An analysis of location record checkpointing interval for mobility
database in PCS networks
Hung-Hsin ChangÆ Ming-Feng Chang Æ Chien-Chao Tseng
Published online: 31 January 2008
Springer Science+Business Media, LLC 2008
Abstract Mobility database that stores the users’ location records is very important to connect calls to mobile users on personal communication networks. If the mobility database fails, calls to mobile users may not be set up in time. This paper studies failure restoration of mobility database. We study per-user location record checkpointing schemes that checkpoint a user’s record into a non-volatile storage from time to time on a per-user basis. When the mobility database fails, the user location records can be restored from the backup storage. Numeric analysis has been used to choose the optimum checkpointing interval so that the overall cost is minimized. The cost function that we consider includes the cost of checkpointing a user’s location record and the cost of paging a user due to an invalid location record. Our results indicate that when user registration intervals are exponen-tially distributed, the user record should never be checkpointed if checkpointing costs more than paging. Otherwise, if paging costs more, the user record should be always checkpointed when a user registers.
Keywords Personal communications services Mobility database Location register (HLR/VLR) Failure restoration Checkpoint
1 Introduction
To set up a call in time to a mobile user in a cellular network, such as GSM (Global System for Mobile Communications) and UMTS (Universal Mobile Tele-communications System), it is necessary to constantly keep track of the mobile user’s location. In GSM and UMTS, user location records are stored in a two-level database that consists of HLR (Home Location Register) and VLR (Visitor Location Register) [1]. The HLR resides in the user’s home network and maintains mobile users’ profile information and the current visited VLRs. For each visiting user in the location areas managed by a VLR, the VLR stores the user’s subscription information and current location. When a mobile user crosses a location area, the user needs to register to the VLR and/or the HLR. Thus, the mobility database, HLRs and VLRs, are frequently modi-fied for location tracking and queried for call delivery. If the mobility database fails, calls to mobile users may not be set up in time because of invalid location records.
Many mobility database restoration schemes have been studied. ETSI (European Telecommunications Standards Institute) recommends periodically autonomous registration [2] where a mobile user is required to register its location with the mobility database periodically even if the user does not cross a location area. Therefore, after a location data-base fails, an invalid location record can be restored sooner by the autonomous registration, and the number of calls lost due to invalid location records is reduced. Haas and Lin [3] considered the tradeoff between the cost of autonomous H.-H. Chang (&)
Department of MIS, Chin-min Institute of Technology, MiaoLi, Taiwan, R.O.C.
e-mail: hhchang@csie.nctu.edu.tw M.-F. Chang C.-C. Tseng
Department of Computer Science, National Chiao-Tung University, Hsinchu, Taiwan, R.O.C.
M.-F. Chang
e-mail: mfchang@csie.nctu.edu.tw C.-C. Tseng
e-mail: cctseng@csie.nctu.edu.tw DOI 10.1007/s11276-008-0097-2
registration and the penalty of lost calls due to invalid location records. They suggested that the autonomous reg-istration interval should be chosen to be approximately equal to the call inter-arrival time. Fang et al. [4] considered the same cost function, and their study concluded that the optimal choice of autonomous registration interval may not be unique. They also showed that the optimal value can be found under certain traffic conditions. In addition, Fang et al. [5] showed that the optimal autonomous registration interval depends on the weighting ratio between the regis-tration signaling cost and the lost-call cost. To further reduce the time to restore invalid location records, Haas and Lin [6] proposed a demand re-registration scheme where mobile users are requested to re-register after the database fails. This scheme reduces the time to restore the location database. However, since user registration requires radio contact, this demanded re-registration from a large number of mobile users may cause repeated channel collisions, and thus waste wireless resources. Lin and Lin [7] studied a similar problem, the registration interval of badge-based location tracking system. Their results indicated that the channel collisions can be reduced by using exponential registration intervals without increasing the probability of losing calls due to invalid location records.
