model the behavior of an MS in the femtocell/ macrocell network as follows: Consider the timing diagram in Fig. 2. Without loss of generality, the macrocell belongs to LA Lm, and the femtocells belongs to Lf. The radio coverage
areas of femtocells in Lf are discontinuous. When the MS
passes through these discontinuous femtocells, it switches between Lmand Lf. More specifically, the MS stays in Lffor
a period tfand then moves to Lmfor another period tm.
During the timer period tc between two consecutive call
request arrivals, for i 1, let tm;ibe the ith time that the MS
visits Lm after the previous call request arrival, and tf;i be
the ith time that the MS visits Lf after the previous call
request arrival. By convention, when i ¼ 0, tm;i(tf;i) refers to
the time period when the previous call arrives in a macrocell (in a femtocell). In the DR algorithm, each tf;i is
associated with the delay timer with length td. In the
analytical model, we make the following three assumptions: . A1. The call request arrivals to an MS form a Poisson process with rate , i.e., the intercall arrival time tcis
exponentially distributed with the density function fðtÞ ¼ et. The Poisson process assumption is
widely used in teletraffic analysis to model the call request arrival behavior [16], [17].
. A2. The tm;iand tf;irandom variables are i.i.d. with
the general density function fmðtÞ and ffðtÞ, the
mean 1=m and 1=f, and the Laplace transform
fmðsÞ and f
fðsÞ, respectively.
. A3. The td random variable is exponentially
dis-tributed with the mean 1= and the density function fdðtÞ ¼ et. From implementation perspectives,
fixed td seems to be a convenient choice. The
complexities of generating fixed td and exponential
tdare basically the same in terms of implementation
cost [18]. We will extend exponential tdto fixed tdin
simulation experiments.
During tc, let tc;ibe the time period between when the MS
visits Lf for the ith time and when the next call request
arrives. The density function of tc;iis denoted by fc;iðtÞ. Since
tcis exponentially distributed, from the PASTA property of
Poisson processes [19], tc;i has the same distribution as tc,
i.e., the density function fc;iðtÞ ¼ et. Fig. 2 illustrates four
scenarios that may occur during period tc. In Fig. 2a, the
previous call request arrives when the MS is in Lm, and the
next call request arrives when the MS is in Lf. In Fig. 2b,
both call requests arrive at Lm. In Fig. 2c, both call requests
arrive at Lf. In Fig. 2d, the previous call request arrives at
Lf, and the next call request arrives at Lm.
The notations used in the analytical models are summar-ized as follows:
. tc: The time period between two consecutive call
request arrivals to the MS. The density function of tc
is fðtÞ ¼ et.
. tc;i: The time period between when the MS visits Lf
for the ith time and when the next call request arrives. The density function of tc;i is fc;iðtÞ ¼ et.
. td: The delay period. The density function of td is
fdðtÞ ¼ et.
. tf;i: The ith time that the MS visits Lf after the
previous call request arrival (i.e., the MS is in the overlapped femtocell). The density function, mean, and Laplace transform of tf;i are ffðtÞ, 1=f, and
ffðsÞ, respectively.
. tm;i: The ith time that the MS visits Lm after the
previous call request arrival (i.e., the MS is in the non-overlapped area of the macrocell). The density function, mean, and Laplace transform of tm;i are
fmðtÞ, 1=m, and fmðsÞ, respectively.
. Nc: The number of crossings for the MS during tc.
. Nr: The number of registrations executed by the MS
during tc.
. rðtdÞ: The signaling overhead ratio for the DR
algorithm.
. ðtdÞ: The potential offload traffic ratio for the DR
algorithm.
. m: The time period between when the previous call
request arrives at Lmand when the MS visits Lffor
the first time.
3.1 Derivation of Signaling Overhead Ratio rðtrðtddÞÞ
To derive the rðtdÞ performance, we first derive E½Nrð0Þ
and then E½NrðtdÞ, respectively, described in Sections 3.1.1
and 3.1.2. Applying the derivation results, (17) and (30), into (1), we have rðtdÞ ¼ ½1 f fð þ Þ þ : ð3Þ 3.1.1 Derivation of E½Nrð0Þ
If td¼ 0 (i.e., the 3GPP algorithms are exercised), the MS
immediately executes a registration when it moves from Lm
to Lf or moves from Lf to Lm. Then, we have
E½Nrð0Þ ¼ E½Nc:
We consider two cases to derive Pr½Nc¼ k for k 1:
Case I: The previous call arrives when the MS is in Lm.
