Per-User Checkpointing
for Mobility Database Failure Restoration
Yi-Bing Lin, Fellow, IEEE
Abstract—This paper studies the failure restoration of mobility database for Universal Mobile Telecommunications System (UMTS). We consider a per-user checkpointing approach for the Home Location Register (HLR) database. In this approach, individual HLR records are saved into a backup database from time to time. When a failure occurs, the backup record is restored back to the mobility database. We first describe a commonly used basic checkpoint algorithm. Then, we propose a new checkpoint algorithm. An analytic model is developed to compare these two algorithms in terms of the checkpoint cost and the probability that a HLR backup record is obsolete. This analytic model is validated against simulation experiments. Numerical examples indicate that our new algorithm may significantly outperform the basic algorithm in terms of both performance measures.
Index Terms—Checkpoint, failure restoration, General Packet Radio Service (GPRS), Home Location Register, Universal Mobile Telecommunications System (UMTS).
æ
1
I
NTRODUCTIONT
HISpaper studies failure restoration of mobilitydata-bases for Universal Mobile Telecommunications System (UMTS) and/or General Packet Radio Service (GPRS) [13], [1]. UMTS and GPRS support wireless Internet applications [2]. In these networks, the Home Location Register (HLR) is a database used for mobile user information management. All permanent subscriber data are stored in this database. An HLR record consists of three types of information: Mobile Station (MS) Information such as the telephone number and the International Mobile Subscriber Identity (used by the MS to access the network), Service Information such as service subscription, service restrictions, and supplemen-tary services, and Location Information such as the address of the Serving GPRS Support Node (SGSN) where the MS resides. The location information in the HLR is updated whenever the MS moves to a new SGSN. To access the MS, the HLR is queried to find the current SGSN location of the MS. Note that both the MS and service information items are only occasionally updated. On the other hand, an MS may move frequently and the location information is often modified. Details of HLR operations due to call delivery can be found in [13].
If the HLR fails, one will not be able to access the MSs. To guarantee service availability to the MSs, database recovery is required after an HLR failure. In UMTS/GPRS [1], the HLR recovery procedure works as follows: The HLR database is periodically checkpointed. After an HLR failure, the database is restored by reloading the backup informa-tion. There are several approaches to checkpointing the HLR database. In the all-record checkpoint approach, all HLR records are saved into the backup at the same times [8], [5], [11]. The checkpoint overhead for this approach is very high and is typically performed at midnight when the HLR
activities are infrequent. Alternatively, checkpointing can be exercised for individual mobile users, which is referred to as per-user checkpointing [3], [9], [18], [12], [16]. We describe two algorithms for the per-user checkpoint approach. The first algorithm (referred to as Algorithm I) is the same as all-record checkpointing, except that the checkpoint frequencies for individual MSs may be different. The second algorithm (referred to as Algorithm II) is a new approach proposed in this paper.
Algorithm I (The Basic Algorithm). For every MS, we define a timeout period tp. In Fig. 1, the tptimeouts occur at time t0, t1, t2, t4, and t9. When this timer expires, checkpoint is performed to save the HLR record of the MS. Therefore, the checkpoint interval tc is equal to the timeout period tp. After a failure (see t6 in Fig. 1), the HLR record in the backup database is restored to the HLR. The backup copy is obsolete if the HLR record is updated between the last checkpoint and when the failure occurs (i.e., a registration occurs in ½t4; t6 in Fig. 1). After the HLR record is restored, one of the following two events may occur next:
. The record may be updated again if the MS issues a registration (i.e., t8< t7 in Fig. 1) or
. the record may be accessed due to an incoming call to the MS (i.e., t7< t8 in Fig. 1).
After a failure, if the backup record is obsolete and the next event to the MS is an incoming call (t7< t8 in Fig. 1), then the call is lost. On the other hand, if the next event is a registration, then the location information of the HLR record is modified and the record is up to date again.
