C
2006 Springer Science + Business Media, Inc. Manufactured in The Netherlands.
An Improved GGSN Failure Restoration Mechanism for UMTS
PHONE LIN ∗and GUAN-HUA TUDept. Comp. Sci. & Info. Engr., National Taiwan University, Taipei, R.O.C.
Abstract. Universal mobile telecommunications system (UMTS) provides packet-switched data services for mobile users. To efficiently deliver packets in the UMTS core network, the PDP contexts (i.e., the routing information) are maintained in the volatile storage (e.g., memory) of SGSN, GGSN, and UE. The GGSN routes packets between the UMTS core network and external data networks, and thus has heavy traffic and computation loading, which may result in PDP contexts lost or corrupted, and the QoS of the UMTS network may degrade significantly. To resolve this issue, 3GPP 23.007 proposes a mechanism for GGSN failure restoration. In this mechanism, the corrupted PDP contexts can be restored through the PDP Context Activation procedure. However, this incurs extra signaling cost to the network. To reduce the network signaling cost and delay for restoration of the corrupted PDP contexts, this paper proposes an improved mechanism “GGSN Failure Restoration” (GFR) with different backup algorithms. The analytic models and simulation experiments are conducted to evaluate GFR. Our study indicates that the GFR mechanism can significantly reduce the cost for the PDP context restoration.
Keywords: failure restoration, GGSN, UMTS
1. Introduction
3GPP proposed the 3rd generation wireless system, Univer-sal mobile telecommunications system (UMTS) [6,8,10], to provide high speed transmission services for packet-switched (PS) domain and circuit-switched (CS) domain services for mobile users. Figure 1 illustrates the UMTS network archi-tecture. UMTS consists of the UMTS terrestrial radio ac-cess network (UTRAN) and the core network. In this ar-chitecture, a user equipment (UE) communicates with the UTRAN through the air interface Uu [2]. In the core net-work, the serving GPRS support node (SGSN) delivers the packets between the UEs and their counter-parts in the exter-nal data network. The gateway GPRS support node (GGSN) interworks with the external data network using less network protocols (e.g., Internet protocol) or connection-oriented network protocols (e.g., X.25). The GGSN is con-nected with SGSNs via an IP-based GPRS backbone net-work. The mobility databases HLR and VLR maintain the location information for mobile users. The MSC provides the circuit-switched services for mobile users. To efficiently deliver the packets in the core network, the packet data pro-tocol (PDP) contexts (i.e., the routing information) are main-tained in the volatile storage (e.g., memory) of SGSN, GGSN, and UE. The details of the contents in a PDP context can be found in [5,6]. Before a UE starts a connection to the ex-ternal data network, the PDP Context Activation procedure is invoked to establish a session from the UE to the appli-cation server in the external data network through SGSN and GGSN. At this moment, the PDP contexts are created in GGSN, SGSN, and UE for the session, respectively. If the
∗Corresponding author.
E-mail: plin@csie.ntu.edu.tw
QoS requirement for the activated session is changed, the PDP Context Modification procedure is executed to modify the PDP contexts. When the user terminates the connection, the network exercises the PDP Context Deactivation proce-dure to deactivate the PDP contexts in GGSN, SGSN, and UE. For the details of the three procedures, readers may refer to [6].
In UMTS Release 4 [3] and UMTS Release 5 [7], 3GPP evolved the UMTS system to the all-IP architecture which integrates the IP and the wireless technologies. In this archi-tecture, the traffic for the CS domain services are packetized and delivered through the UMTS core network so that the net-work can be utilized more efficiently. Obviously, the traffic and computation loading of the GGSN in the core network increases in the UMTS system, and its stability affects the performance of the UMTS network significantly. As men-tioned previously, the PDP contexts in the GGSN are referred to efficiently route the packet traffic. Due to the increasing reference rate of the PDP context, an activated PDP context is more likely to be lost or corrupted. When an activated PDP context is lost or corrupted, the corresponding session is inter-rupted, and the application (run between the UE and the server in the external data network) is terminated. The QoS of the UMTS network degrades significantly. To resolve this issue, 3GPP 23.007 [4] defines the necessary fault tolerance mech-anism for GGSN, which is known as the “Basic” mechmech-anism in this paper. In the Basic mechanism, the corrupted PDP con-texts can be restored through the basic restoration procedure or the GGSN restart procedure, whose details are illustrated in Section 2. In the restoration procedure or the GGSN restart procedure, the PDP Context Activation procedure is invoked to reactivate the corrupted PDP context, which results in extra signaling cost to the network, or unexpected delay. Specifi-cally, at least 8 signaling messages should be exchanged in
Figure 1. The UMTS network architecture.
the UMTS network for the restoration of a corrupted PDP context. Typically, a GGSN can support more than 10,000 simultaneously activated data sessions; e.g., Lucent’s GGSN implementation [9] can accommodate 40,000 ongoing data sessions. In other words, a GGSN failure may cause more than 10,000 ongoing data sessions to be interrupted, and at least 80,000 message exchanges are required to restore the corrupted PDP contexts.
To reduce the network signaling cost and delay for the restorations of the corrupted PDP contexts, this paper pro-poses an improved mechanism GFR (GGSN Failure Restora-tion) with three backup algorithms, GBA1, GBA2, and GBA3. The paper is organized as follows. In Section 2, the Basic mechanism in 3GPP 23.007 is briefly described. Section 3 describes the GFR mechanism, and the GBA1, GBA2, and GBA3 backup algorithms. Section 4 proposes analytical
mod-Figure 2. The message flow for the restoration procedure.
els for the GFR mechanism with different backup algorithms. Section 5 evaluates the performances for the Basic mecha-nism in 3GPP and the GFR mechamecha-nism with different backup algorithms. Section 6 gives a concluding remark.