See Figs. 2a and 2b.
Case II: The previous call arrives when the MS is in Lf.
See Figs. 2c and 2d.
Let NI;c and NII;c be the number Nc conditioning on
Cases I and II, respectively. We express Pr½Nc¼ k by
Pr½Nc¼ k ¼ Pr½NI;c¼ k Pr½Case I
þ Pr½NII;c¼ k Pr½Case II:
ð4Þ As shown in Fig. 2, the timing diagram for the MS alters between tm;i and tf;i. According to the alternating renewal
process [20], we have
Pr½Case I ¼ E½tm;i E½tm;i þ E½tf;i
¼ f mþ f ð5Þ and Pr½Case II ¼ m mþ f : ð6Þ
We apply (5) and (6) into (4) to yield Pr½Nc¼ k ¼
fPr½NI;c¼ k þ mPr½NII;c¼ k
mþ f
; ð7Þ where Pr½NI;c¼ k and Pr½NII;c¼ k are derived as follows:
The derivation of Pr½NI;c¼ k: Consider Case I in Figs. 2a
and 2b. Let m be the time period between when the
previous call request arrives at Lmand when the MS visits
Lf for the first time, i.e., m is the residual life of tm;0. Let
rmðtÞ be the density function of m. From the residual life
theorem [20] and the previous work [10], the Laplace transform of rmðtÞ is obtained by rmðsÞ ¼ m s ½1 fmðsÞ: ð8Þ
Let tM;k¼ mþPki¼1ðtf;iþ tm;iÞ and
tF ;k¼ mþ tf;1þ
Xk i¼1
ðtm;iþ tf;iþ1Þ:
By convention, tM;0¼ m and tF ;0¼ mþ tf;1. Assume that
tM;k and tF ;k have the density functions fM;jðtÞ and fF ;jðtÞ
with the Laplace transforms f
M;kðsÞ and fF ;k ðsÞ, respectively.
From the convolution rule of Laplace transform, we have fM;k ðsÞ ¼ r mðsÞ½fmðsÞffðsÞ k ð9Þ and fF ;k ðsÞ ¼ rmðsÞffðsÞ½fmðsÞffðsÞk: ð10Þ In the following, we consider two cases, Case Ia (i.e., the next call request arrives when the MS is in Lf) and Case Ib
(i.e., the next call request arrives when the MS is in Lm) to
derive Pr½NI;c¼ k.
Case Ia: See Fig. 2a. The previous call request arrives during tm;0, and the next call request arrives during tf;jþ1
where j 0. In this case, tM;j< tc< tF ;j, and k must be an
odd number, i.e., k ¼ 2j þ 1. Then, we have Pr½NI;c¼ 2j þ 1 ¼ Pr½tM;j< tc< tF ;j ¼ Pr½tc> tM;j Pr½tc> tF ;j ¼ Z 1 tc¼0 Z tc tM;j¼0 fM;jðtM;jÞetcdtM;jdtc Z 1 tc¼0 Z tc tF ;j¼0 fF ;jðtF ;jÞetcdtF ;jdtc ¼ f M;jðÞ fF ;j ðÞ: ð11Þ
Apply (8), (9), and (10) into (11) to have Pr½NI;c¼ 2j þ 1 ¼ m ½1 fmðÞ½1 ffðÞ ½fmðÞffðÞj: ð12Þ Case Ib: See Fig. 2b. The previous call request arrives during tm;0, and the next call request arrives during tm;j
where j 1. In this case, tF ;j1< tc< tM;j, and k must be an
even number, i.e., k ¼ 2j. Similar to the derivation of (12), we have Pr½NI;c¼ 2j ¼ Pr½tF ;j1< tc< tM;j ¼ m ffðÞ1 fmðÞ2 fmðÞffðÞ j1 : ð13Þ
The derivation of Pr½NII;c¼ k: Consider Case II in Figs. 2c
and 2d. The derivation for Pr½NII;c¼ k is similar to that for
Pr½NI;c¼ k except that in Case II, the previous call request
arrives during tf;0and then the MS alters between the time
period pairs ðtf; tmÞ. Thus, we have