Algorithm II (Lin’s Algorithm). The intuition behind our algorithm is simple: If registration activities are very frequent (i.e., a registration always occurs before the tp timer expires), then Algorithm II behaves exactly the same as Algorithm I. On the other hand, if no registration has occurred before the tptimer expires, then there is no need to checkpoint the record (because the backup copy is still valid). In this case, checkpoint is performed when the next registration occurs.
In Algorithm II, a three-state finite state machine (FSM) is implemented for an HLR record. The state diagram for the FSM is shown in Fig. 2. Initially, the FSM is in state 0, and
. The author is with the Deparment of Computer Science and Information Engineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C. E-mail: liny@csie.nctu.edu.tw.
Manuscript received 31 Oct. 2003; revised 3 Jan. 2004; accepted 9 Feb. 2004; published online 27 Jan. 2005.
For information on obtaining reprints of this article, please send e-mail to: tmc@computer.org, and reference IEEECS Log Number TMC-0182-1003.
the tp timer starts to decrement. If a registration event occurs before the tptimer expires, the FSM moves to state 1, and remains in state 1 until the tp timeout event occurs. Then, the FSM moves back to state 0, the HLR record is checkpointed into the backup, and the tp timer is restarted. If the timeout event occurs at state 0, then the FSM moves to state 2, and the tp timer is stopped. If a registration event occurs at state 2, the FSM moves to state 0, a checkpoint is performed, and the tptimer is restarted.
Consider the timing diagram in Fig. 3. At time t0, the FSM is at state 0 (when a registration occurs). At time t1, the next registration occurs and the FSM moves from state 0 to state 1(where tm¼ t1 t0is the interregistration interval). At time t2, the tp timer expires and the FSM moves from state 1to state 0 (where tc¼ tp¼ t2 t0). At time t3, the tp timer expires again and the FSM moves from state 0 to state 2. At time t4, a registration occurs. The FSM moves from state 2 to state 0, and tc¼ m ¼ t4 t2, where m is the excess life or residual time of tm.
Two output measures are considered to investigate the checkpoint performance:
. E½tc: the expected checkpoint interval. The larger the E½tc value, the lower the checkpoint overhead. That is, the checkpoint cost is proportional to the checkpoint frequency 1=E½tc. We use EI½tc and EII½tc to represent the E½tc values for Algorithms I and II, respectively.
. : the probability that the HLR record in the backup is obsolete when a failure occurs. The smaller the value, the better the checkpoint performance. We use I and II to represent the values for Algorithms I and II, respectively.
. Ic: Improvement of Algorithm II over Algorithm I in terms of the E½tc measure.
. I: Improvement of Algorithm II over Algorithm I in terms of the measure.
In a typical checkpoint approach, fixed tpis selected [7], [8]. Since many HLR records will be performed per-user checkpointing, Exponential tp distribution is selected in our study to avoid congestion caused by a large number of simultaneous checkpoints. In [14], we showed that similar performance results were observed for both fixed and Exponential checkpoint approaches. On the other hand, Exponential checkpointing exhibits Exponential backoff property for resolving contention of checkpoint traffic [10]. Such an advantage is not found in the fixed checkpoint approach. The Exponential random variable tp has the density function
fpðtpÞ ¼ etp
Since tc¼ tp in Algorithm I, the expected checkpoint interval is
EI½tc ¼ E½tp ¼ 1
: ð1Þ
After a failure, the HLR record is restored from the backup. This backup copy is obsolete if the record in the HLR has been modified since last checkpoint. In Fig. 1, a failure occurs at time t6 which is a random observer of the intercheckpoint interval ½t4; t9 and the interregistration interval ½t5; t8. In this figure, the interval tm m is the residual time of tm, and m is the reverse residual time. Similarly, p is the reverse residual time of tp. Consider a random variable t with the probability density function fðtÞ, the distribution function F ðtÞ ¼Ry¼0t fðyÞdy, the expected value E½t, and the Laplace transform fðsÞ ¼R1
t¼0fðtÞestdt. Let be the residual time of t with the density function rðÞ, the probability distribution function RðÞ, and the Laplace transform rðsÞ. From [17],
rðÞ ¼1 F ðÞ
E½t and r
ðsÞ ¼1 fðsÞ
E½ts : ð2Þ Note that the reverse residual time distribution is the same as the residual time distribution [10], and (2) also holds for the reverse residual time. From (2), the density function rpðtÞ is the same as fpðtÞ for the Exponential distribution. That is,
rpðtÞ ¼ fpðtÞ ¼ et:
Let I be the probability that the HLR backup is obsolete when a failure occurs in Algorithm I. In Fig. 1, the backup copy is obsolete if t4< t5< t6. Let c¼ pwith the density function rpðcÞ be the reverse residual time tc¼ tp. Then,
I ¼ Pr½c> m ¼ Z 1 m¼0 rmðmÞ Z 1 c¼m ecd cdm ¼ rmðÞ ¼ 1 E½tm 1 fmðÞ : ð3Þ
2
M
ODELING OFA
LGORITHMII
This section derives the expected checkpoint interval EII½tc and the probability II of obsolete HLR backup record for
Fig. 1. The timing diagram for Algorithm I.