2. The basic mechanism
This section describes the GGSN failure restoration mech-anism proposed in 3GPP 23.007, where the corrupted PDP contexts are restored through the restoration procedure or the GGSN restart procedure. The details are given as follows.
The Restoration Procedure: Figure 2 illustrates the message
flow for this procedure. When an activated PDP context in the GGSN is corrupted, it is restored when one of the two following events occurs in the GGSN:
Event 1. The GGSN receives a mobile terminated protocol
data unit (PDU; from the external data network) for which no valid PDP context exists. If the GGSN has the static PDP information for the PDP address of the PDU (i.e., the GGSN can retrieve the IP address of the SGSN that cur-rently serves the mobile user; see Steps 2–3 in figure 2(a)), the GGSN initiates the Network-Requested PDP Context Activation procedure [6] before delivering the PDU (see Steps 4–7 in figure 2(a)). Otherwise (i.e., the GGSN does not have the static PDP information), the GGSN discards the received PDU and returns an appropriateErrormessage depending on the protocol used between the GGSN and the external data network. Note that in the latter case, the cor-rupted PDP context cannot be restored, and the application is terminated.
Figure 3. The message flow for the GGSN restart procedure.
Event 2. The GGSN receives a tunnel PDU (from the SGSN)
for which no PDP context exists. The GGSN discards the tunnel PDU and sends anError Indicationmessage [5] to the originating SGSN (see Step 3 in figure 2(b)). Then the originating SGSN deactivates the PDP context and sends an
Error Indicationmessage to the originating UE (see Step 4 in
figure 2(b)). The UE performs the PDP Context Activation procedure [6] to reactivate the PDP context (see Step 5 in figure 2(b)).
The GGSN Restart Procedure: Figure 3 illustrates the
mes-sage flow for this procedure. In this procedure, the SGSN detects if the GGSN has been restarted through the polling function. As shown in Case 1 in figure 3, if no restart has been performed by the GGSN, then the SGSN takes no actions. Otherwise (i.e., the SGSN detects a restart in a GGSN with which the SGSN has one or more activated PDP contexts; see Case 2 in figure 3), the SGSN deacti-vates all these PDP contexts and then requests the UEs to reactivate them. In the GGSN, a GGSN Restart counter (denoted as CRg) is maintained in the non-volatile storage (i.e., when the GGSN is powered off, the value of CRgis not destroyed) to count the number of restart actions that have been performed on the GGSN. After the GGSN is restarted, the CRgcounter is incremented by one (see Step 0, Case 2, figure 3). Each SGSN (with which the GGSN is in contact) maintains a GGSN Restart counter (denoted as CRs,g) to record the number of restarts that have been exercised on the GGSN. The polling function consists of three steps:
Step 1. The SGSN sends anEcho Requestmessage [5] to the GGSN, and starts a timer Tp. It expects to receive anEcho
Responsemessage [5] from GGSN before Tp expires. If
the Tptimer expires, the SGSN recognizes that the polled GGSN fails.
Step 2. Upon receipt ofEcho Request, the GGSN responds the SGSN anEcho Responsemessage in which the CRg value is included.
Step 3. When the SGSN receives Echo Response, it stops the Tp timer and compares the values of CRg and CRs,g. If CRs,g = CRg (see Step 3, Case 1, figure 3), the SGSN recognizes that the GGSN has not restarted before the GGSN received theEcho Requestmessage, and the SGSN takes no action. Otherwise (i.e., CRs,g = CRg; see Step 3, Case 2, figure 3), the SGSN recognizes that the GGSN has restarted before the GGSN received the previousEcho
Re-questmessage from SGSN. The SGSN deactivates all the
PDP contexts related to the GGSN and sets CRs,g← CRg. The SGSN waits for a time period, and then returns to Step 1.
3. An improved GGSN failure restoration mechanism
This section proposes an improved mechanism GFR (GGSN Failure Restoration) with three different backup algorithms, GBA1, GBA2, and GBA3. The details of GFR are given be-low.
During an activated session, when the GGSN receives or sends a PDU (which may contain user data or network signal-ing message) from or to the SGSN, the correspondsignal-ing fields in the PDP context are modified. In GFR, the GGSN back-ups the PDP context into the nonvolatile storage (e.g., hard disk) at some checkpoints by using the backup algorithms (to be elaborated later). A flag D(that is backuped into the non-volatile storage when being changed) is maintained in the volatile storage to indicate if the backuped PDP context is valid. If D= 0, the PDP context in the non-volatile storage is consistent with that in the volatile storage. Otherwise (i.e., D= 1), the PDP context in the non-volatile storage is incon-sistent with that in the volatile storage. Initially, D is set to 0. During an activated session, D is maintained as follows.
r
When the PDP context is modified (i.e., new PDU arrives), D is set to 1.r
When the PDP context is backuped into the non-volatile storage, D is set to 0.r
When the D value is changed from 1 to 0 or changed from 0 to 1, the GGSN writes the D flag into the non-volatile storage.The basic restoration procedure and the GGSN restart pro-cedure are modified as follows.
The Restoration Procedure is similar to that in the Basic
mechanism. The difference is that when the GGSN receives a mobile terminated PDU (from the external network) or a tunnel PDU (from the SGSN) for which no valid PDP context exists in the volatile storage, the GGSN restores the backuped PDP context and its corresponding D flag into the volatile storage. If D= 0, the corrupted PDP context
Figure 4. xi, tf,i, ta, and tk.
is restored. Otherwise (i.e., D= 1), the UE is requested to reactivate the PDP context.
