Broadcast approach for UMTS mobility database recovery

Broadcast Approach for UMTS

Mobility Database Recovery

Sok-Ian Sou, Student Member, IEEE, and Yi-Bing Lin, Fellow, IEEE

Abstract—The Universal Mobile Telecommunications System (UMTS) provides high bandwidth packet data services to mobile users. To support mobility management, an MM context is established for every mobile station in its corresponding Serving GPRS Support Node (SGSN). When the SGSN fails, all MM contexts in the SGSN are corrupted. These MM contexts must be recovered or data delivery to the mobile stations will fail. This paper describes a broadcast approach that allows the MS to detect lost MM context in SGSN and therefore speeds up the process for SGSN recovery. We propose an analytic model to evaluate the performance of the broadcast approach. The analytic model is validated against simulation experiments. Based on our study, the network operator can select the appropriate parameter values in the broadcast approach for various traffic conditions.

Index Terms—Broadcast, Mobility Management (MM) Context, Serving GPRS Support Node (SGSN), Universal Mobile Telecommunications System (UMTS).

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evolved from General Packet Radio Service (GPRS) [5], [13], [14] to support high-speed packet switched (PS) data for accessing versatile multimedia services. In UMTS, a Serving GPRS Support Node (SGSN, Fig. 1a) keeps track of the locations of Mobile Stations (MSs, Fig. 1b) to provide access control. The SGSN is connected to the UMTS Terrestrial Radio Access Network (UTRAN) that consists of Node Bs (Fig. 1c) and Radio Network Controller (RNC, Fig. 1d). An MS communicates with Node Bs based on the Wideband CDMA (WCDMA) radio technology [9]. The Cell Broadcast Center (CBC, Fig. 1e) connecting to the RNC is responsible for Cell Broadcast Service (CBS) [1], [14]. Specifically, the CBC determines the time and the set of cells to broadcast a CBS message and the period at which the CBS message broadcast should be repeated. The Operations & Maintenance Center (OMC, Fig. 1f) monitors and controls the RNC and the core network nodes such as SGSN and CBC [13]. The network operator can configure the network nodes and deal with the failure problems through the OMC.

To receive the data services, an MS first registers its location to the SGSN by performing a PS attach procedure. In this procedure, the SGSN establishes a Mobility Manage-ment (MM) context for the MS. The MM context consists of four types of information:

. MS identity information, including International Mobile Subscriber Identity (IMSI), Packet Temporary Mobile Subscriber Identity (P-TMSI), Mobile Subscriber ISDN Number (MSISDN), and so on,

. location information, including, e.g., routing area (RA) and service area code, and

. security information and radio resource information, including, e.g., radio access capability, a ciphering algorithm, and authentication vectors [12].

More details about these fields can be found in [5], [13], [14]. In UMTS, an MS is identified by IMSI and P-TMSI. IMSI is the unique subscriber identity of the MS. P-TMSI is a temporary identity allocated by the SGSN at the registration and call setup to avoid sending the IMSI over the air. In order to track the MS, the cells (the radio coverages of Node Bs) in the UMTS service area are grouped into several RAs. The MS informs the SGSN of its location through the RA update procedure. This procedure is executed when an attached MS detects that it has entered a new RA or when the periodic RA update timer expires [13]. For the purpose of discussion, we refer to these two kinds of RA updates as normal SGSN registration. In the RA update procedure, the current location of the MS is stored in the MM context. To deliver data services to an MS, the SGSN tracks the RA of the MS using the MM context.

1.1 3GPP Failure Restoration

Several failure restoration methods have been studied for Global System for Mobile Communications (GSM) network nodes. For example, Visitor Location Register (VLR) record restoration is initiated by one of the following three events: MS registration, MS call origination, and MS call termina-tion [6], [8], [13]. For a GSM Home Locatermina-tion Register (HLR), it is mandatory to save the updates into nonvolatile storage. Changes of service information are saved into the backup storage device immediately after any update. The location information is periodically checkpointed, that is, the information is periodically transferred from the HLR into the backup. Updating the service information is done infrequently since most subscribers rarely change their service profiles after subscription, and the immediate backup update operations do not cost too much. After an

. The authors are with the Department of Computer Science, National Chiao Tung University, Hsinchu 30010, Taiwan, ROC.