Checkpointing has also been use to enhance the reliability of a mobility database in presence of failures. UMTS recommends that the mobility database is periodically checkpointed to a non-volatile storage [8]. After a mobility database failure, the user location information can be restored from the non-volatile storage. Checkpointing mobility database is more cost-effective than autonomous registration, because accessing a local non-volatile storage is in general cheaper and faster than accessing a radio channel. If a user’s location record is not checkpointed every time when it is updated, the restored record may be out-of-date. In this case, to set up a call, the network can page the user at the location areas around the out-of-date location. Lin [9] derived the optimal checkpointing interval to balance the checkpointing cost against the paging cost, and showed that a user record need not be checkpointed if the checkpointing frequency is higher than 10 times or lower than 0.1 times of the user’s moving rate. Wang et al. [10] proposed an aperi-odic checkpointing scheme where checkpointing of location database is not performed periodically but is triggered by a threshold on the number of uncheckedpointed location records. They also showed that aperiodic checkpointing outperforms periodic checkpointing when the threshold value is not large. Lin [11] proposed a per-user checkpoint-ing algorithm where a user record is checkpointed only if the user record is modified when the checkpointing timer for the user expires. Otherwise, checkpointing is performed when the user registers for the next time. Since mobile users exhibit different characteristics in terms of registration and calling
behavior, per-user checkpointing schemes can serve each user better than a whole-system scheme, but the system has to maintain a checkpointing timer for each user. This timer maintenance job seems to be a large overhead to the system, but the hashed and hierarchical timing wheels, designed by Varghese and Lauck [12], take constant (O(1)) time to maintain n outstanding timers, i.e., the time complexity is independent of the number of timers.
In summary, per-user checkpointing schemes can serve each user best without much overhead. However, no analysis has been done on the choice of the checkpointing intervals for per-user checkpointing scheme. In this paper, we study three per-user checkpointing schemes and con-sider a cost function consisting of the checkpointing cost and the paging cost. Numeric analysis was used to derive the optimal checkpointing frequency when user registration interval is exponentially distributed.
Note that checkpointing and rollback-recovery has long been used to reduce the expected execution time of long-running computation [13–16]. A job run on a computer can be modeled as a transition through a sequence of computa-tion states enabled by computing of the processor(s). When a failure occurs, the computation of the job can be restarted from the most recent checkpoint (an error-free computation state saved before). The transition of computation state is extremely rapid given today’s computation power, typically trillions of times per second. On the other hand, the check-pointing of program state is costly due to its size and the relatively slow speed of nonvolatile memory. The question is how often to checkpoint so that the total computation time is minimized. This checkpointing and rollback-recovery problem becomes more complicated if one considers parallel processing issues of multi-processor system [17,18], or the checkpoint location issue of a moving server system [19].
In our work, the checkpointing of the location database of personal communications services (PCS) is different from that of the computation state in two aspects. First, the current user location is not computed from the previous location. When the database fails and the backup has an invalid location record, the valid location can only be restored by paging the user or by a latter user registration. Second, a user location changes at a very slow rate, typi-cally once in dozens of minutes; on the other hand, the checkpointing of a location record can be done in a flash, typically tens of miniseconds, since it is only a couple of bytes. Therefore, when a user registers a new location (this occurs once in a couples of minutes), we consider whether the user location record needs to be checkpointed or not. If we decide to checkpoint, and since it is unnecessary to checkpoint more than once in an inter-registration interval, the remaining question is when to do it. The location checkpointing can be described as a delayed event after the user registers. The question is how long the delay is. In this
paper, the delay is determined by two types of timers (fixed and exponential) and the expected expiration interval of the timers varies in the range of 0-?.
The rest of the paper is organized as follows. Section2 describes three per-user checkpoint algorithms, and their analytic models are presented in Sect.3. Numeric results are discussed in Sect.4. Conclusions are given in Sect.5.
2 Three per-user checkpointing algorithms
To simplify our discussion, all the events that lead to location update of a mobile user, such as registration, call origination, and crossing of location areas, will be referred to as regis-tration. Since accessing a radio channel is more expensive than accessing a local storage, we assume that no autono-mous registration is performed. Note that for a per-user database checkpointing algorithm, the checkpointing timer and the registration interval for each user may be different.