The GGSN Restart Procedure is similar to that in the Basic
mechanism, except that after the GGSN restarts, instead of incrementing the CRgcounter, it restores all the backuped PDP contexts and the corresponding Dflags into the volatile storage.
To determine the checkpoints when the GGSN backups the PDP context into the non-volatile storage, we propose three backup algorithms, GBA1, GBA2, and GBA3. Consider the timing diagram in figure 4. Let ta denote the duration time of a session. For i ≥ 1, let xi be the period between the time when the i − 1st PDU arrives and the time when the ith PDU arrives. By convention, x0= 0, and the 0th PDU arrival
is the PDU that activates the PDP context for the session. Figure 5 illustrates the timing diagrams for the three backup algorithms.
GBA1: See figure 5(a). The GGSN backups the PDP
con-text into the non-volatile storage for every time interval TG1.
GBA2: See figure 5(b). The GGSN maintains a counter CRG2 for the PDP context. Initially, CRG2 is set to 0. When the PDP context is modified (i.e., a PDU arrives), CRG2 is incremented by one, and then compared with a threshold value KG2. If C RG2 < KG2, GGSN takes no actions. If CRG2 = KG2, the PDP context is backuped into the non-volatile storage, and CRG2is reset to 0.
GBA3: See figure 5(c). When the PDP context is created
for a session, a timer TG3 starts. When the PDP con-text is modified, the GGSN restarts TG3. When the TG3 timer expires (i.e., no PDU arrives during the time period of TG3), the PDP context is backuped to the non-volatile storage.
The proposed GFR mechanism can be deployed in the UMTS system without introducing any new component and modify-ing the protocol of the UMTS network. This mechanism is considered practical and cost-effective.
4. Analytical models
This section proposes analytic models for the Basic mecha-nism and the GFR mechamecha-nism with GBA1, GBA2, and GBA3. The notation is listed in Appendix A.
Consider the timing diagram in figure 4. In a session, sup-pose that in a GGSN, when a PDU arrives, with probability 1− α, the arrival PDU deactivates the PDP context, and the session ends, and with probabilityα, the session continues. Assume that the PDU inter-arrival times xiare i.i.d. with ex-ponential density function fx(xi)= μxe−μxxiand mean 1/μx. Exponential periods are used in the analytic models to provide the mean value analysis, and indicate the performance trends for our mechanism and the Basic mechanism. The effects of higher moments for general distribution are studied based on our simulation experiments.
Let ta be the elapsed time of a session. Then the density function fa(ta) for tacan be expressed as
fa(ta)= ∞ k=0 ta x1=0 ta−x1 x2=0 ta−x1−x2 x3=0 · · · × ta−x1−x2−x3−···xk−1 xk=0 αk (1− α) k i=1 μxe−μxxi × μxe−μx(ta−x1−x2−···−xk)d xkd xk −1d xk−2...dx1 (1) and its Laplace transform is
fa∗(s)= ∞ k=0 αμx s+ μx k (1− α)μx s+ μx = (1− α)μx s+ (1 − α)μx (2) As shown in figure 4, for i ≥ 1, let tf,i denote the time in-terval between the time when the i th PDP context corruption occurs and the time when the i+ 1st PDP context corrup-tion occurs, tf,0denotes the interval between the time when the PDP context is activated and the time when the first PDP context corruption occurs in the session. For all i ≥ 0, tf,i are assumed to be i.i.d. exponential random variables with the exponential density function ff(tf,i)= ηe−ηtf,i. Let N
f be the number of PDP context corruptions in a session. Then
Figure 5. Timing diagrams for GBA1, GBA2, and GBA3. we have Pr[Nf = n] = ∞ ta=0 (ηta)n n! e−ηtafa(t a) dta = ηn n! (−1)nd nf∗ a(s) dsn s=η (3)
From Appendix B, we have dnf∗ a(s) dsn = (−1)nn!(1− α)μx [s+ (1 − α)μx]n+1 and (3) is rewritten as Pr [Nf = n] = (1− α)μx η + (1 − α)μx η η + (1 − α)μx n
The expected value of Nf can be obtained as follows.
E[Nf]= ∞ n=1 nPr[Nf = n] =∞ n=1 n (1− α)μx η + (1 − α)μx η η + (1 − α)μx n = η (1− α)μx (4)
For an activated session, there are at least two PDU arrivals. One PDU is for the PDP context activation, and the other is for the PDP context deactivation. Let Nmbe the number of the PDU arrivals (including the PDU arrival that activates the PDP context but excluding the last PDU arrival that deactivates the PDP context) in a session. Then
and its expected value is E[Nm]= ∞ n=1 [nαn−1(1− α)] = 1 1− α (5)
For k≥ 1, let tkbe the duration time of the first k PDU arrivals (i.e., tk= x1+x2+x3+· · ·+xk) [11]. By convention, t0= 0.