E-mail: {sisou, liny}@csie.nctu.edu.tw.

Manuscript received 7 Sept. 2005; revised 10 June 2006; accepted 18 Oct. 2006; published online 7 Feb. 2007.

For information on obtaining reprints of this article, please send e-mail to: tmc@computer.org, and reference IEEECS Log Number TMC-0268-0905. Digital Object Identifier no. 10.1109/TMC.2007.1031.

HLR failure, the data in the backup are reloaded into the HLR [7], [13].

The 3GPP SGSN failure restoration is described as follows: When an SGSN fails, all MM contexts in the SGSN may be corrupted. If so, after restarting the SGSN, the MM contexts are lost and no MS can conduct RA update through P-TMSI. Consider Fig. 2. Suppose that, after the SGSN has restarted, an MS performs the RA update procedure by sending the P-TMSI as its identity (Step 1.1). Because the MM context for the MS (identified by the P-TMSI) no longer exists in the SGSN, the SGSN rejects the RA update request with a “Network Failure” cause (Step 1.2) [3]. The MS then performs PS attach by using the IMSI as its identity (Step 2.1). Finally, the SGSN accepts the PS attach. The MM context is reestablished and the SGSN allocates a new P-TMSI to the MS (Step 2.2). The MS acknowledges to the SGSN that the P-TMSI is received (Step 2.3).

1.2 Broadcast-Based SGSN Failure Restoration In the SGSN failure restoration, if the MS is “smart” enough to detect that the MM context does not exist in the SGSN, it can directly perform PS attach (Step 2) without executing RA update (Step 1) in Fig. 2 and, thus, reduce the network signaling traffic. To address this issue, we propose a broadcast approach where the first two messages in Fig. 2 are eliminated. Therefore, the network signaling traffic reduced is 40 percent. Furthermore, our approach allows the MS to detect lost MM context in SGSN, which speeds up the process for SGSN recovery.

The broadcast approach for SGSN recovery is described as follows: When the OMC is alerted by the restart of a recovered SGSN (Step 1, Figs. 3a and 3b), a specific broadcast message "MM Reset" is issued from the OMC. The MSs in the serving area of the SGSN listen to this message via the broadcast channel. We propose two methods for the MM Reset message delivery:

. The first method (Fig. 3a) utilizes the L3 message (RRC SYSTEM INFORMATION TYPE 3) on the broadcast channel [4]. Through the Broadcast Con-trol Channel (BCCH) or Packet BCCH (PBCCH), the UTRAN broadcasts this L3 message (which includes the cell and GPRS related information) to the MSs. The MM Reset information is carried in the reserved field of this message (Step 2.2, Fig. 3a). The delivery path for this method is ð1Þ ! ð2Þ ! ð3Þ in Fig. 1. Note that, in standard UMTS operation, the MS should listen to the broadcast channel for the L3-message with or without our approach. Therefore, no extra overhead will be incurred in this method. . The second method (Fig. 3b) utilizes the CBC to

deliver a SIM-specific broadcast short message [1], [2]. In UMTS, the CBS message (e.g., road traffic information) is broadcast to the MSs within a particular region through the Cell Broadcast Chan-nel (CBCH). This mechanism is reused to broadcast the MM Reset information in an SIM-based message (Step 2.2, Fig. 3b). The delivery path for this method is ð4Þ ! ð5Þ ! ð2Þ ! ð3Þ in Fig. 1. Note that this method requires one additional signaling message. When an MS receives the MM Reset message, it uses the IMSI as its identity to perform PS attach (Step 3.1, Figs. 3a

Fig. 1. The UMTS broadcasting architecture.