Pr½NII;c¼ 2j ¼ f fmðÞ½1 ffðÞ 2 ½fmðÞffðÞ j1 ; ð14Þ and Pr½NII;c¼ 2j þ 1 ¼ f ½1 ffðÞ½1 fmðÞ ½fmðÞffðÞ j : ð15Þ Apply (12), (13), (14), and (15) into (7), and for k 1, we have Pr½Nc¼ k ¼ 2mf ðmþ fÞ 1 f mðÞ 1 f fðÞ f mðÞffðÞ k1 2; odd k; mf ðmþ fÞ n ffðÞ1 fmðÞ2 þf mðÞ 1 f fðÞ 2o fmðÞf fðÞ k 21; even k: 8 > > > > > > > > > > > > < > > > > > > > > > > > > : ð16Þ
Then, from (16), we have E½Nrð0Þ ¼ E½Nc ¼ X1 k¼1 k Pr½Nc¼ k ¼ 2mf ðmþ fÞ : ð17Þ 3.1.2 Derivation of E½NrðtdÞ
Consider the time period tf;i for i 1. Let be the
probability that the MS executes the registration during tf;i (i.e., td< tf;i) under the condition that the next call
request does not arrive during tf;i, that is,
¼ Pr½td< tf;ijtc;i> tf;i ¼
Pr½td< tf;i< tc;i Pr½tc;i> tf;i ¼ R1 td¼0 R1 tf;i¼td R1 tc;i¼tf;ie tc;if
fðtf;iÞetddtc;idtf;idtd
R1 tf;i¼0
R1 tc;i¼tf;ie
tc;if
fðtf;iÞdtc;idtf;i
¼f
fðÞ ffð þ Þ
ffðÞ :
ð18Þ
Let be the probability that the MS executes the registration before the next call request arrives under the condition that the next call request arrives during tf;i, and we have
¼ Pr½td< tc;ijtc;i< tf;i ¼
Pr½td< tc;i< tf;i Pr½tc;i< tf;i ¼ R1 td¼0 R1 tc;i¼td R1
tf;i¼tc;iffðtf;iÞe
tc;ietddt f;idtc;idtd 1 f fðÞ ¼ þ þ þ ffð þ Þ f fðÞ 1 f fðÞ : ð19Þ
Let NI;rðtdÞ and NII;rðtdÞ denote NrðtdÞ conditioning on
Cases I and II, respectively. Then, Pr½NrðtdÞ ¼ k is
expressed as Pr½NrðtdÞ ¼ k ¼ Pr½NI;rðtdÞ ¼ k Pr½CaseI þ Pr½NII;rðtdÞ ¼ k Pr½CaseII ¼fPr½NI;rðtdÞ ¼ k þ mPr½NII;rðtdÞ ¼ k mþ f : ð20Þ
The derivation of Pr½NI;rðtdÞ ¼ k: Similar to the derivation
for Pr½NI;c¼ k, we consider Case Ia (i.e., the next call
request arrives when the MS is in Lf) and Case Ib (i.e., the
next call request arrives when the MS is in Lm) to derive
Pr½NI;rðtdÞ ¼ k.
Case Ia: The previous call request arrives during tm;0,
and the next call request arrives during tf;jþ1. See Fig. 2a.
In this case, the MS has NI;c¼ 2j þ 1 crossings. The MS
visits the macrocell for j times and the overlapped femtocell for j þ 1 times (i.e., tf;1, tm;1, tf;2, tm;2; . . . ; tf;j,
tm;j, tf;jþ1). For 1 i j, if the MS executes a registration
during tf;i (i.e., td< tf;i), then after tf;i (i.e., at the
beginning of tm;i), a registration will be executed.
Other-wise (i.e., the MS does not execute a registration during tf;i;
i.e., td> tf;i), after tf;i (i.e., at the beginning of tm;i), no
registration will be executed.
Among NI;c¼ 2j þ 1 crossings, for NI;rðtdÞ ¼ k, if k is an
odd number, a registration is executed during tf;jþ1.
Otherwise (i.e., k is an even number), a registration is not executed during tf;jþ1. Then, we have
Pr½NI;rðtdÞ ¼ kjNI;c¼ 2j þ 1 ¼ j k1 2 k12ð1 Þj k1 2; odd k; j k 2 k2ð1 Þj k 2ð1 Þ; even k: 8 > > > < > > > : ð21Þ
Case Ib: The previous call request arrives during tm;0,
and the next call request arrives during tm;j where j 1.
See Fig. 2b. In this case, the MS has NI;c¼ 2j crossings.