Three per-user database checkpointing algorithms are depicted in Fig.1. The notation used in the figures is described as follows. tr denotes the interval between two
consecutive registrations and TCdenotes the checkpointing
timer. In general, when TC expires, the user record is
checkpointed if it has been updated.
• Periodically checkpointing a modified record (FIXED) The first scheme is essentially the same as the UMTS checkpointing method except that it is performed on a
per-user basis and that only a modified location record is checkpointed. It works as follows,
1. When a user record is checkpointed, a timer, TC, of
fixed expiration interval is set on (see t0in Fig.1(a)).
2. When TCexpires, if the user record has been modified,
the user record is checkpointed (see t3 and t6 in
Fig.1(a)). Otherwise, if the user record has not been modified when TC expires, TC is restarted (see t4 in
Fig.1(a)) and the process repeats.
This scheme will be referred to as FIXED, because a timer of fixed expiration interval is used.
• Lin’s per-user checkpointing algorithm with an expo-nential timer (LINEXP)
Lin presented a per-user checkpointing algorithm [11], which is illustrated in Fig.1(b). His algorithm assumes that timer TC is exponentially distributed with mean 1/k. The
algorithm is described as follows,
1. TCis started when a user record is checkpointed (see t0
in Fig. 1(b)).
2. When TCexpires, if the user record has been updated
(see t3in Fig.1(b)), it is checkpointed. Otherwise, if
the user record has not been updated (see t4 in
Fig.1(b)), the user record is checkpointed at the next user registration (see t5in Fig.1(b)).
Lin’s algorithm differs from the FIXED scheme in that when the timer expires and the user record is not modified, the user record is checkpointed at the next user registration, but scheme FIXED waits until the timer expires after the next user registration. This algorithm will be referred to as LINEXP.
• Lin’s per-user checkpointing algorithm with a fixed checking interval (LINFIX)
To study the effects of exponential timers and fixed tim-ers, we apply fixed timers to Lin’s per-user checkpointing algorithm. The algorithm is identical to LINEXP except that timer TC is of fixed expiration interval. An example user
registration and checkpointing scenario can be found in Fig.1(c). This algorithm will be referred to as LINFIX.
3 Numeric analysis
The cost function we consider in the paper includes the cost of paging a user with an invalid location record and the cost of checkpointing a user’s location record. Let Pibdenote
the probability that a user record in the backup database is invalid when the main database fails. When an invalid user record is encountered by an incoming call, the network pages the user. Let tf denote the average database failure
interval. It can be shown that the paging cost is
tr tr
TC TC TC
t0 t1 t2 t3 t4 t5 t6
checkpointing
interval checkpointinginterval TC
tr tr
TC TC
t0 t1 t2 t3 t4 t5 t6
checkpointing
interval checkpointinginterval
tr tr
λ λ λ λ
t0 t1 t2 t3 t4 t5 t6
checkpointing
interval checkpointinginterval
Timer expire Registration Checkpoint
a) FIXED b) LINEXP c) LINFIX tr tr TC TC TC t0 t1 t2 t3 t4 t5 t6 checkpointing
interval checkpointinginterval
tr
proportional to Pib/tf. Let I denote the expected length of
the checkpointing interval. The checkpointing cost is pro-portional to 1/I. Let cbdenote the cost of checkpointing a
location record, and cpdenote the expected cost to page a
user with an invalid location record due to mobility data-base failure. For the cost function we consider, the checkpointing cost equals to cb(1/I), and the paging cost
equals to cp(Pib/tf). The cost function is given as follows
C¼ cb 1=I þ cp Pib=tf
ð1Þ We will study the effects of changing the expiration interval of TCon the total cost, and try to find the optimal
timeout interval to minimize the total cost. In our analysis, tris assumed to be exponentially distributed with mean 1/u.
The failure of mobility database is assumed to be a random distribution with a mean value an order larger than 1/u (the expected inter-registration interval).
• FIXED
Let T denote the expiration interval of timer TC.
Con-sider two consecutive checkpoints, checkpoints A and B, as shown in Fig.2. At checkpoint A, the user record is checkpointed and timer TC is activated. Since the user
registers after TCexpires for the (i - 1)th time and before
the ith time, the user record is checkpointed when TC
expires for the ith time, at checkpoint B.