Fig. 2. Message flow for the registration of MS.

Fig. 3. Message flows for the MM context reestablishment. (a) MM Reset message delivery through BCCH/PBCCH. (b) MM Reset message delivery through CBCH.

and 3b). Therefore, the RA update messages (Steps 1.1 and 1.2, Fig. 2) are saved. It is possible that the MS is temporarily out of the radio coverage and therefore does not receive the MM Reset message. In the broadcast approach, the MM Reset message is periodically retrans-mitted. The retransmitted period is typically a fixed value Tr and the maximal number of retransmissions is Nr. Two

important measures of the broadcast approaches are: . Pf: the probability that the MS fails to receive the

MM Reset message.

. E½NL: the expected number of lost packets.

After the SGSN restarts, the MM context for an MS is recovered in two cases:

Case 1. The MS receives the MM Reset message and then performs the PS attach procedure using IMSI.

Case 2.The MS performs the normal SGSN registration (see Section 1).

Before the registration/attach is performed, it is possible that some incoming packets have been delivered to the MS. In this case, these data packets are discarded (and are therefore lost) because the MM context does not exist in the SGSN [5]. In the next section, an analytic model is proposed to investigate the impact of Tr and Nr on Pf and E½NL.

The remainder of the paper is organized as follows: Section 2 proposes an analytic model for modeling the broadcast approach. Section 3 uses numerical examples to investigate the performance of the broadcast approach. Section 4 gives concluding remarks.

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Based on the broadcast approach described in Section 1.2, this section proposes an analytic model to derive two output measures:

. the probability Pf that an MS fails to receive the

MM Reset message after this message is transmitted Nrþ 1 times (including the first transmission and

Nr retransmissions) and

. the expected number E½NL of lost packets between

when the SGSN restarts and when the MM context of the MS is reestablished.

2.1 Deriving the Probability Pf

To model an unreliable wireless link, two states for the link are considered: “Good” and “Bad.” In the “Bad” state, the wireless link is of bad quality and the MS fails to receive the MM Reset message. In the “Good” state, the wireless link is of good quality and the MS can receive the MM Reset message. Consider the timing diagram in Fig. 4, where the

first, second, ith, i þ 1st, and Nrþ 1 MM Reset messages

occur at 0, 1, 2 ,3, and 4, respectively. Note that the

second to the Nrþ 1st MM Reset messages are for

retransmissions. The retransmitted period is a fixed value Tr¼ 1 0¼ 3 2. Let PB be the probability that an MS

fails to receive the first MM Reset message at 0. That is, PB

is the probability that the wireless link is in the “Bad” state when the SGSN restarts. For 1  i  Nr, suppose that the

MS fails to receive the ith MM Reset message at 2. Let PBB

be the probability that the MS fails to receive the i þ 1st MM Reset message at 3¼ 2þ Tr. In other words, PBB is the

probability that the wireless link is in the “Bad” state at time 2þ Trgiven that the wireless link is in the “Bad” state

at 2. Therefore, Pf can be derived as

Pf¼ PBPBBNr: ð1Þ

In (1), the MS fails to receive the first transmission of the MM Reset message with probability PB, and then the MS

fails to receive the Nr consecutive retransmissions of the

MM Reset message with probability PBBNr. PB and PBBare

derived as follows: Let random variables tB and tG be the

periods that a wireless link is in the “Bad” and the “Good” states, respectively. Fig. 5 shows the state transition rate diagram of the wireless link, where tB and tG have

exponential distributions with rates B and G. We will

relax the exponential assumption in simulation experiments to be elaborated later. Since the SGSN restart can be considered as a random observer of the wireless link, from the alternative renewal theory [15], PB can be expressed as

PB¼ E½tB E½tB þ E½tG ¼ G Bþ G : ð2Þ PBB is derived as follows: From Fig. 5, we define the

stochastic process fXðtÞ; t  0g, where

XðtÞ ¼ 0; if the MS is in the }Bad} state at time t; 1; if the MS is in the }Good} state at time t: 