The MS visits the overlapped femtocell for j times and the macrocell for j times (i.e., tf;1, tm;1, tf;2, tm;2; . . . ; tf;j,
tm;j). Among NI;c¼ 2j crossings, for NI;rðtdÞ ¼ k, k must
be an even number. Then, similar to the derivation of (21), we have Pr½NI;rðtdÞ ¼ kjNI;c¼ 2j ¼ j k 2 k2ð1 Þj k 2: ð22Þ
From (21) and (22), we have
Pr½NI;rðtdÞ ¼ k
¼ X1 j¼k1
2
Pr½NI;rðtdÞ ¼ kjNI;c¼ 2j þ 1 Pr½NI;c¼ 2j þ 1;
odd k; X1
j¼k 2
Pr½NI;rðtdÞ ¼ kjNI;c¼ 2j þ 1 Pr½NI;c¼ 2j þ 1
þX
1 j¼k
2
Pr½NI;rðtdÞ ¼ kjNI;c¼ 2j Pr½NI;c¼ 2j;
even k: 8 > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > : ð23Þ Applying (12), (13), (21), and (22) into (23), we obtain
Pr½NI;rðtdÞ ¼ k ¼ m1 fmðÞ 1 f fðÞ fmðÞf fðÞ k1 2 1 ð1 Þf mðÞffðÞ kþ1 2 ; odd k; m 1 f mðÞ 1 ð1 Þf mðÞffðÞ fmðÞ f mðÞ 1 ð1 Þf mðÞffðÞ k 2þ1 fmðÞf fðÞ k 2; even k: 8 > > > > > > > > > > > > > < > > > > > > > > > > > > > : ð24Þ
The derivation of Pr½NII;rðtdÞ ¼ k: We consider Case IIa
(i.e., the next call request arrives when the MS is in Lf) and
Case IIb (i.e., the next call request arrives when the MS is in Lm) to derive Pr½NII;rðtdÞ ¼ k.
Case IIa: The previous call request arrives during tf;0, and
the next call request arrives during tf;j where j 1. See
Fig. 2c. In this case, the MS has NII;c¼ 2j crossings. The MS
visits the overlapped femtocell for j times and the macrocell for j times (i.e., tm;1, tf;1, tm;2, tf;2; . . . ; tm;j, tf;j). At the
beginning of tm;1(after tf;0), the MS executes a registration if
the MS has executed a registration during tf;0. For 1 i < j,
if the MS executes a registration during tf;i (i.e., td< tf;i),
then after tf;i(i.e., at the beginning of tm;iþ1), a registration is
executed. Otherwise (i.e., the MS does not execute a registration during tf;i; i.e., td> tf;i), then after tf;i, at the
beginning of tm;iþ1, no registration is executed.
Among NII;c¼ 2j crossings, for NII;rðtdÞ ¼ k, if k is an
odd number, a registration is executed during tf;0 and no
registration is executed during tf;j or no registration is
executed during tf;0 and a registration is executed during
tf;j. Otherwise (i.e., k is an even number), the registrations
are executed during tf;0 and tf;j or no registration is
executed neither during tf;0 nor during tf;j. Then, we have
Pr½NII;rðtdÞ ¼ kjNII;c¼ 2j ¼ j 1 k1 2 2k12ð1 Þj k1 21ð1 Þ; odd k; j 1 k 2 1 k21ð1 Þj k 22 þ j 1k 2 k2ð1 Þj k 21ð1 Þ2; even k: 8 > > > > > > > > > > > > < > > > > > > > > > > > > : ð25Þ
Case IIb: The previous call request arrives during tf;0, and
the next call request arrives during tm;jþ1 where j 0. See
Fig. 2d. In this case, the MS has NII;c¼ 2j þ 1 crossings
where the MS visits the overlapped femtocell for j times and the macrocell for j þ 1 times (i.e., tm;1, tf;1, tm;2,
tf;2; . . . ; tm;j, tf;j, tm;jþ1). Among NII;c¼ 2j þ 1 crossings,
for NII;rðtdÞ ¼ k, if k is an odd number, a registration is
executed during tf;0. Otherwise (i.e., k is an even number),
no registration is executed during tf;0. Then, we have
Pr½NII;rðtdÞ ¼ kjNII;c¼ 2j þ 1 ¼ j k1 2 k12ð1 Þj k1 2; odd k; j k 2 k2ð1 Þj k 2ð1 Þ; even k: 8 > > > < > > > : ð26Þ
From (25) and (26), we rewrite Pr½NII;rðtdÞ ¼ k ¼ X1 j¼kþ1 2