The density function fk(tk) of tkis expressed as
fk(tk)= ⎧ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎨ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎪ ⎩ 0, if k= 0 tk x1=0 tk−x1 x2=0 tk−x1−x2 x3=0 · · · tk−x1−x2−x3−...,xk−1 xk=0 ×αk k i=1 μxe−μxxi d xkd xk−1d xk−2, dx1, if k> 0 (6) and its Laplace transform is
fk∗(s)= αμx s+ μx k (7) Let PG, f be the probability that the PDP context is corrupted in a session. As shown in figure 4, PG, f can be derived as follows: PG, f = ∞ k=0 Pr[tk< tf,0< tk+ xk+1] =∞ k=0 ∞ tk=0 ∞ tf,0=tk ∞ xk+1=tf,0−tk × fk(tk)ηe−ηtf,0μ xe−μxxk+1d xk+1dtf,0dtk = η η + μx ∞ k=0 ∞ tk=0 fk(tk)e−ηtkdtk = η η + μx ∞ k=0 fk∗(η) = η η + μx− αμx (8) Let Pf be the probability that the PDP context is corrupted, and the backuped PDP context is invalid, and P( f|G, f )be the conditional probability that under the condition when the PDP context is corrupted, the backuped PDP context is invalid, and then we have
P( f|G, f )
= [Pr Backup is invalid PDP context is corrupted] = Pr[PDP context is corrupted, and backup is invalid]
Pr[PDP context is corrupted]
= Pf
PG, f (9)
Let Nr be the number of the PDP context reactivations exe-cuted due to PDP context corruption in a session. Then Nris obtained as follows
Nr = NfP( f|G,J) and E[Nr]= E[Nf]P( f|G,J) (10)
By applying E[Nf] in (4) into (10), (10) is rewritten as E[Nr]=
η
(1− α)μx
P( f|G, f ) (11)
Let Nb be the number of the backups executed for a PDP context in a session. Suppose that the dr cost is introduced to the network to reactivate a PDP context, and the db cost is required for each backup. The total cost dtintroduced in a session is expressed as
dt = dbE[Nb]+ drE[Nr] (12) In the following, we derive E[Nb], Pf, E[Nr], and dt for the Basic mechanism, and the GFR mechanism with GBA1, GBA2 and GBA3.
4.1. The analytic model for the Basic mechanism
In the Basic mechanism, since no backup is exercised by the GGSN, we have
E[Nb]= 0 (13)
When the PDP context is corrupted, the PDP context becomes invalid. Then
P( f|G, f )= 1 (14)
From (10), (14), and (4), the E[Nr] for the Basic mechanism is
E[Nr]= E[Nf]= η (1− α)μx
(15) By applying (13) and (15) into (12), we have the dt for the Basic mechanism as dt = dbE[Nb]+ drE[Nr]= dr η (1− α)μx (16) 4.2. The analytic model for GFR with GBA1
Suppose that in GFR with GBA1, the value y of the TG1timer has the exponential distribution with the density function fG1(y)= γG1e−γG1yand mean 1/γG1. As shown in figure 5(a),
similar to the derivation of Pr[Nf = n] in (3), Pr[Nb = n] for the GFR with GBA1 mechanism is obtained as follows:
Pr [Nb= n] = ∞ ta=0 (γG1ta)n n! e−γG1ta fa(ta)dta = (1− α)μx γG1+ (1 − α)μx γG1 γG1+ (1 − α)μx n (17) and E[Nb]= ∞ n=1 n Pr[Nb= n] =∞ n=1 n (1− α)μx γG1 + (1 − α)μ x
× γG1 γG1+ (1 − α)μx n = γG1 (1− α)μx (18) For the analysis of Pf, E[Nr], and dtfor the GFR with GBA1, the derivations are too complicated and are not conducted in this paper. Instead, we use simulation experiments to analyze the three values.
4.3. The analytic model for GFR with GBA2
In GFR with GBA2, in a session, the GGSN backups the PDP context for every KG2PDU arrivals (see figure 5(b)), and then
Nb=
Nm KG2
In this study, we obtain an approximated value for the mean of Nbby using the following equation.
E[Nb]= E[Nm] KG2 (19) From (5), we have E[Nm]= 1/(1−α), and (19) can be rewrit-ten as E[Nb]= 1 (1− α)KG2 (20) Consider the timing diagram in figure 5(b). The Pf prob-ability for GFR with GBA2 is
Pf = ∞
k=0
Pr [the PDP context is corrupted in the interval xk+1, and the PDP context is not backuped for the kth PDU arrival]
=∞ k=0
Pr[tk< tf,0< tk+ xk+1and k mod KG2= 0](21)
Then (21) can be approximately obtained by using the fol-lowing equation: Pf = 1− 1 KG2 ∞ k=0 Pr[tk< tf,0< tk+ xx+1] (22) From (8), (22) is rewritten as Pf = 1− 1 G2 PG, f (23)
By applying (23) into (9), the P( f|G, f )probability for GFR
with GBA2 is
P( f | G, f ) = Pf/PG, f = 1 − KG21 (24)
Apply (24) into (11), and we have E[Nr]= η (1− α)μx 1− 1 KG2 = η(KG2− 1) (1− α)μxKG2 (25) By applying (20) and (25) into (12), we have the dt cost for GFR with GBA2 as follows.