Since tB and tG are exponentially distributed with fixed

rates, this stochastic process forms a homogeneous con-tinuous-Time Markov chain. Let pijðtÞ be the transition

probability that the process is in state j at time s þ t given that it was in state i at time s (for i, j ¼ f0 or 1g and s, t  0). Therefore, PBB can be expressed as

PBB¼ p00ðTrÞ; Tr 0: ð3Þ

In (3), PBB is the probability that the MS is in state 0 at

3¼ 2þ Tr given that it was in state 0 at 2, where

p00ð0Þ ¼ 1 and p01ð0Þ ¼ 0: ð4Þ

Fig. 4. Timing diagram for deriving Pf.

Define qijas the rate at which the process moves from state i

to state j (for i, j ¼ f0 or 1g). Then,

q00¼ B; q01¼ B; q10¼ G; q11¼ G: ð5Þ

According to the forward Chapman-Kolmogorov equation for the continuous-time Markov chain [10] and from (5), we have dp00ðtÞ dt ¼ Bp00ðtÞ þ Gp01ðtÞ; dp01ðtÞ dt ¼ Gp01ðtÞ þ Bp00ðtÞ: ( ð6Þ By using (4) as initial conditions to solve (6), we have

p00ðtÞ ¼ 1 Bþ G   Gþ BeðBþGÞt h i : ð7Þ From (3) and (7), PBBis derived as

PBB¼ 1 Bþ G   Gþ BeðBþGÞTr h i : ð8Þ Finally, by substituting (2) and (8) into (1), we have

Pf¼ G Bþ G   _ Gþ BeðBþGÞTr Bþ G  Nr : ð9Þ 2.2 Deriving the Expected Number E½NL of Lost

Packets

This subsection derives the expected number E½NL of lost

packets. Consider the timing diagram in Fig. 6, where the SGSN restart occurs at 5and the MS receives the MM Reset

message at 6. Let tm¼ 6 5. From (2) and (8), the

prob-ability mass function of tmcan be derived in three cases:

Case 1. tm¼ 0. In this case, the MS successfully receives the

first MM Reset message with probability 1  PB.

Case 2. tm¼ iTr for 1  i  Nr. In this case, the MS fails to

receive the first MM Reset message transmission (with probability PB) and the subsequent i  1 MM Reset

message retransmissions (with probability PBBi1). Then,

the MS successfully receives the i þ 1st MM Reset message (with probability 1  PBB).

Case 3. tm! 1. In this case, the MS fails to receive all MM

Reset messages (including the first transmission and Nr

retransmissions) with probability Pf.

From Cases 1-3 and for 1  i  Nr, we have

Pr½tm¼ t ¼ 1 PB; t¼ 0; PBPBBi1ð1  PBBÞ; t¼ iTr; Pf; t! 1: 8 < : ð10Þ

is, at 7, the wireless link is of good quality. Let tu¼

7 5 have the exponential distribution with mean 1=u.

Let tl be the period between when the SGSN restarts and

when the MM context of the MS is reestablished. Thus, tl¼ minftm; tug. During the tlperiod, the incoming packets

of the MS will be discarded [5] because the MM context does not exist in the SGSN. Let NL be the number of lost

packets during tl. Then, the expected number E½NL of lost

packets is derived as follows.

Assume that the interarrival time tp of the incoming

packets have an exponential distribution with rate p. Since

the incoming packet arrivals form a Poisson process, the expected number of lost packets in tlcan be expressed as

E½NL ¼ pE½tl ¼ pE½minftm; tug: ð11Þ

We derive (11) based on the three cases in (10) as follows: E½tl ¼ E½tljtm¼ 0 Pr½tm¼ 0 ð12Þ þX Nr i¼1 E½tljtm¼ iTr Pr½tm¼ iTr ð13Þ þ E½tljtm! 1 Pr½tm! 1: ð14Þ In (12), Pr½tm¼ 0 ¼ 1  PB, tl¼ minf0; tug ¼ 0, and E½tljtm¼ 0 Pr½tm¼ 0 ¼ 0: ð15Þ

In (13), there are two possibilities for deriving E½tljtm¼ iTr.