Pr½NII;rðtdÞ ¼ kjNII;c¼ 2j Pr½NII;c¼ 2j
þX 1 j¼k1 2 Pr½NII;rðtdÞ ¼ kjNII;c¼ 2j þ 1 Pr½NII;c¼ 2j þ 1; odd k; X1 j¼k 2
Pr½NII;rðtdÞ ¼ kjNII;c¼ 2j Pr½NII;c¼ 2j
þX 1 j¼k 2 Pr½NII;rðtdÞ ¼ kjNII;c¼ 2j þ 1 Pr½NII;c¼ 2j þ 1; even k: 8 > > > > > > > > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > > > > > > > > : ð27Þ
Apply (14), (15), (25), and (26) into (27) to yield Pr½NII;rðtdÞ ¼ k ¼ f1 ffðÞ f mðÞffðÞ k1 2 1 ð1 Þf mðÞffðÞ kþ1 2 0 @ 1 A 1þ ð1 2Þf mðÞ 2ð1 ÞfmðÞffðÞ ; odd k; f 1 f fðÞ fmðÞffðÞ k 2 f fðÞ 1 ð1 Þf mðÞffðÞ k 2þ1 0 @ 1 A 1 f fðÞ ð þ 2Þf mðÞffðÞ ð1 Þf fðÞ 1 f mðÞffðÞ ; even k: 8 > > > > > > > > > > > > > > > > > > < > > > > > > > > > > > > > > > > > > : ð28Þ
The probability Pr½NrðtdÞ ¼ k can be obtained by
applying (24) and (28) into (20). Then, we have E½NrðtdÞ ¼ X1 k¼1 k Pr½NrðtdÞ ¼ k ¼2mf þ ð Þf fðÞ ðmþ fÞð þ Þ : ð29Þ
Applying (18) and (19) into (29), we have E½NrðtdÞ ¼
2mf½1 ffð þ Þ
ðmþ fÞð þ Þ
: ð30Þ
3.2 Derivation of Potential Offload Traffic Ratio ðtðtddÞÞ
In the 3GPP algorithms, the LAI stored in the location database is Lf as long as the MS is in the overlapped
femtocell, and the same applies for Lmas long as the MS is
in the macrocell. When a call request arrives during tf and
tm, by querying the LAI information in the location
database, the call request is processed by the overlapped femtocell and macrocell, respectively. Since the MS alters between tm and tf, from the alternating renewal process
[20], the probability pð0Þ that a call arrives during tf is
pð0Þ ¼ E½tf E½tm þ E½tf
¼ m mþ f
: ð31Þ
As shown in Fig. 2, the MS shifts between staying in the macrocell and the overlapped femtocell for tm and tf.
Suppose that the MS moves from the macrocell to the overlapped femtocell at t, and leaves the femtocell at t þ tf.
In the DR algorithm, at t, the registration is suspended until the delay timer with length td expires. During the
period ½t; t þ minðtd; tfÞ, the LAI stored in the database is
Lm, and if a call request arrives, it is processed by the
macrocell. During the period ½t þ minðtd; tfÞ; t þ tf, the LAI
stored in the database is Lf, and if a call request arrives, it
is processed by the femtocell. Let t0m¼ tmþ minðtd; tfÞ,
and t0
f¼ tf minðtd; tfÞ, and we have E½t0m ¼ E½tm þ
E½minðtd; tfÞ and E½t0f ¼ E½tf E½minðtd; tfÞ. In other
words, the LAI is alternatively changed between t0m and
t0f. During t0
f, all call request arrivals are processed by the
femtocell. Therefore, pðtdÞ is the probability that a call
arrives during t0
f. According to the alternating renewal
process, we have pðtdÞ ¼ E½t0 f E½t0 m þ E½t0f ¼E½tf E½minðtd; tfÞ E½tm þ E½tf ; ð32Þ where E½minðtd; tfÞ ¼ Z 1 tf¼0 Z tf td¼0 tdffðtfÞetddtddtf þ Z 1 tf¼0 Z 1 td¼tf tfffðtfÞetddtddtf ¼1 f fðÞ : Then, (32) is rewritten as pðtdÞ ¼ m½ fþ fffðÞ ðmþ fÞ : ð33Þ
Then, we apply (31) and (33) into (2) to yield ðtdÞ ¼
fþ fffðÞ
: ð34Þ
4
P
ERFORMANCEE
VALUATIONIn this section, we first analyze the accuracy of the analytical models proposed in this paper through the simulation experiments, and then study the rðtdÞ and ðtdÞ
perfor-mances of the DR algorithm.