Let Qi denote the probability that the interval between
two consecutive checkpoints is of length iT, i.e., the user registers between time (i - 1)T and iT. We have
Qi¼
ZiT ði1ÞT
ueutdt¼ euði1ÞTð1 euTÞ
The expected checkpointing interval can be obtained as follows. IFIXED¼ X1 i¼1 iTQi¼ T 1 euT ð2Þ
Since the inter-registration interval has an IID (independent identically distribution). The user registrations can be modeled as a renewal process. The behavior of checkpointings is also a renew process; because at each checkpoint, timer TC is restarted and the
registration interval is exponentially distributed. For a reliable mobility database, we expect the interval between two consecutive database failures is significantly larger than the user registration interval and the checkpointing interval. In this situation, the time when the database fails can be seen as a random observer to the renew process of user registration and that of checkpointing. The backup user record is invalid only after the user registers and before the record is checkpointed. If the main database fails during this period, the system restores an invalid backup record. Thus, we have
Pib FIXED¼ X1 i¼1 ZiT ði1ÞT ueutðiT tÞdt 0 B @ 1 C A , IFIXED ¼ 1 1 e uT uT ð3Þ
From (1) to (3) the cost function can be obtained as follows, CFIXED¼ cb 1 euT T þ cp tf 11 e uT uT ¼cp tf þ1 u ucb cp tf 1 euT T ð4Þ
Our goal is to minimize the cost by choosing an appropriate T. d dT 1 euT T ¼ 1 þ1 uT euT , T2
Since euT= 1 + uT + (uT)2/2! + (uT)3/3! + and uT[ 0, we have 1þuTeuT 1 and 1 þ1þuTeuT
=T2 0 for
T C 0, u C 0. This leads to that 1eTuT is a monotonic decreasing function of T. From (4), we can draw the conclusions below,
1. If ucb\ cp
tf ; CFIXED is a monotonic increasing function of T. CFIXEDcan be minimized when T = 0, i.e., the
expiration interval of the timer is of length 0. At each user registration, since the timer must have expired, the user record should be checkpointed. In this case, CFIXED = ucb.
2. If ucb[ cp
tf ; CFIXEDis a monotonic decreasing function of T. CFIXEDcan be minimized when T = ?, i.e., the
expiration interval of the timer is of infinite length. Since the timer never expires, the user record should never be checkpointed. In this case CFIXIED¼
cp tf : 3. If ucb¼ cp tf ; CFIXIED¼ ucb¼ cp tf; CFIXED is a constant independent of T. T can be any value, i.e., at a user registration, the user record can be either checkpointed or not checkpointed. The cost of checkpointing the record and the cost of not checkpointing (the expected paging cost) are the same.
Timer expire Registration Checkpoint The user registers checkpoint A t T TCexpires 1st time (i-1)T checkpoint B
. . .
iT TCexpires (i-1)th time TCexpires ith timeNote that the minimum cost that scheme FIXED can achieve equals to Min ucb;
cp
tf
:
• LINEXP
The analysis of the LINEXP is similar to that of the FIXED. Considering two consecutive checkpoints, there are two possible conditions as shown in Fig.3. For Case I, shown in Fig.3(a), the user registers before timer TCexpires, so that the
checkpointing interval is equal to the expiration interval of timer TC(s in Fig.3(a)). For Case II, shown in Fig.3(b), the
user registers after timer TCexpires, so that the checkpointing
interval is equal to the user registration interval (t in Fig.3(b)). Since the registration interval and the checkpointing timer are both exponentially distributed, the expected length of checkpointing interval can be obtained by adding the intervals of both conditions.
ILINEXP¼ Z1 0 Zs t¼0 s ueut keksdtds þ Z1 0 Z1 t¼s t ueut keksdtds ¼1 kþ k uðkþ uÞ ð5Þ
For Case I, the backup user record is invalid only after the user registration at time t. For Case II, the backup user record is always up-to-date because when the user registers, the record is also checkpointed. From the random observer property, Pibcan be obtained as follows.