If tu< iTr, we have tl¼ tu. Since tu is exponentially

distributed, we have E½tljtm¼ iTr; tu< iTr Pr½tu< iTr ¼ Z iTr tu¼0 tuueutudtu ¼ 1 u   1 euiTr    iTreuiTr: ð16Þ If tu iTr, we have tl¼ tm¼ iTr. Therefore, E½tljtm¼ iTr; tu iTr Pr½tu iTr ¼ iTr Z 1 tu¼iTr ueutudtu ¼ iTreuiTr: ð17Þ

We combine (16) and (17) to yield E½tljtm¼ iTr ¼ 1 u   1 euiTr   : ð18Þ For 1  i  Nr, Pr½tm¼ iTr ¼ PBPBBi1ð1  PBBÞ. From

(18), we have E½tljtm¼ iTr Pr½tm¼ iTr ¼PB u ð1  PBBÞ 1  euiTr   PBBi1: ð19Þ In (14), Pr½tm! 1 ¼ Pf. It is clear that tl¼ minftm!

1; tug ¼ tuand

E½tljtm! 1 Pr½tm! 1

¼ E½tujtm! 1Pf ¼

Pf

u

: ð20Þ Substituting (15), (19), and (20) into (12), (13), and (14), E½tl

can be rewritten as (21). Finally, from (2), (11), and (21), the expected number E½NL of lost packets is derived as (22),

where PBB and Pf can be obtained from (8) and (9).

E½tl ¼ 1 u   PBð1  PBBÞ XNr i¼1 1 euiTr   PBBi1þ Pf " # ¼ 1 u  ( PBð1  PBBÞ ( 1 PBBNr 1 PBB e uTr_{½1  ðe}uTr_P BBÞNr 1 euTr_P BB ) þ Pf ) ; ð21Þ E½NL ¼ p u  ( _ Gð1  PBBÞ Bþ G   ( 1 PBBNr 1 PBB e uTr_{½1  ðe}uTr_P BBÞNr 1 euTr_P BB ) þ Pf ) : ð22Þ The analytic model developed in this paper is validated against the simulation experiments. The simulation model follows the discrete event approach described in [12] and the details are omitted. The discrepancies between analytic analysis (specifically, (9) and (22)) and the simulation experiments are within 3 percent in most cases (see Figs. 7, 8, 10, and 11).

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This section uses numerical examples to investigate the performance of the broadcast approach. Based on the analytic model developed in the previous section, we show how Nr and Tr affect the probability Pf and the expected

number E½NL of lost packets. The input parameters are

listed in Table 1. To simplify our study, G, Tr, u, and p

are normalized by B. The effects of the input parameters

are described as follows.

Effects of Tr and Nron Pf.Fig. 7 plots Pf as a function

of Tr and Nr, where the values for the input parameters

except Trand Nr follow the default values listed in Table 1.

This figure shows that Pf decreases as Tr increases. This

effect becomes insignificant when Tr 5=B for all Nr

values. The phenomenon is explained as follows: If Tr is

set too small, it is more likely that the wireless link for an MS does not leave the “Bad” state during the Nr

consecutive MM Reset message broadcastings. On the other hand, when Tr is sufficiently large, the randomness

of state change for the wireless link is in effect, and the MM Reset message is transmitted at the “Good” state with the probability 1  PB. For example, for Nr¼ 1, Pf