As shown in (3) and (34), rðtdÞ and ðtdÞ are obtained if
the closed-form expressions of f
mðsÞ and ffðsÞ exist. In this
study, we apply the Gamma distribution for the residence times tmand tf. The Gamma distribution is selected because
it can approximate many types of distributions, it has a closed-form expression for its Laplace transform, and it has been widely used in many previous works (e.g., [9], [10], [11]) to reflect the MS mobility.
Suppose that the Gamma density functions fmðtÞ and
ffðtÞ are with the means 1=m and 1=f, the shape
parameters m and f, the variances vm¼ 1=ð m2mÞ and
vf¼ 1=ð f2fÞ, and the Laplace transforms
fmðsÞ ¼ mm mmþ s m and ffðsÞ ¼ ff ffþ s f :
Then, we have rðtdÞ ¼ ff ffþþ f þ ð35Þ and ðtdÞ ¼ fþ f f ffþf f : ð36Þ
We develop the simulation model for the DR algorithm based on the discrete event-driven approach, one widely used in MCN studies (e.g., [17], [21]). The simulation model is similar to that in [17], so the details are not presented in this paper. In our study, the input parameters m, f, and
are normalized by . For example, if we set the expected intercall arrival time E½tc ¼ 1= ¼ 50 minutes [14], ¼ 10
means that the expected delay period E½td ¼ 1= ¼ 5
minutes. In other words, our study results are dependent on the call arrival rate . For the DR algorithm to be effective, must be estimated very accurately. Accurate measurements are available in existing CN nodes (i.e., mobile switching centers or GPRS support nodes).
The analytical and simulation results are validated against each other. As shown in Table 2, the errors between the analytical and simulation results fall within 1 percent, demonstrating consistent findings from both our analytical models and simulation experiments.
In the following, we investigate the effects of input parameters on rðtdÞ and ðtdÞ for the DR algorithm.
Section 4.1 studies the effects of MS mobility. Section 4.2 studies the effects of tdwith fixed and exponential setups.
4.1 Effects of MS Mobility
This section studies the effects of MS mobility behaviors on the rðtdÞ and ðtdÞ performances. From (3) and (34), it is
clear that rðtdÞ and ðtdÞ are independent from the
distribution for tm, indicating that the MS mobility behavior
in nonoverlapped areas of the macrocell does not affect the rðtdÞ and ðtdÞ performances. Therefore, in the following,
we only study the effects of MS mobility behavior in the overlapped femtocell.
Effects of mean of femtocell residence time 1=f: In Fig. 3, we
study the effects of the femtocell residence time, where E½td is set from 105= (i.e., 0.03 seconds) to 102= (i.e.,
30 seconds), m¼ 25 (i.e., E½tm ¼ 2 minutes), and vm¼
1=2
m. We set vf ¼ 100=2f to simulate the real MS mobility
behavior that the MS either stays in the femtocell for a long period or just passes by the femtocell.
As shown in Fig. 3a, rðtdÞ decreases as f increases. A
larger f implies that the MS stays in the overlapped
femtocell for a shorter period. This is when a transient phenomenon might likely occur, during which more regis-tration traffic can be avoided in the DR algorithm. Fig. 3a also indicates that the longer we set the delay timer, the more registration avoided, i.e., rðtdÞ decreases as E½td increases. In
Fig. 3a, we observe that the DR algorithm reduces at least 85 percent of registration signaling overhead.
On the other hand, in Fig. 3b, ðtdÞ decreases as f
increases, i.e., with the delay timer, the transient phenom-enon reduces traffic offloading capability of the femtocell. We observe that the DR algorithm causes at most 24 percent of the degradation of the traffic offloading capability (i.e., ðtdÞ 76% when f¼ 103 and E½td ¼ 102=). To
summarize, the DR algorithm significantly reduces the registration signaling overhead. Meanwhile, the DR algo-rithm sustains good performance for the traffic offloading capability of the femtocell.