dt = db 1 (1− α)KG2 + η(K G2− 1) (1− α)μxKG2 (26) 4.4. The analytic model for GFR with GBA3
In GBA3, assume that the value y of the TG3 timer has an exponential distribution with density function fG3(y)=
γG3e−γG3y. Consider the timing diagram in figure 5(c). After
the i th PDU arrives, the PDP context is backuped if xi+1 is larger than the value of TG3. Let β be the probability that xi+1 > y, and then β = Pr[xi+1> y] = ∞ y=0 ∞ xi+1=y μxe−μxxi+1γG3e−γG3yd xi +1d y = γG3 μx+ γG3 (27) By using the GBA3 backup algorithm, for each PDU arrival (which causes the PDP context to be modified) in a session, with probability β, the PDP context is backuped. Then we have Nb= β Nmand E[Nb]= β E[Nm]. From (5) and (27),
E[Nb]= γG3
(1− α)(μx+ γG3)
(28) The Pf for GFR with GBA3 is derived as follows. As shown in figure 6, consider the time intervals tk, xk+1, y, and tf,0. If tk< tf,0< tk + xk+1 and xk+1 < y (see figure 6(a)), or if tk< tf,0< tk+ y and y < xk+1 (see figure 6(b)), then as the PDP context is corrupted, the backuped PDP context is
invalid. Pf = ∞ k=0 {Pr[tk< tf,0< tk+ xk+1 and xk+1 < y] + Pr[tk< tf,0< tk+ y and y < xk+1]} =∞ k=0 Pr[tk< tf,0< tk+ min(xk1, y)] (29) Let z= min(xk+1,y) and with density function fz(z). We have
fz(z)= d 1− ∞ xk+1=z μxe−μxxk+1d xk +1 × ∞ y=z γG3e−γG3ydy dz = μxe−(μx+γG3)z+ γG3e−(μx+γG3)z (30)
Replace min(xk+1, y) in (29) with z, and we obtain Pf = ∞ k=0 Pr[tk < tf,0< tk+ z] =∞ k=0 ∞ tk=0 ∞ tf,0=tk ∞ z=tf,0−tk × fk(tk) ff(tf,0) fz(z)dzdtf,0dtk =∞ k=0 ∞ tk=0 ∞ tf,0=tk ∞ z=tf,0−tk fk(tk)ηe−ηtf,0μxe−(μx+γG3)z + γG3e−(μx+γG3)zdzdt f,0dtk =∞ k=0 (C+ D) (31) where C = ∞ tk=0 ∞ tf,0=tk ∞ z=tf,0−tk × fk(tk)ηe−ηtf,0μxe−(μx+γG3)zdzdt f,0dtk and D= ∞ tk=0 ∞ tf,0=tk ∞ z=tf,0−tk × fk(tk)ηe−ηtf,0γG3e−(μx+γG3)zdzdt f,0dtk From Appendix C, we have
C= ημx (μx+ γG3)(η + μx+ γG3) αμx η + μx k and D= ηγ G3 (μx+ γG3)(η + μx+ γG3) αμ x η + μx k Then (31) is rewritten as Pf = ∞ k=0 ημ x (μx+ γG3)(η + μx+ γG3) αμ x η + μx k + ηγG3 (μx+ γG3)(η + μx+ γG3) αμx η + μx k = η(η + μx) (η + μx+ γG3)(η + μx− αμx) (32) By applying Pf (obtained in (32)) and PG, f (obtained in (8)) into (9), the P( f|G, f )for GFR with GBA3 is obtained as
fol-lows. P( f|G, f )= Pf/PG, f = η(η + μx) (η + μx+ γG3)(η + μx− αμx) η η + μx− αμx = η + μx η + μx− γG3 (33) Apply (33) into (11), and we have E[Nr] for GFR with GBA3:
E[Nr]= η (1− α)μx η + μ x η + μx+ γG3 (34) The dtcost for GFR with GBA3 can be obtained by applying E[Nr] in (34) and E[Nb] in (28) into (12), that is,
dt = db γG3 (1− α)(μx+ γG3) + dr η(η + μx) (1− α)μx(η + μx+ γG3) (35) 4.5. Simulation validation
From (16), (26), and (35), the dtcost for the Basic, GFR with GBA2 and GBA3 mechanisms can be computed. From (18), (20), and (28), we calculate the E[Nb] values for the GFR with GBA1, GBA2, and GBA3 mechanisms. We also conduct sim-ulation experiments for the four mechanisms. The simsim-ulation technique used in this paper is similar to that used in [11], and the details are omitted. Table 1 lists the P( f|G, f )for GBA2
and GBA3), dt(for Basic, GBA2, and GBA3) and E[Nb](for GBA1, GBA2, and GBA3) obtained from simulation and analysis. In this table, the errors between the simulation ex-periments and analytic data are within 1%, which indicates that the simulation results match closely with the analytic data.
5. Numerical results
In this section, we investigate the dtand P( f|G, f )performances for the Basic mechanism, the GFR mechanism with differ-ent backup algorithms. To simplify our description, we use GBA1, GBA2, and GBA3 to denote the GFR with the GBA1, GBA2, and GBA3 algorithms, respectively. As described in
Table 1
The P( f|G, f ), E[Nb] and dt values: simulation vs. analysis (α = 99.93%,
n= 2 × 10−4μX, dr =105db,γG1=101μx, KG2= 10, and γG3=19μx).
Outputs Simulation Analysis Error
Basic dt 8.5356× l04db 8.5714× l04db 4.17× 10−3 GBA1 E[Nb] 142.1 142.857 5.3× 10−3 GBA2 dt 7.7079× 104db 7.7285× 104db 2.67× 10−3 E[Nb] 141.62 142 2.68× 10−3 P( f|G, f ) 90.19% 90% 2.1× 10−3 GBA3 dt 7.6960× l04db 7.7287× l04db 4.23× 10−3 E[Nb] 142.05 142.857 5.65× 10−3 P( f|G, f ) 90.14% 90% 1.53× 10−3
Section 4, the GBA2 mechanism uses the KG2 counter to determine the checkpoints to backup the PDP context, and the GBA1 and GBA3 mechanisms maintain the TG1and TG3 timers to determine the checkpoints, where the values of TG1 and TG3are exponentially generated with means 1/γG1 and 1/γG3, respectively. For GBA1, we have a variant algorithm where the TG1 timer is set up with a fixed value 1/γG1. This variant algorithm is denoted as GBA1 f.