PB2¼ ₁₁1

 2

when Tr> 5=B. Fig. 7 also quantitatively

indicates how to choose Tr and Nr values to ensure that

the Pf value is under a predefined threshold set by the

mobile operator. For example, if the mobile operator requires that the Pf value is less than 0.6 percent (see the

dashed line in Fig. 7), then we can choose Tr¼ 1=B for

Nr¼ 3 or Tr¼ 2=B for Nr ¼ 2. Note that, for Nr¼ 1, no

matter what Tr value is chosen, this requirement cannot be

satisfied. Compared with the setup ðTr; NrÞ ¼ ð2=B; 2Þ, the

advantage of the setup ðTr; NrÞ ¼ ð1=B; 3Þ is that the MS

can receive the MM Reset message earlier. The disadvan-tage of this setup is that extra broadcast cost is incurred for more retransmissions.

Fig. 7. Effects of Tr and Nr on Pf (G¼ 10B, VB¼ 1=B2, and VG¼ 1=G2).

Fig. 8. Effects of Bon Pf(Tr¼ 5=B, VB¼ 1=B2, and VG¼ 1=G2).

TABLE 1 Input Parameters

Effects of B on Pf.Fig. 8 plots Pf as a function of B.

This figure shows that Pf decreases as B increases. The

nontrivial observation is that, if the wireless link quality is sufficiently good ðB> 100GÞ, we can control Pf< 1%for

Nr¼ 0. When B is small, it increases Nr and significantly

decreases Pf. For example, for B¼ 50G, Pf decreases

from 1.96 percent to 0.05 percent when Nrincreases from 0

to 1. If the mobile operator requires that the Pfvalue is less

than 2 percent (see the dashed line in Fig. 8), then we can choose Nr¼ 1 when B ¼ 10Gor Nr ¼ 0 when B 50G.

Effects of VB and VGon Pf.Fig. 9 plots Pf as a function

of the variances VB and VG for the “Bad” and “Good”

periods, respectively. When Nr¼ 0, from the alternative

renewal theory [15], Pfis not affected by VBand VGand the

“” lines ðNr¼ 0Þ are horizontal. Fig. 9a shows that Pf

significantly increases when VB increases for Nr> 0. This

phenomenon can be explained as follows: As the variance VB increases, more long and short tB periods are observed.

We assume that the wireless link is of bad quality when the SGSN restarts. Since the SGSN restart can be modeled as a random observer of the wireless link, the SGSN restart is more likely to fall in the long tB periods than the short tB

periods [15]. In this case, it is possible that the wireless link is still of bad quality when the MM Reset message is retransmitted. Therefore, the performance of Pf degrades

when VB increases.

Fig. 9b shows that, for Nr > 0, Pf also significantly

increases when VG increases. This phenomenon can be

explained as follows: As the variance VG increases, more

long and short tGperiods are observed, and the number of

short tG periods is larger than the number of long tG

periods. When the wireless link of the MS leaves the “Bad” state, it is more likely that the MS enters an alternative renewal period pair (tG, tB), where tB is longer than tG.

Therefore, when the next broadcast occurs, the wireless link is probably in the “Bad” state again. In other words, the performance of Pf degrades as VG increases.

Effects of Trand uon E½NL. Fig. 10 plots the expected

number E½NL of lost packets as a function of Tr and the

normal SGSN registration rate u. This figure shows that

E½NL is a decreasing function of u. E½NL is more sensitive

to the change of Trwhen uis small than when uis large.

As Tr increases, E½NL decreases then increases. This

Fig. 9. Effects of VBon Pf(Tr¼ 5=B, G¼ 10B). (a) VG¼ 1=G2. (b) VB¼ 1=B2.

Fig. 10. Effects of Tron E½NL (Nr¼ 2, G¼ 10B, VB¼ 1=B2, VG¼ 1=G2and 1=p¼ 5=B).

Fig. 11. Effects of Nr on E½NL (Tr¼ 5=B, G¼ 10B, VB¼ 1=B2, VG¼ 1=G2, and 1=p¼ 5=B).

phenomenon is explained as follows: When Tris small (e.g.,

Tr 3=B), the probability Pf significantly decreases (see

Fig. 7) as Tr increases. Therefore, in most cases, tl¼ tm is

small and E½NL decreases as Trincreases. When Tris large

(e.g., Tr 4=B), Pfis insignificantly affected by the change

of Tr. In this case, tmincreases as Tr increases. Therefore, tl

and E½NL increase as Tr increases.