In the following, we discuss how to set up the delay timer adapting to different MS mobility behaviors to achieve better rðtdÞ performance while minimizing the loss in traffic offload
capability. Observe the “” curves in Figs. 3a and 3b, where f¼ 103(i.e., E½tf ¼ 3 seconds). In this mobility scenario,
the MS stays in the overlapped femtocell for transient periods. Fig. 3a indicates how the rðtdÞ values drop linearly
(i.e., better rðtdÞ performance is obtained; from 9 to
TABLE 2
Validation of the Simulation and Analysis Results
Fig. 3. The effects of f on rðtdÞ and ðtdÞ (m¼ 25, vm¼ 1=2m,
2.3 percent) as E½td increases from 105= to 102=.
However, Fig. 3b indicates that when E½td 103=, the
ðtdÞ performance decreases slightly (from 100 to 95 percent)
as E½td increases, but when E½td > 103=, the ðtdÞ
performance drops very quickly (from 95 to 76 percent). To summarize, we prefer to set E½td 103=(i.e., 3 seconds).
For other mobility scenarios, f ¼ , f ¼ 10, and f¼
100 (see “.”, “?”, and “ ” curves), we prefer to set E½td ¼ 102= (i.e., 30 seconds) because when E½td ¼
102=, we achieve the best rðt
dÞ performance with loss
of traffic offloading capability no larger than 5 percent (i.e., ðtdÞ ¼ 95%).
Effects of variance of femtocell residence time vf: In Fig. 4,
we study the effects of the variance vf of the femtocell
residence time, where E½td is set from 105= (i.e.,
0.03 seconds) to 102= (i.e., 30 seconds),
m¼ 25,
f ¼ 100, and vm¼ 1=2m. As vf increases, it is more
likely to observe an MS with short and long residence time in an overlapped femtocell, so the MS mobility behavior in the femtocell is more “dynamic.”
For short tf periods, it is more likely that an MS moves
out of an overlapped femtocell before the delay timer td
expires. The MS has less chance to execute the registration in the overlapped femtocell, reducing more signaling overhead caused by registration. Therefore, we observe rðtdÞ decreases as vf increases in Fig. 4a.
On the other hand, for longer tfperiods, the MS is more
likely to have call requests through the long-residence femtocell. More requests are potentially processed by the femtocell. Therefore, larger ðtdÞ is observed as vf increases
in Fig. 4b.
To summarize, when the MS mobility is more dynamic, the DR algorithm can work more effectively (i.e., both rðtdÞ
and ðtdÞ have better performance when vf is larger).
In addition to the Gamma distribution, in this study, we also considered the Weibull distribution for MS mobility behaviors, which has also been widely used to approximate real MS mobility patterns in many MCN studies (e.g., [22], [23]). Note that the Weibull distribution does not have a closed-form expression for its Laplace transform [24]. There-fore, the closed-form expressions of rðtdÞ and ðtdÞ for the
Weibull distribution do not exist in our analytical models. Instead, we run simulation experiments to study effects of MS mobility on rðtdÞ and ðtdÞ for the Weibull distributed
residence times. We observe similar performance trends for
both the Weibull and Gamma distributions, and thus, we do not include the performance evaluation for the Weibull distributed residence times.
4.2 Effects of Fixed and Exponential ttdd
In Fig. 5, based on the simulation experiments, we study rðtdÞ and ðtdÞ against E½tf for fixed and exponential td,
where m¼ 25, vm¼ 1=2m, vf¼ 100=f2, and tf is Gamma
distributed. We observe that the performance trends of rðtdÞ
and ðtdÞ for fixed tdare similar to those for exponential td.
In Fig. 5a, when E½td ¼ 101=and E½td ¼ 102=, rðtdÞ
for fixed td is about 0.5 percent lower than that for
exponential td. As E½tf increases from 103= to 1=, this
difference remains the same.
On the other hand, in Fig. 5b, as E½tf increases from
103= to 1=, the difference between ðt
dÞ of fixed td and
that of exponential td diminishes from 2.5 to 0 percent for
E½td ¼ 102=, and from 15 to 0 percent for E½td ¼ 101=.
This difference is larger when E½td is longer.
To summarize, the performance trends for E½td ¼ 101=
and E½td ¼ 102=are very similar. To achieve better rðtdÞ
and ðtdÞ, we suggest to use exponential td setup when
E½tf < 101=and use fixed tdsetup when E½tf 101=.