Fig. 2. The state diagram for Algorithm II.
Algorithm II. Consider the timing diagram in Fig. 3. In Algorithm II, if the tptimer is restarted due to the tptimeout event (i.e., a transition from state 1 to state 0; see t2in Fig. 3), then the next checkpoint interval is tc¼ maxðm; tpÞ. On the other hand, if the tptimer is restarted due to a registration event (i.e., a transition from state 2 to state 0; see t4in Fig. 3), then the next checkpoint interval is tc¼ maxðtm; tpÞ. The two random variables maxð
m; tpÞ and maxðtm; tpÞ are not the same in general. To distinguish the above two cases, state 0 is split into state 01 and state 02. If a checkpoint occurs due to a registration event, then the FSM moves from state 2to state 02. If a checkpoint occurs due to a tptimeout event, then the FSM moves from state 1 to state 01. Fig. 4 redraws the state diagram in Fig. 2 with these two new states. Let xbe the probability that the FSM is in state x. Then, with probabilities
p1¼ 01 01þ 02 and p2¼ 02 01þ 02 ; ð4Þ
the random variable tc can be expressed as
tc¼ p1maxðm; tpÞ þ p2maxðtm; tpÞ: ð5Þ In Fig. 4, it is clear that the transition probability from state 1 to state 01 is 1. Similarly, the transition probability from state 2 to state 02 is 1. Let the transition probabilities from state 02 to state 1 and state 2 be paand pb, respectively. Similarly, let the transition probabilities from state 01 to state 1 and state 2 be pc and pd, respectively. These transition probabilities are derived as
pa¼ fmðÞ; pb¼ 1 fmðÞ pc¼ rmðÞ; pd¼ 1 rmðÞ
: ð6Þ
From Fig. 4, the limiting probabilities x are expressed as follows: 1¼ 01þ 02þ 1þ 2 1¼ 01 2¼ 02 1¼ pc01þ pa02 2¼ pd01þ pb02 9 > > > > = > > > > ; : ð7Þ
With the above equations, (4) is solved to yield p1¼ fmðÞ 1þ f mðÞ rmðÞ and p2¼ 1 r mðÞ 1þ f mðÞ rmðÞ : ð8Þ From (5), the density function for tc is
fcðtcÞ ¼ p1etcRmðtcÞ þ rmðtcÞ rmðtcÞetc ð9Þ þ p2 etcFmðtcÞ þ fmðtcÞ fmðtcÞetc
: ð10Þ
Based on the relationship between tp, tm, and m, fcðtcÞ can be reinterpreted in two cases:
Case 1. The first term in the second bracket of (9) (and (10)) represents the situation when tp> m (or tp> tm). Case 2. The second and third terms in the second bracket of
(9) (and (10)) represent the situation when tp< m (or tp< tm).