Effects of Nron E½NL. Fig. 11 plots E½NL as a function

of Nr and u. E½NL decreases as Nr increases. When Nr is

small, the effect of changing Nr is significant. Conversely,

E½NL is not sensitive to the change of Nrwhen Nris large.

Based on the above discussion, Fig. 11 quantitatively indicates how to set the Nr value. For example, we may

choose Nr¼ 2 when 1=u¼ 25=B.

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This paper studied the UMTS mobility database recovery. We described a broadcast approach that allows the MS to detect lost mobility management context in SGSN and therefore speeds up the process for SGSN recovery. In this approach, a broadcast message is periodically retrans-mitted. The retransmitted period is Tr and the maximal

number of retransmissions is Nr. An analytic model is

developed to investigate the impact of Tr and Nr on the

broadcast approach. The output measures considered are the probability Pf that an MS fails to receive the broadcast

message and the expected number E½NL of the lost packets.

We make the following observations in our study:

. Pf decreases as the retransmitted period Tr

in-creases. This effect becomes insignificant when Tr  5=B.

. Pf decreases as the rate B(that a wireless link is in

the “Bad” state) increases. When the wireless link quality is sufficiently good (e.g, B> 100G), we can

control Pf < 1%without retransmission (i.e., Nr¼ 0).

. When Nr¼ 0, Pf is not affected by the variances VB

and VG for the “Bad” and “Good” periods,

respec-tively. For Nr> 0, Pfsignificantly increases when VB

(or VG) increases.

. E½NL is a decreasing function of the normal SGSN

registration rate u. For a specific uvalue, when Tr

increases, E½NL decreases then increases.

. E½NL decreases as Nr increases. When Nr is small

(e.g., Nr < 2), the effect of changing Nris significant.

Conversely, E½NL is not significantly affected by the

change of Nr when Nr is large (e.g., Nr  3).

Based on the above discussion, the network operator can select the appropriate Tr and Nr values for various traffic

conditions based on our study. As a final remark, the broadcast approach proposed in this paper can also be used for Visitor Location Register (VLR) failure restoration in the circuit-switched domain [6], [8], [11].

A

The authors would like to thank the editor and the anonymous reviewers. Their valuable comments have significantly improved the quality of this paper. Their efforts are highly appreciated. This work was sponsored in part by NSC Excellence project NSC 94-2752-E-009-005-PAE,

NSC 94-2219-E-009-001, and NSC 94-2213-E-009-104, NTP VoIP Project under grant number NSC 94-2219-E-009-002, NTP Service IOT Project under grant number NSC 94-2219-E-009-024, Intel, Chung Hwa Telecom, IIS/Academia Sinica, the ITRI/NCTU Joint Research Center, and MoE ATU.

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

[15] S.M. Ross, Stochastic Processes. John Wiley & Sons, 1996. Sok-Ian Sou received the BSCSIE and MSCSIE degrees from National Chiao Tung University (NCTU), Taiwan, in 1997 and 2004, respec-tively. She is currently a PhD candidate in the Department of Computer Science, NCTU. Her current research interests include the design and analysis of personal communications ser-vices networks, mobile computing, and perfor-mance modeling. She is a student member of the IEEE.

Yi-Bing Lin (M ’96, SM ’96, F ’03) is the chair, professor, and CS college dean at National Chiao Tung University. His current research interests include wireless communications and mobile computing. He has published more than 200 journal articles and more than 200 con-ference papers. He is the coauthor with Imrich Chlamtac of the book Wireless and Mobile Network Architecture (John Wiley & Sons). He is a fellow of the IEEE, ACM, AAAS, and IEE.