5
C
ONCLUSIONSIn this paper, we proposed a DR algorithm to reduce signaling overhead caused by frequent registrations, while noticing the slight decrease in traffic offloading capability of femtocells. To avoid registrations during the transient period, in the DR algorithm, we introduce a delay timer to postpone the registration until the timer expires. We conducted analytical models and simulation experiments to study the performance of the DR algorithm in terms of the signaling overhead ratio rðtdÞ and potential offload traffic
ratio ðtdÞ. The analytical model is generally enough to
accommodate various MS mobility behaviors. Our perfor-mance study can provide network operators with guide-lines to configure the delay timer. Our study indicates that the DR algorithm can significantly reduce the signaling overhead with slight loss of traffic offloading capability of the femtocells. Moreover, when the MS mobility is more dynamic, the DR algorithm can work more effectively, i.e., lower signaling overhead ratio and higher potential offload traffic ratio.
Fig. 4. The effects of vf on rðtdÞ and ðtdÞ (m¼ 25, f¼ 100,
vm¼ 1=2m). Fig. 5. The effects of fixed and exponential t( d on rðtdÞ and ðtdÞ
A
CKNOWLEDGMENTSThe authors thank the four anonymous reviewers for their valuable comments, which significantly improved the quality of this paper. Phone Lin’s work was supported in part by NSC 100-2221-E-002-176, NSC 100-2221-E-002-184, NSC 2219-E-002-015, NSC 101-2219-E-002-002, NSC 100-2219-E-007-010, the National Science Council, National Taiwan University, Intel Corporation under Grants NSC 100-2911-I-002-001 and 101R7501, Chunghwa Telecom, Arcadyan Technology Corporation, and ICL/ITRI. Yi-Bing Lin’s work was supported in part by NSC 100-2221-E-009-070, Chunghwa Telecom, IBM, Arcadyan Technology Cor-poration, ICL/ITRI, Nokia Siemens Networks, and the MoE ATU plan.
R
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Huai-Lei Fu received the bachelor and master degrees in computer science and information engineering (CSIE) from Tatung University and Yuan Ze University (YZU) in 2005 and 2007, respectively. He is currently working toward the PhD degree in the Department of CSIE, National Taiwan University (NTU). His research interests include machine-to-machine communications network, multicast and broadcast service, mobi-lity management, performance modeling, and wireless sensor network. He has received the YZU Academic Silver Medal Award in 2006, the YZU School Work Silver Medal Award in 2006, the Y. Z. Hsu Scholarship Award in 2006 and 2007, and the NTU Outstanding Student Award (Academic Category) in 2009. He is a student member of the IEEE.
Phone Lin received the BSCSIE and PhD degrees from National Chiao Tung University in 1996 and 2001, respectively. He is a professor at National Taiwan University (NTU) in the Department of Computer Science and Information Engineering, Graduate Institute of Networking and Multimedia, Telecommunica-tions Research Center, Optoelectronic Biomedi-cine Center, and Intel-NTU Connected Context Computing Center. He has served on the editorial boards of many journals, including the IEEE Transactions on Vehicular Technology, IEEE Wireless Commu-nications, and ACM/Springer Wireless Networks, has been a guest editor for IEEE Wireless Communications and ACM/Springer Mobile Networks and Applications, and has been involved with several prestigious conferences, such as serving as the technical program chair for WPMC 2012. He has received numerous awards, including the 2010 Junior Researcher Award from Academia Sinica, the 2009 Ten Outstanding Young Persons Award of Taiwan, the 2007 IEEE ComSoc Asia-Pacific Young Researcher Award, the 2006 Youth Engineer Award of the Chinese Institute of Electrical Engineering, the 2005 Wu Ta You Memorial Award of NSC, and the 2005 Fu Suu-Nien Award of NTU. He is a senior member of the IEEE and a member of the ACM.
Yi-Bing Lin is the vice president and a lifetime chair professor at National Chiao Tung Univer-sity. He serves on the editorial board of the IEEE Transactions on Vehicular Technology and has been a chair for prestigious conferences includ-ing ACM MobiCom 2002 and a guest editor for several journals including IEEE Transactions on Computers. 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, the 2006 Academic Award from the Ministry of Education, the 2008 Award for Outstanding Contributions in Science and Technology from the Executive Yuan, the 2011 National Chair Award, and the TWAS Prize in Engineering Sciences in 2011 from the Academy of Sciences for the Developing World. He is on advisory or review boards for the Ministry of Economic Affairs, Ministry of Education, Ministry of Transportation and Commu-nications, and National Science Council. He is a member of the board of directors for Chunghwa Telecom. He is a fellow of the IEEE, AAAS, ACM, and IET.