Therefore, (9) and (10) can also be reexpressed as fcðtcÞ ¼ fc1ðtcÞ þ fc2ðtcÞ; where fc1ðtcÞ ¼ fmðÞetcR mðtcÞ 1þ f mðÞ rmðÞ þ½1 r mðÞetcFmðtcÞ 1þ f mðÞ rmðÞ ð11Þ is the density function for Case 1, and
fc2ðtcÞ ¼ fmðÞ r mðtcÞ rmðtcÞetc 1þ f mðÞ rmðÞ þ½1 r mðÞ fmðtcÞ fmðtcÞetc 1þ f mðÞ rmðÞ : ð12Þ
is the density function for Case 2.
From (9) and (10), the expected checkpoint interval for Algorithm II is EII½tc ¼ Z 1 tc¼0 tcfcðtcÞdtc ¼ A1f mðÞ 1þ f mðÞ rmðÞ þ A2½1 r mðÞ 1þ f mðÞ rmðÞ ; ð13Þ where A1¼ Z 1 tc¼0 tcetcRmðtcÞdtcþ Z 1 tc¼0 tcrmðtcÞdtc Z 1 tc¼0 tcrmðtcÞetcdtc ð14Þ ¼ d rmðsÞ s h i ds 8 < : 9 = ; s¼ þE½m þ drmðsÞ ds s¼ ð15Þ ¼r mðÞ þ E½m: ð16Þ
The first term in (15) is derived from the first term in (14) using the single integral rule and the linear scaling rule of Laplace transform [19]. The third term in (15) is derived from the third term in (14) using the linear scaling rule of Laplace transform. Similarly,
A2¼ Z 1 tc¼0 tcetcFmðtcÞdtcþ Z 1 tc¼0 tcfmðtcÞdtc Z 1 tc¼0 tcfmðtcÞetcdtc ¼f mðÞ þ E½tm: ð17Þ
From (13), (16), and (17), we have EII½tc ¼ p1 r mðÞ þ E½m þ p2 fmðÞ þ E½tm : ð18Þ
For the probability II of obsolete HLR backup record in Algorithm II, there is no close-form expression when arbitrary fmðtmÞ is used. In this paper, we consider mix-Erlang density function for tm, which is expressed as
fmðtmÞ ¼ Xj i¼1 qi ðitmÞni1 ðni 1Þ! " # ieitm; ð19Þ wherePji¼1qi¼ 1, iare the scale parameters and niare the shape parameters. The mix-Erlang distribution is selected because it has been proven as a good approximation to many other distributions as well as measured data [6], [10]. For purposes of illustration, it suffices to derive II by considering tm with Erlang distribution where the density function is fðn; ; tmÞ ¼ ðtmÞn1 ðn 1Þ! " # etm
(i.e., j ¼ 1 in (19)). It is straightforward to extend our results with Erlang tm distribution to the results with mix-Erlang distribution. Let F ðn; ; tmÞ be the Erlang distribution function. Then, Fðn; ; tmÞ ¼ 1 X n1 j¼0 ðtmÞj j! " # etm; ð20Þ ¼ 1 1 Xn j¼1 fðj; ; tmÞ ð21Þ and the Laplace transform fðn; ; sÞ is expressed as
fðn; ; sÞ ¼ þ s n
: ð22Þ
The reverse residual time m of tm has the density function rðn; ; mÞ, the distribution function Rðn; ; mÞ, and the Laplace transform rðn; ; sÞ. Since E½t
m ¼n, from (2) and (21), rðn; ; mÞ ¼ 1 n Xn j¼1 fðj; ; mÞ; Rðn; ; mÞ ¼ 1 n Xn j¼1 Fðj; ; mÞ; ð23Þ and rðn; ; sÞ ¼ ns 1 þ s n : ð24Þ
Consider a checkpoint interval tc. Let us revisit the two cases mentioned before:
Case 1. tc¼ maxðtm; tpÞ ¼ tp or maxðm; tpÞ ¼ tp: The HLR record is always updated in this tc interval. The tc density function for this case is expressed in (11). Case 2. tc¼ maxðtm; tpÞ ¼ tm or maxðm; tpÞ ¼ m: The HLR
record is never updated in this tcinterval. The tcdensity function for this case is expressed in (12).