Pib LINEXP¼ Z1 0 Zs t¼0 s t ð Þ ueut keksdtds 0 @ 1 A , ILINEXP ¼ u 2 u2þ ku þ k2 ð6Þ
From (1), (5), and (6), the cost function can be obtained as follows, CLINEXP ¼cb 1 kþ k uðkþ uÞ þcp tf u 2 u2þ ku þ k2 ¼ucbþ cp tf ucb u 2 u2þ ku þ k2 ð7Þ Since d dk 1 u2þkuþk2 ¼ uþ2kð Þ u2þkuþk2 ð Þ2 0 for k 0; u 0; 1
u2þkuþk2 is a monotonic decreasing function of k. We also obtain the following results, which are essentially the same as those obtained from FIXED. Note that the expected timeout interval of the exponential timer is 1/k.
1. If ucb\ cp
tf ; CLINEXPis a monotonic decreasing function of k. The optimum CLINEXP= ucb, when k = ?, i.e.,
the timeout interval of the checkpointing timer is of length 0.
2. If ucb[ctp
f; CLINEXPis a monotonic increasing function of k. The optimum CLINEXP¼
cp
tf ; when k = 0, i.e., the timeout interval of the checkpointing timer is of infinite length. 3. If ucb ¼ cp tf ; CLINEXP¼ ucb¼ cp tf; a constant indepen-dent of k. k can be any value.
• LINFIX
Since this algorithm is identical to algorithm LINEXP except that it utilizes a checkpointing timer with fixed expiration interval. The two checkpointing cases of LIN-EXP shown in Fig.3can also be used to analyze LINFIX. For Case I, the checkpointing interval is equal to the expiration interval of the timer, which is T. For the Case II, the checkpointing interval is equal to the user registration interval (t). The expected length of checkpointing interval can be obtained as follows.
ILINFIX¼ ZT 0 T ueutdtþ Z1 T t ueutdt¼ T þe uT u ð8Þ
Pibequals to the probability that the main database fails
in Case I after the user registration.
Pib LINFIX ¼ ZT 0 T t ð Þ ueutdt 0 @ 1 A , ILINFIX ¼ 1 1 uTþ euT ð9Þ
From (1), (8) and (9), the cost function can be obtained as follows, CLINFIX¼ cb TþeuT u þcp tf 1 1 uTþ euT ¼cp tf þ ucb cp tf 1 uTþ euT ð10Þ Since d dT 1 uTþeuT ¼u 1eð uTÞ uTþeuT ð Þ2 and e -uTB1 for T C 0,
u C 0, we get u 1eð uTÞ
uTþeuT
ð Þ2 0: Thus,
1
uTþeuT is a monotonic decreasing function of T. We can obtain same results as in the FIXED and LINEXP.
1. If ucb\ cp
tf; CLINFIX is a monotonic increasing function of T. The optimum CLINFIX= ucb, when T = 0.
t u TC TC s s t checkpointing interval checkpointing interval u a) Case I b) Case II C C
2. If ucb[ cp
tf ; CLINFIXis a monotonic increasing function of T. The optimum CLINFIX¼
cp tf; when T = ?. 3. If ucb¼ cp tf; CLINFIX¼ ucb¼ cp
tf: T can be any value. It is important to note that the analyses of three algo-rithms all lead to the same conclusions. If the checkpointing cost out-weights the paging costðucb[
cp
tfÞ; we should never checkpoint a user record. On the other hand, ifcp
tf [ ucb; we should use a duplicated database.