In our study, the input parameters are normalized byμx. For example, if the mean of the PDU inter-arrival times is 1/μx = 1 second, then η = 10−3μx implies that averagely 16.6 minutes, the PDP context is corrupted. When the PDU inter-arrival times are exponentially distributed, the mean val-ues E[Nb/Nm] of GBA1, GBA2, and GBA3 can be calculated. For a fair comparison for the performances of GBA1, GBA2, and GBA3, we set up the TG1, KG2and TG3values based on an equal expected value E[Nb/Nm]= 10%. Similar results are observed for various E[N b/Nm] values and will not be presented in the paper. Therefore, we set up γG1= μx/10 for GBA1 and GBA1 f, KG2=10 for GBA2, and γG3 =
μx/9.
Effects ofα on P( f|G, f )and dt: Figure 7 plots P( f|G, f )and dt as functions of 1− α, where η = 2 × 10−4μxand dr = 3 × 105db. Figure 7(a) shows that 1− α insignificantly affects P( f|G, f )for the five mechanisms. From (14), (24), and (33),
it is obvious thatα is not the factor that affects P( f|G, f )
Basic, GBA2, and GBA3. Figure 7(a) also indicates that the P( f|G, f )for GBA1, GBA1f, GBA2, and GBA3 are almost identical with 90%. In this figure, we set the expected value E[Nb/Nm]=10% for GBA1, GBA1J, GBA2, and GBA3, and averagely the PDP context is backuped for 10% PDU arrivals.
In figure 7(b), we observe that dtis a decreasing function of 1−α. As 1−α increases, a session is more likely to end, and shorter time period of the session is observed. Thus the probability that PDP context is corrupted during a session becomes small. The network cost caused by the PDP con-text restoration (i.e., drE[Nr]) drops, and lower total cost dt is observed. Figure 7(b) indicates that the dt values of GBA1, GBA1 f, GBA2, and GBA3 are almost identical,
Figure 7. Effects ofα on P( f|G, f )and dt(η = 2×10−4μx; dr= 3×10−4db).
and about 12% improvement over the Basic mechanism is observed.
Effects of η on P( f|G, f )and dt: Figure 8 plots P( f|G, f )and dt as functions of 1/n, whereα = 99.93% and dr= 3 × 105db. Figure 8(a) indicates that the values of P( f|G, f ) for the five mechanisms change slightly as 1/η increases. Equa-tions (14) and (24) indicate thatη is not the factor affecting P( f|G, f )Basic and GBA2. For GBA3, from equation (33),
we know thatη is shown in the numerator and the denom-inator of equation (33), and the effects of η on P( f|G, f )
for GBA3 is considered minor. Similar to the effects ofα on P( f|G, f ), we see the same phenomenon caused by the
effects ofη.
In Figure 8(b), dt is a decreasing function of 1/η. As 1/η increases, the time period between two PDP context corruption becomes longer. Thus the probability that the PDP context is corrupted during a session becomes small, and lower network cost drE[Nr] is expected. From (12), it is clear that E[Nr] is a major factor dominating the dtcost. Therefore, with a larger 1/η, E[Nr] decreases, and smaller dtvalues are observed.
Effects of the Variance of PDU Inter-Arrival Times: Based
Figure 8. Effects ofη on P( f|G, f )and dt(α = 99.93%; dr= 3 × 105db).
and dt performances for GBA1, GBA1 f, GBA2, and GBA3 when the PDU inter-arrival times are gamma dis-tributed with mean 1/μx and variance vμx = 1/(μ
2
xω), whereω is the shape parameter and ω > 0. Figure 9 plots P( f|G, f )and dtas functions ofvμx, whereη = 2×10−4μx,
α = 99.93% and dr = 3 × 105db. In this figure, the ex-pected values of E[Nb/Nm] for GBA1, GBA1 f, GBA2, and GBA3 are set to 10%. In figure 9, we observe that when vμx> 1/μ
2
x, GBA1, GBA1 f, and GBA3 signifi-cantly outperform GBA2 in terms of P( f|G, f )and dt. As
vμx increases, the improvement is more significant. This
is due to the fact that when vμx becomes larger, more
small PDU inter-arrival times are observed. On the other hand, it is more likely to observe an extremely long PDU inter-arrival time in a session. If the PDP context can be backuped immediately at the beginning of the long PDU inter-arrival period, the backuped PDP context is valid un-til the end of the long PDU inter-arrival period. Consider the long PDU inter-arrival time (which is between when jth PDU arrives and when j+ 1st PDU arrives). When GBA1, GBA1J, or GBA3 is adopted as the backup al-gorithms, since they are both timer-based, the PDP con-text is likely to be backuped for the j th PDU arrival. On the other hand, for GBA2 (counter-based), if j mod KG2= 0, then the PDP context is not backuped for the
Figure 9. Effects of variance of PDU inter-arrival times on P( f|G, f )and
dt(η = 2 × 10−4μx; α = 99.93%; dr= 3 × 105db).
jth PDU arrival. When the PDU inter-arrival time be-comes long, the PDP context corruption is more likely to occur in this interval. Thus, we observe that as vμx
in-creases, the P( f|G, f )improvement of GBA1, GBA1 f, or
GBA3 over GBA2 becomes significant. For the dt perfor-mance, figure 9(b) shows that the similar trend as that in figure 9(a).