To derive II, we only need to consider Case 1. From (11) and (23), fc1ðtcÞ ¼ p1etc 1 n Xn m¼1 Fðm; ; tcÞ " # þ p2etcFðn; ; tcÞ ¼ p1 n Xn m¼1 gðm; ; tcÞ þ p2gðn; ; tcÞ; ð25Þ where gði; ; tÞ ¼ etFði; ; tÞ ð26Þ ¼ etX i k¼1 k1 ð þ Þk " # fðk; þ ; tÞ: ð27Þ From (2) and (27), the density function of the (reverse) residual time corresponding to gði; ; tÞ is
hði; ; tÞ ¼ etX i k¼1 k1 kð þ Þk " # Xk j¼1 fðj; þ ; tÞ: ð28Þ Let cbe the reverse residual time of tc(see Fig. 3) in Case 1. The density function of c is
rc1ðcÞ ¼ p1 n Xn m¼1 hðm; ; cÞ " # þ p2hðn; ; cÞ: ð29Þ From (29), II is derived as II ¼ Pr½c> m ¼ Z 1 m¼0 rðn; ; mÞ Z 1 c¼m rc1ðcÞdcdm ¼ p1 n Xn m¼1 Z 1 m¼0 rðn; ; mÞ Z 1 c¼m hðm; ; cÞdcdm þ p2 Z 1 m¼0 rðn; ; mÞ Z 1 c¼m hðn; ; cÞdcdm ¼ p1 n Xn m¼1 A3ðmÞ A4ðmÞ þp2 A3ðnÞ A4ðnÞ ; ð30Þ where A3ðmÞ ¼ Z 1 m¼0 rðm; ; mÞ Z 1 c¼m ecd cdm ¼ m 1 þ m ð31Þ
and A4ðmÞ ¼ Z 1 m¼0 rðm; ; mÞ Z 1 c¼m Xm k¼1 k1 kð þ Þk " # X k j¼1 fðj; þ ; cÞdcdm ¼X m k¼1 k1 kð þ Þk " # Xk j¼1 Bðm; jÞ; ð32Þ where Bðm; jÞ ¼ Z 1 m¼0 rðm; ; mÞ Z 1 c¼m fðj; þ ; mÞdcdm ¼X j l¼1 1 mð þ Þ Xm i¼1 Z 1 m¼0 fði; ; mÞfðl; þ ; mÞdm: ð33Þ Our analytic model is validated against simulation experiments (the simulation model is similar to the one we developed in [8], [11], [15] and the details are omitted). In Figs. 5 and 6, the symbols , , and represent simulation data, and the solid curves represent the analytic results. The figures indicate that the errors between the analytic results and the simulation data are within 2 percent.
3
P
ERFORMANCEE
VALUATION OFA
LGORITHMSI
ANDII
This section uses numerical examples to investigate the performance of Algorithms I and II. For purposes of illustration, we consider the simplest mix-Erlang format for the tmdistribution (i.e., j ¼ 2 and n1¼ n2¼ 1 in (19)):
fmðtmÞ ¼ q1e1tmþ ð1 qÞ2e2tm: ð34Þ This density function can be used to approximate the fast and slow movement behaviors of a mobile user. When 1>> 2, it means that with probability q, the user moves very fast (i.e., crossing the SGSN areas with high frequency 1); and with probability 1 q, the user moves very slowly (i.e., crossing the SGSN areas with low frequency 2).