4 Numeric results
Without loss of generality, we let the expected user reg-istration rate, u, to be 1 per unit-of-time. This can be interpreted as one registration per x minutes. A small x means the user registers frequently. We consider expo-nential registration interval and examine the effects of the timeout interval (T) on the expected checkpointing interval (I) and on the probability of invalid backup record at database failure (Pib). The expiration interval of timer TC
used in FIXED and LINFIX varies in the range 0.2–8 unit-of-time. In addition, the expected expiration interval of the exponential timer in LINEXP also varies in the range 0.2– 8. The curves in Fig.4(a) are obtained from Eqs.2,5, and 8, and those in Fig.4(b) from Eqs.3,6, and9. The results indicate that all three algorithms obtain similar results; both the expected checkpointing interval and the probability of invalid backup record increase as the timeout interval increases. The differences between the three algorithms are small, but for a given timeout interval, LINFIX has the smallest Pib at the cost of the shortest checkpointing
interval, I. When the timeout interval is larger than 4 (i.e., four times the registration interval), all checkpointing algorithms act much the same. This is because when a long checkpointing timer expires, the user record is most likely modified and needs to be checkpointed for all algorithms. Figure5 shows the cost functions at various paging costs; the user registration interval is exponential distrib-uted. The curves are obtained from Eqs. 4, 7, and 10. Without loss of generality, let u = 1, cb= 1, and
cp
tf vary in the range of 0.5–1.5. The results indicate when ucb¼
cp tf; 0 2 4 6 8 1 2 3 4 5 6 7 8 9 a) Checkpoint Interval T I FIXED LINEXP LINFIX 0 2 4 6 8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
b) Probability of Invalid Backup T
Pib Fig. 4 Comparison of
checkpointing algorithms for exponential registration interval
0 2 4 6 8 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 a) FIXED T t s o C 0 2 4 6 8 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 b) LINEXP T t s o C 0 2 4 6 8 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 1.5 c) LINFIX T t s o C 0.5 0.75 1.0 1.25 1.5 c t p f
Fig. 5 Cost functions for various paging costs (exponential registration interval)
the cost of all algorithms equals to 1ð¼cp
tf ¼ ucbÞ; and the total cost is independent of the timer expiration interval. Furthermore, when cp
tf [ ucb; the cost increases as the timeout interval, T, increases, and when ucb[
cp
tf; the cost decreases as T increases.
5 Conclusions
Checkpointing can be used to enhance the reliability of the location database of PCS networks, since each user exhibits a unique calling and moving behavior, per-user checkpointing schemes can serve the users, as well as the operators, better. In this paper, we have analyzed three per-user location database checkpointing algorithms using numeric analysis. The costs that we considered include the checkpointing cost and the paging cost. Our results indicate that when inter-registration times are exponentially distributed, a user location record should either be always checkpointed at registration, or be never checkpointed at all, depending on the weighting ratio between the checkpointing cost and the paging cost. If the checkpointing cost is of more concern, the user record should never be checkpointed; otherwise, the user record should be always checkpointed (duplicated) at registration. In this paper, we did not investigate the effects of incoming call arrivals on the optimal choice of the checkpointing frequency directly; we assumed that the expected paging cost is known. Further study is needed to obtain the paging cost in the PCS networks. In addition, if paging a user with an invalid location record cannot be done in time, the caller may hang up and the call is lost. It may be meritorious to consider a cost function consisting of the checkpointing, paging and lost-call costs.
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Author Biographies
Hung-Hsin Changreceived the B.S., M.S. and Ph.D. degree in Computer Science and Infor-mation Engineering from the National Chiao-Tung Univer-sity, Taiwan, R.O.C., in 1990, 1995 and 2005. He is currently a teacher in Chin-Min Institute of Technology, Taiwan. His current research interests include design and analysis of wireless net-work, Internet communications, and personal communications network.
Ming-Feng Chang received the Ph.D. degree in Computer Sci-ence from the University of Illinois at Urbana-Cham-paign in 1991. He is currently a Professor in the Department of Computer Science and Informa-tion Engineering, National Chiao-Tung University, Taiwan, R.O.C. His current research interests include design and analysis of Internet communica-tions, personal communications network, mobile payment, and performance modeling.
Chien-Chao Tsengis currently a professor in the Department of Computer Science at National Chiao-Tung University, Hsin-Chu, Taiwan. He received his B.S. degree in Industrial Engineering from National Tsing-Hua Univer-sity, Hsin-Chu, Taiwan, in 1981; M.S. and Ph.D. degrees in Com-puter Science from the Southern Methodist University, Dallas, Texas, USA, in 1986 and 1989, respectively. His research interests include Wireless Internet, Hand-over Techniques for Heterogeneous Networks, and Mobile Computing.