Effects of Pareto PDU Inter-Arrival Times: Based on
the simulation experiments, we also evaluate the P( f|G, f ) and dt performances for Basic, GBA1, GBA2 and GBA3 when the PDU inter- arrival times have a Pareto distri-bution with parametersβ and l. It has been shown that Pareto distribution can approximate the packet traffic very well [1]. The β parameter describes the “heaviness” of the tail of the distribution. The Pareto density function is fx(x)= β l l x β+1 and its expected value is
1 μx = E[x] = β β − 1 l (36)
If β is between 1 and 2, the variance for the distribution becomes infinite. Once a suitable value forβ is selected to
Figure 10. Effects of Pareto PDU inter-arrival times on P( f|G, f )and dt(β =
1.2; η = 2 × 10−4μx; dr= 3 × 105db).
describe the traffic characteristics, the l value is determined by the mean of the distribution (using (36)). In our study,β is set to 1.2. The mean values E[Nb/Nm] of GBA1, GBA1 f, GBA2 and GBA3 are set to 10%, and we set up theγG1, KG2andγG2 as 20μx/191, 10 and 20μx103, respectively. Figure 10 plots P( f|G, f )and dtas functions of 1− α, where η = 2 × 10−4μx and dr = 3 × 105db. Figure 10 shows that the P
( f|G, f )and dt
values for the five mechanisms have the following order: P( f|G, f )(Basic)> P( f|G, f )(GBA2)> P( f|G, f )(GBA1)
> P( f|G, f )(GBA1 f )> P( f|G, f )(GBA3)dt (Basic)
> dt(GBA2)> dt(GBA1)> dt(GBA1 f )> dt(GBA3) The Pareto density function is widely used to simulate the characteristics of the burst-ness for packet data. As the packet traffic becomes bursty (i.e., the PDP context is modified more frequently in a short period), it is more likely to observe a very long PDU inter-arrival time during a session. Therefore, as we explain for the phenomenon whenvμx > 1/μ
2
x (see fig-ure 9), the timer-based mechanisms (i.e., GBA1, GBA1 f, and GBA3) outperform the counter-based mechanism (i.e., GBA2). To conclude, GBA3 has the best performance among the four mechanisms.
6. Conclusions
We proposed an improved GGSN Failure Restoration (GFR) mechanism with different backup algorithms, GBA1, GBA2, and GBA3, to reduce the network signaling cost and delay for the restorations of the corrupted PDP contexts. The GFR backups the PDP context (in volatile storage) into non-volatile storage in GGSN at some checkpoints by using GBA1, GBA2, or GBA3. In GBA1 (a timer-based algorithm), the GGSN backups the PDP context into the non-volatile storage for ev-ery time interval TG1. In GBA2 (a counter-based algorithm), the PDP context is backuped into the non-volatile storage for every KG2PDU arrivals. In GBA3 (a timer-based algorithm), during a session, when the PDP context is modified (i.e., a PDU arrives), GGSN restarts the TG3 timer. When TG3 ex-pires (i.e., no PDU arrives during the time period of TG3), the PDP context is backuped into the non-volatile storage. The GFR mechanism can be applied in the UMTS system without introducing any new component and modifying the protocol of the UMTS network. This mechanism is considered practi-cal and cost-effective, which is very suitable to be deployed in the real system.
The analytic models (for GBA1, GBA2, GBA3, and the Basic mechanism proposed by 3GPP) and simulation exper-iments were conducted to evaluate the performances. Our study indicated that when the PDU inter-arrival times are exponentially distributed, GBA1, GBA2, and GBA3 have almost identical P( f|G, f ) and dt performances, and outper-form the Basic mechanism significantly. When the PDU inter-arrival times have a gamma distribution with large variance or a Pareto distribution (i.e., the packet traffic is bursty), GBA1 and GBA3 outperform GBA2 significantly in terms of P( f|G, f )
and dt. Our study also showed that GBA3 can capture the packet traffic pattern precisely and has the best performance.
Acknowledgments
The authors would like to thank the two anonymous review-ers. Their comments have significantly improved the quality of this paper. P. Lin’s work was sponsored in part by the National Science Council (NSC), R.O.C., under the contract number NSC93-2213-E-002-095, Computer and Communi-cations Research Labs/Industrial Technology Research Insti-tute (CCL/ITRI), Chunghwa Telecom Labs, Microsoft, Tel-cordia Applied Research Center and Taiwan Network Infor-mation Center (TWNIC).
Appendix A: Notation
The notation used in this paper is listed as follows.
r
1− α: the probability that an arrival PDU deactivates the PDP contextr
1/γG3: the expected value of the TG3timerr
η: the PDP context corruption rater
μx: the PDU arrival rater
db: the cost for each backupr
dr: the network cost to reactivate a PDP contextr
dt: the total network cost introduced to a sessionr
E[Nb]: the expected number of the backups executed for a PDP context in a sessionr
E[Nf]: the expected number of PDP context corruptions in a sessionr
E[Nm]: the expected number of PDU arrivals in a sessionr
E[Nr]: the expected number of the PDP contextreactiva-tions in a session executed by the network
r
KG2: the threshold number of PDU arrivals for which the GGSN backups the activated PDP context in GBA2r
Pf: the probability that a PDP context corruption occurs,and the backup of the PDP context is invalid
r
P( f|G, f ): the conditional probability that under thecon-dition when the PDP context is corrupted, the backup is invalid
r
PG, f: the probability that the PDP context is corrupted in a sessionAppendix B: Derivation of dnf∗ a(s)/dsn
Let fa∗(S)= [(1 − α)μx]/[s + (1 − α)μx]. We prove that the following hypothesis is true.
dnfa∗(S) dsn =
(−1)nn!(1− α)μx [s+ (1 − α)μx]n+1 Proof. We prove by induction on n.
Basis: Consider the case when n=1.
fa∗(S)
ds =
(−1)(1 − α)μx [s+ (1 − α)μx]2 and the hypothesis holds.
