Overflow control for cellular mobility database

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520 IEEE TRANSACTIONS ON VEHICULAR TECHNOLOGY, VOL. 49, NO. 2, MARCH 2000

Overflow Control for Cellular Mobility Database

Yi-Bing Lin, Senior Member, IEEE

Abstract—In a cellular phone system, the service area is

parti-tioned into several location areas (LA’s). Every LA is associated with a mobility database called visitor location register (VLR). When a mobile user enters an LA, the user must register to the VLR before receiving any cellular service. If the VLR is full, the registration procedure fails and the system cannot deliver services to the user under the existing cellular technology. To resolve this problem, we propose a VLR overflow control scheme to accom-modate the incoming mobile users during VLR overflow. Our scheme only requires minor modifications to the existing cellular mobility management protocols. Particularly, no modification is made to the mobile phones.

An analytic model is proposed to investigate the performance of the overflow control scheme. When exercising the scheme, the call setup procedure for an “overflow” user is more expensive than that for a “normal” user. Under the range of input parameters consid-ered in our study, we show that even if the VLR overflow situation is serious, the overhead for exercising the overflow control scheme is very low.

Index Terms—Mobility database, overflow control, personal

communication services, visitor location register.

I. INTRODUCTION

C

ELLULAR or mobile communications services facilitate the exchange of information (voice, data, video, image, etc.) for mobile users independent of time, location, and access arrangement [1]–[3]. One of the most important issues in mo-bile communications is mobility management. To understand the mobility management issue, we first introduce the cellular system architecture (see Fig. 1). In this architecture, the cellular service area is covered by a set of base stations. The base stations are responsible for serving the calls to or from the mobile phones (in this figure, the mobile phones are mounted on the vehicles) located in their coverage areas. The base stations are connected to the mobile switching centers (MSC’s) by land links. The MSC is a telephone exchange specially assembled for mobile communications, which interfaces the mobile phones (via base stations) and the public switched telephone network (PSTN). The base stations are grouped into location areas (LA’s). The base stations in an LA are connected to the same MSC. When a mobile user moves from one LA (e.g., New York City) to another (e.g., Los Angeles), the cellular system should be informed of the current location of the user. Otherwise, it is impossible to deliver the services to this user. To support mobility management, protocols such as

Manuscript received June 26, 1997; revised February 23, 1999. This work was supported in part by the National Science Council under Contract NSC88-2213-E009-079.

The author is with the Department of Computer Science and Information En-gineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C. (e-mail: liny@csie.nctu.edu.tw).

Publisher Item Identifier S 0018-9545(00)02542-1.

the EIA/TIA Interim Standard 41 (IS-41) [4] or global system for mobile communications (GSM) mobile application part (MAP) [5] have been defined for cellular systems. The IS-41 protocol is used in advanced mobile phone service (AMPS), IS-136 digital AMPS (DAMPS), and IS-95 code-division multiple-access (CDMA) cellular systems. The GSM MAP protocol is used in GSM, GSM 1800, and GSM 1900 systems. These two protocols follow a two-level database strategy in that they use a two-tier system of home and visited databases. When a user subscribes to the services of a cellular system, a record is created in the system's database called home location register (HLR). The HLR is the location register to which a mobile phone identity is assigned for record purposes such as mobile user information (e.g., directory number, profile information, current location, and validation period). The HLR is part of the cellular network and not under the control of the local exchange carriers. The HLR is connected to the PSTN via SS7 links. Every LA is associated with a database called visitor location register (VLR). The VLR is the location register other than the HLR used to retrieve information for handling of calls to or from a mobile user visiting the LA. When the mobile user visits an LA, a temporary record for the mobile user is created in the corresponding VLR. When the user leaves the LA, the corresponding VLR record is deleted. A VLR may control several MSC areas (and thus the LA’s inside these MSC’s). To simplify our discussion, we assume that every MSC covers an LA, and every VLR controls exactly one MSC (and thus one LA). Our results can be easily generalized to the cases where a VLR controls several MSC’s, and an MSC controls several LA’s. The details of the mobility management algorithms based on VLR and HLR will be elaborated in Section II. The algorithms for multiple LA’s per VLR are given in [5].

In a cellular system, the number of the records in the HLR is the number of the customers in the system. When a customer first subscribes to the service, a permanent HLR record is cre-ated for the customer. Since mobile users of different cellular systems may visit an LA (e.g., the GSM users from England and Taiwan may visit Hong Kong), the number of the records in the VLR changes dynamically. Specifically, new records are created when users move in, and obsolete records are deleted when the corresponding users move out. Furthermore, the number of the records in the corresponding VLR may be larger than that of the HLR. The VLR may overflow if too many mobile users move into the LA in a short period. If the VLR is full when a mobile user arrives, the user fails to “register” in the database and thus cannot receive cellular service. This phenomenon is called VLR

overflow. To resolve this problem, Section III proposes a VLR

overflow control scheme that allows users to receive services when a VLR is full. The performance of the overflow control scheme is investigated in Section IV.