Based on (34), we compute EI½tc; I, EII½tc, and II. For Algorithm I, EI½tc is expressed in (1), which is not affected by the tmdistribution. From (3),
I ¼ 1 q 1 þ1 q 2 1 1 q1 1þ ð1 qÞ2 2þ : ð35Þ From (18), EII½tc ¼ p1C1þ ð1 p1ÞC2; ð36Þ where p1¼ q1 1þ þð1 qÞ2 2þ 1þ q1 1þ þð1 qÞ2 2þ I 1 ; C1¼ q 1 þ1 q 2 1 1 2þ q 1 2 1 1 2ð 1þ Þ þ ð1 qÞ 1 2 2 2 2ð 2þ Þ ; and C2¼ q 1 1 þ 1 ð1þ Þ þ ð1 qÞ 1 2 þ 2 ð2þ Þ : From the derivation in the previous section,
II¼ 2q21 ð21þ Þð1þ Þ þ 2ð1 qÞ 2 2 ð22þ Þð2þ Þ : ð37Þ
Fig. 5. The checkpoint overhead (¼ ð1þ 2Þ=2). (a) Checkpointing
cost for Algorithm I. (b) Improvement of Algorithm II over Algorithm I. Fig. 6. The probability of obsolete HLR backup record after failure (¼ ð1þ 2Þ=2). (a) Obsolete record probability for Algorithm II.
To compare Algorithm II with Algorithm I, we define two improvement indicators. The indicator Ic represents the percentage of checkpoint cost saved by Algorithm II over Algorithm I. Since the checkpoint cost is proportional to the checkpoint frequency, Ic is defined as
Ic¼ 1 EI½tc 1 EII½tc 1 EI½tc ¼EII½tc EI½tc EII½tc : ð38Þ
Another indicator Irepresents the percentage of reduction for provided by Algorithm II over Algorithm I. That is
I¼
I II I
: ð39Þ
Fig. 5a plots the checkpoint frequency (i.e., 1=EII½tc) curves based on (36). Fig. 5b plots the Ic curves based on (38). In these figures, ¼ ð1þ 2Þ=2, and the checkpoint frequency is normalized by 2. Fig. 5a shows the intuitive result that the checkpoint cost for Algorithm II is an increasing function of the registration frequency. The nontrivial result is that the checkpoint cost can be quantitatively computed through our model. Fig. 5b shows that Algorithm II significantly outperforms Algorithm I in terms of reducing the checkpoint cost.
Based on (37), Fig. 6a plots II against 1=2. When 1=2 increases, the variance of interregistration interval increases. Therefore, we will observe a small number of checkpoint intervals that experience many registrations and a large number of checkpoint intervals that experience no registration. From the description of Algorithm II, it is also clear that the checkpoint intervals without registration are longer than the intervals with registrations. Since a failure is a random observer of the checkpoint intervals, the failure time is more likely to fall in a checkpoint interval without any registration. Therefore, IIdecreases as 1=2increases (this phenomenon is also true for Algorithm I). Based on (39), Fig. 6b indicates that Algorithm II provides 20-55 percent improvement over Algorithm I in terms of performance.
4
C
ONCLUSIONSWe studied failure restoration of Home Location Register (HLR) for UMTS and GPRS. By utilizing per-user check-point, an HLR record is saved into a backup database from time to time. When a failure occurs, the backup record is restored to the HLR. We first described a commonly used basic checkpoint algorithm (referred to as Algorithm I). Then, we proposed a new checkpoint algorithm called Algorithm II. An analytic model was developed to compare these two algorithms in terms of the checkpoint cost and the probability of obsolete HLR backup record. The analytic model was validated against simulation experiments. For all input parameter values considered in this paper, Algorithm II can save more than 50 percent of the checkpoint cost over Algorithm I. For the performance of , Algorithm II demonstrates 20-55 percent improvement over Algorithm I. As a final remark, we note that failure restoration for a SGSN (or a visitor location register in the circuit switched service domain) is very different from HLR failure restoration described in this paper. No checkpoint-ing is performed for a SGSN because all MS records in the SGSN are temporary, and it is useless to store these temporary records into backup. Details of SGSN failure restoration can be found in [7], [4], [11].
A
CKNOWLEDGMENTSThis work was sponsored in part by Chair Professorship of Providence University, IIS/Academia Sinica, FarEastone, and CCL/ITRI. Equations (35) and (36) were contributed by Sok-Ian Sou under NSC Excellence project NSC93-2752-E-0090005-PAE.