Inductive Step: Suppose that the hypothesis holds when n =
k. For n= k + 1, we have dk+1f∗ a(s) dsk+1 = d dkf∗ a(s) dsk ds = d (−1)kk!(1− α)μ x [s+ (1 − α)μx]k+1 ds = (−1)(k + 1)(−1)kk!(1− α)μx [s+ (1 − α)μx]k+2 = (−1)(k+1)(k+ 1)!(1 − α)μx [s+ (1 − α)μx](k+1)+1
Thus the hypothesis holds for all cases.
Appendix C: Derivations of C and D
C = ∞ tk=0 ∞ tf=tk ∞ z=tf,0−tk × fk(tk)ηe−ηtf,0μxe−(μx+γG3)zdzdt f,0dtk = ημx ∞ tk=0 ∞ tf,0=tk ∞ z=tf,0−tk × fk(tk)e−ηtf,0μxe−(μx+γG3)zdzdt f,0dtk = ημx (μx+ γG3)(η + μx+ γG3) ∞ tk=0 fk(tk)e−ηtkdtk = ημ x (μx+ γG3)(η + μx+ γG3) fk∗(η) Then from (7), we obtain
C= ημ x (μx+ γG3)(η + μx+ γG3) αμ x η + μx k
Similar to the derivation of C, we have D as follows. D= ∞ tk=0 ∞ tf,0=tk ∞ z=tf,0−tk × fk(tk)ηe−ηtf,0γG3e−(μx+γG3)zdzdt f,0dtk = ηγ G3 (μx+ γG3)(η + μx+ γG3) αμ x η + μx k (37) References
[1] M. Cheng and L.-F. Chang, Wireless dynamic channel assignment per-formance under packet data traffic, IEEE Journal on Selected Areas in Communications 17(7) (1999) 1257–1269.
[2] 3GPP, 3rd Generation Partnership Project; Radio Interface Protocol Architecture. Technical Report Technical Specification 3G TS 25.301 version 3.4.0 (2000-03) (2000).
[3] 3GPP, 3rd Generation Partnership Project; Technical Specification Group Services and System Aspects; Architecture Principles for Re-lease 2000; ReRe-lease 2000. Technical Report Technical Specification 3G TR 23.821 version 1.0.1 (2000-07) (2000).
[4] 3GPP, 3rd Generation Partnership Project; Technical Specification Group Core Network; Restoration Procedures; Release 5. Technical Report Technical Specification 3G TS 23.007 version 4.0.0 (2001-03) (2001).
[5] 3GPP, 3rd Generation Partnership Project; Technical Specification Group Core Network; General Packet Radio Service (GPRS); GPRS Tunneling Protocol (GTP) across the Gn and Gp Interface; Release 5. Technical Report Technical Specification 3G TS 29.060 version 5.0.1 (2002-01) (2002).
[6] 3GPP, 3rd Generation Partnership Project; Technical Specification Group Services and Systems Aspects; General Packet Radio Ser-vice (GPRS); SerSer-vice Description; Stage 2; Release 5. Technical Re-port Technical Specification 3G TS 23.060 version 5.0.0 (2002-01) (2002).
[7] 3GPP, 3rd Generation Partnership Project; Technical Specification Group Services and System Aspects; IP Multimedia Subsystem (IMS);
Stage 2 (Release 5). Technical Report Technical Specification 3G TS 23.228 version 5.11.0 (2003-12) (2003).
[8] H. Holma and A. Toskala, WCDMA for UMTS (John Wiley & Sons 2000).
[9] http://www.lucent.com.
[10] Y.-B. Lin and I. Chlamtac, Wireless and Mobile Network Architectures (John Wiley & Sons, 2001).
[11] P. Lin, Y.-B. Lin and I. Chlamtac, Modeling frame synchronization for UMTS high-speed downlink packet access, IEEE Transactions on Vechicular Technology 52(1) (2003).
[12] P. Lin, Y.-B. Lin and J.-Y. Jeng, Improving GSM call completion by call re-establishment, IEEE Journal on Selected Areas in Communications 17(7) (1999) 1305–1317.
Phone Lin (M’02) received his BSCSIE degree and
Ph.D. degree from National Chiao Tung Univer-sity, Taiwan, R.O.C. in 1996 and 2001, respectively. From August 2001 to July 2004, he was an Assis-tant Professor in Department of Computer Science and Information Engineering (CSIE), National Tai-wan University, R.O.C. Since August 2004, he has been an Associate Professor in Department of Com-puter Science and Information Engineering (CSIE), National Taiwan University, R.O.C. His current research interests include personal communications services, wireless
In-ternet, and performance modeling. Dr. Lin is a Guest Editor for IEEE Wireless Communications special issue on Mobility and Resource Man-agement. He is also an Associate Editorial Member for the WCMC Jour-nal. P. Lin’s email and website addresses are plin@csie.ntu.edu.tw and http://www.csie.ntu.edu.tw/ plin, respectively.
Guan-Hua Tu received his B.S.C.S.I.E degree
from National Central University, Taiwan, R.O.C., in 2001 and his Master degree in Computer Science from National Taiwan University, Taiwan, R.O.C., in 2003. He is currently a software engineer in Me-diaTek Inc. His resarch interests include personal communication services, mobile computing, and performance modeling.
![Figure 5. Timing diagrams for GBA1, GBA2, and GBA3. we have Pr[N f = n] = ∞ t a =0 (ηt a ) nn! e −ηt a f a (t a ) dt a = η n n! (−1) n d n f a ∗ (s)dsn
s =η (3)](https://thumb-ap.123doks.com/thumbv2/9libinfo/8875578.250064/5.892.157.732.125.704/figure-timing-diagrams-gba-gba-gba-ηt-ηt.webp)