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Fig. 1. An illustrative cellular system architecture.

II. MOBILITYMANAGEMENT INEXISTINGSYSTEMS This section describes mobility management for the existing cellular systems based on IS-41 [4] or GSM [5]. Four algorithms are described. Algorithm I (registration) and Algorithm II (can-cellation) are used for location update. Algorithm III (call orig-ination) and Algorithm IV (call termorig-ination) are used for call control. With the location update procedure, the HLR maintains the current LA address of every mobile user and guarantees that the mobile user has exactly one VLR record. The call origina-tion procedure utilizes the VLR record to set up a call initiated by a mobile user. The call termination procedure utilizes both theHLR and VLR records to set up a call terminated at a mobile user.

Suppose that user moves from location area LA1 to lo-cation area LA2. The registration procedure is performed be-tween the HLR and (the VLR for LA2), and the cancella-tion (deregistracancella-tion) procedure is performed between the HLR and (the VLR for LA1).

Algorithm I. Registration (see Fig. 2):

Step 1) (Registration Request)

Step 1.1) The mobile phone of sends a registra-tion message to .

Step 1.2) creates a temporary VLR record for .

Step 1.3) forwards the registration request to the HLR. This message reg msg is

MAP UPDATE LOCATION in GSM and isREGNOTin IS-41.

Step 2) (Registration Response)

Step 2.1) The HLR updates the location of . This location information will be used to set up calls terminated at .

Step 2.2) The HLR acknowledges the reg-istration operation and sends 's

pro-file to . This message reg ack is

MAP UPDATE LOCATION ack in GSM and is regnot in IS-41. The profile provides necessary information for to originate phone calls.

Step 2.3) sends an acknowledgement to the mo-bile phone.

Note 1: In GSM, the mobile phone sends the temporary mo-bile subscriber identity (TMSI) to in Step 1) [5]. then uses the TMSI to find the mobile phone's international mobile subscriber identity (IMSI). The IMSI is used by to locate 's HLR.

Note 2: In Step 1), authentication (to check if is a legal user) may be performed in separate message ex-changes.

After has moved from to , 's VLR record in is obsolete and is deleted as described in the following algorithm.

Algorithm II. Cancellation (see Fig. 3):

Step 1) The HLR sends a cancellation message to 's old VLR . This message cancel msg is

MAP CANCEL LOCATION in GSM and is

REGCANCin IS-41. Step 2) deletes 's record.

Step 3) sends a cancellation acknowledgement to the HLR. This message cancel msg is

MAP CANCEL LOCATION ack in GSM and is

regcancin IS-41.

When originates a call, the following algorithm is exe-cuted. Note that the authentication procedure is omitted to sim-plify our description.

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Fig. 2. The registration operation.

Fig. 3. The cancellation operation.

Algorithm III. Call Origination (see Fig. 4):

Step 1) The mobile phone sends the call origination request to the MSC.

Step 2) The MSC forwards the request to

. The message call req is

MAP SEND INFO FOR OUTGOING CALL in GSM and isORREQin IS-41.

Step 3) checks the 's profile and grants the call request. The message call ack is

MAP SEND INFO FOR OUTGOING CALL ack

in GSM and isorreqin IS-41.

Step 4) The MSC sets up the trunk according to the standard PSTN call setup procedure.

To deliver a call to , the following algorithm is executed. Without loss of generality, we assume that the calling party is a wireline user.

Algorithm IV. Call Termination (see Fig. 5):

Step 1) The calling party dials the phone number of . This phone number is mobile station ISDN number (MSISDN) in GSM or mobile identification number (MIN) in IS-41. The request is sent to the originating switch in PSTN. In GSM, this originating switch is a

Gateway MSC.

Step 2) The originating switch sends a location query message to the HLR. This message loc req is

MAP SEND ROUTING INFORMATION in GSM and isLOCREQin IS-41.

Step 3) The HLR identifies the address of 's VLR (i.e., ) and sends a query message to obtain the routing information. This message rout req is

MAP PROVIDE ROAMING NUMBER in GSM and isROUTREQin IS-41.

Step 4) creates the routable address of and sends it back to the HLR. This routable address rout addr

is the mobile station roaming number (MSRN) in GSM and the temporary local directory number (TLDN) in IS-41. The message rout ack is

MAP PROVIDE ROAMING NUMBER ack in GSM and isroutreqin IS-41.

Step 5) The HLR returns the routable address to the originating switch. This message loc ack is

MAP SEND ROUTING INFORMATION ack

in GSM and isloc reqin IS-41.

Step 6) The originating switch sets up the trunk to the MSC based on the routable address.

Step 7) The MSC pages the mobile phone and the call path is established.

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Fig. 4. The call origination operation.