R
EFERENCES[1] 3GPP, 3rd Generation Partnership Project; Technical Specification Group Services and Systems Aspects; General Packet Radio Service (GPRS); Service Descripton; Stage 2, Technical Specifica-tion 3G TS 23.060 version 4.1.0 (2001-06), 2001.
[2] P. Agrawal, G. Omidyar, and A. Wolisz, IEEE Wireless Commu-nications Magazine, special issue on mobile and wireless Internet: architectures and protocols, 2002.
[3] G. Cao, “Proactive Power-Aware Cache Management for Mobile Computing Systems,” IEEE Trans. Computers, vol. 51, no. 6, pp. 608-621, 2002.
[4] M.-F. Chang, Y.-B. Lin, and S.-C. Su, “Improving Fault Tolerance of GSM Network,” IEEE Network, vol. 1, no. 12, pp. 58-63, 1998. [5] ETSI/TC, Restoration Procedures, Version 4.2.0, Technical Report
Recommendation GSM 03.07, ETSI, 1993.
[6] Y. Fang and I. Chlamtac, “Teletraffic Analysis and Mobility Modeling for PCS Networks,” IEEE Trans. Comm., vol. 47, no. 7, pp. 1062-1072, July 1999.
[7] Y. Fang, I. Chlamtac, and H. Fei, “Analytical Results for Optimal Choice of Location Update Interval for Mobility Database Failure Restoration in PCS Networks,” IEEE Trans. Parallel and Distributed Systems, 2000.
[8] Z. Haas and Y.-B. Lin, “On Optimizing the Location Update Costs in the Presence of Database Failures,” ACM/Baltzer Wireless Networks J., vol. 4, no. 5, pp. 419-426, 1998.
[9] A. Kahol, S. Khurana, S. Gupta, and P. Srimani, “An Efficient Cache Management Scheme for Mobile Environment,” Proc. IEEE Int’l Conf. Distributed Computing Systems (ICDCS), 2000.
[10] F.P. Kelly, Reversibility and Stochastic Networks. John Wiley & Sons, 1979.
[11] Y.-B. Lin, “Failure Restoration of Mobility Databases for Personal Communication Networks,” ACM-Baltzer J. Wireless Networks, vol. 1, pp. 365-372, 1995.
[12] Y.-B. Lin, “A Cache Approach for Supporting Life-Time Universal Personal Telecommunication Number,” ACM-Baltzer Wireless Networks, vol. 2, pp. 155-160, 1996.
[13] Y.-B. Lin and I. Chlamtac, Wireless and Mobile Network Architec-tures. John Wiley & Sons, 2001.
[14] Y.-B. Lin and P. Lin, “Performance Modeling of Location Tracking Systems,” ACM Mobile Computing and Comm. Rev., vol. 2, no. 3, pp. 24-27, 1998.
[15] Y.-B. Lin and V.K. Mak, “Eliminating the Boundary Effect of a Large-Scale Personal Communication Service Network Simula-tion,” ACM Trans. Modeling and Computer Simulation, vol. 4, no. 2, 1994.
[16] Y.-B. Lin, W.-R. Lai, and J.-J. Chen, “Effects of Cache Mechanism on Wireless Data Access,” IEEE Trans. Wireless Comm., vol. 2, no. 6, 2003.
[17] S.M. Ross, Simulation. Academic Press, 1996.
[18] J. Shim, P. Scheuermann, and R. Vingralek, “Proxy Cache Algorithms: Design, Implementation, and Performance,” IEEE Trans. Knowledge and Data Eng., vol. 11, no. 4, pp. 549-562, July/ Aug. 2000.
[19] E.J. Watson, Laplace Transforms and Applications. Birkhauserk, 1981.
Yi-Bing Lin received the BSEE degree from the National Cheng Kung University in 1983 and the PhD degree in computer science from the University of Washington in 1990. He is chair professor in the Department of Computer Science and Information Engineering (CSIE), National Chiao Tung University (NCTU). Dr. Lin is a fellow of the IEEE and the ACM.