Fig. 5. The call termination operation.

III. MOBILITYMANAGEMENT INOVERFLOWSYSTEMS When a VLR is full, the incoming mobile users cannot reg-ister using Algorithm I and thus cannot receive cellular services. To resolve this problem, we propose the VLR overflow control algorithms O-I, O-II, O-III, and O-IV. Our approach allows new users to receive services when the VLR is full. In our overflow control scheme, an extra flag (one bit) is required in the HLR records. No modifications are made to the mobile phone.

Algorithm O-I. Registration (see Fig. 6): If is not full, then Algorithm I is executed. If is full, then the following steps are executed.

Step 1) (Registration Request)

Step 1.1) This step is the same as that in Algorithm I.

Step 1.2) The database is full. follows a replace-ment policy to select a record to be deleted ( in Fig. 6). The storage for the deleted record is used to store the 's information. The selected user (i.e., ) is called the overflow user.

The replacement policy may be based on var-ious heuristics. For example, may select a record randomly, select the oldest record, or se-lect an inactive record (i.e., the user has not had call activities recently). may select as the overflow user (i.e., ) and do not create the VLR record for .

Step 1.3) forwards the registration request to the HLR with the indication that 's record is deleted due to database overflow.

Step 2) (Registration Response)

Step 2.1) The HLR updates the location of and sets the overflow flag in 's record (to indicate that does not have a VLR record for ). Note that may be identical to as pointed out in Step 1.2).

Step 2.2) The HLR acknowledges the registration operation and sends 's profile to (if is the overflow user, then the message does not include the profile information).

Step 2.3) sends an acknowledgement to the mo-bile phone.

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Fig. 6. The registration operation (overflow).

Fig. 7. The cancellation operation (overflow).

Algorithm O-II. Cancellation: If is not an overflow user at , then Algorithm II is executed to cancel 's VLR record in . If is an overflow user at , then does not have a record in . The cancellation operation simply resets the overflow flag of 's HLR record if is not an overflow user in (see Fig. 7). The call origination for an overflow user is described below.

Algorithm O-III. Call Origination (see Fig. 8):

Step 1) The mobile phone sends the call origination re-quest to as described in Steps 1) and 2) in Algorithm III.

Step 2) cannot find 's record and denies the call request.

Steps 3-4) The mobile phone initiates the registration pro-cedure and Algorithm O-I is executed.

Steps 5-6) The mobile phone reissues the call origination request and Algorithm III is executed.

To deliver a call to an overflow user, the following algorithm is exercised.

Algorithm O-IV. Call Termination (see Fig. 9):

Step 1) (Location Query)

Step 1.1) The calling party dials the phone number of . The request is sent to the originating switch in PSTN.

Step 1.2) The originating switch sends a location query message to the HLR.

Step 1.3) The HLR identifies that is an overflow user and sends a query message to obtain the

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Fig. 8. The call origination operation (overflow).

routing information. The user profile informa-tion is attached in the message.

Step 2) (Location Response)

Step 2.1) If is not full, then a record for is cre-ated. If is full, then a user record is deleted and is used to store 's information. cre-ates the routable address of and sends it back to the HLR. If the VLR record is not available, the details of the routable address creation are described in [5]. If a record is replaced ( in Fig. 9), the replacement information is included in the message.

Step 2.2) The HLR returns the routable address to the originating switch. If a record is replaced, the overflow flags (for and in Fig. 9) are updated at the HLR.

Step 2.3) The originating switch sets up the trunk to the MSC based on the routable address. Step 2.4) The MSC pages the mobile phone and the

call path is established.

With Algorithms O-I–O-IV, an LA can accommodate unlim-ited number of mobile users as long as the number of simulta-neous phone calls to these users is no larger than the size of the database (this situation never occurs in the real world).

IV. MODELING THEOVERFLOWCONTROLSCHEME When exercising the overflow control scheme, we are inter-ested in several performance issues.

Issue I. What is the stationary probability that the VLR overflow situation occurs?

Issue II. What is the probability that the VLR record of a mobile user is never replaced due to VLR overflow?

Issue III. What is the probability that the call activities of a user is not affected by VLR overflow? Note that an “affected” call connection (i.e., Algorithms O-III and O-IV) is more complicated than a “unaffected” call connection (i.e., Algorithms III and IV). Issue III is different from Issue II. The call procedure is af-fected by VLR overflow if Algorithm O-III (for call origination) and Algorithm O-IV (for call termination) are exercised during call setup. After a VLR record replacement, the user may not originate or receive any call before moving out of the LA. Thus

.

To address the above issues, we make the following assump-tions.

Assumption I. Let be the expected number of users in an LA. The expected value can be obtained from operation, administra-tion, and maintenance (OA&M) mea-surements in the cellular systems.

Assumption II. Let the residence time of a user in the LA have a general density function with the Laplace transform

and the mean . The measurements for the arrival and the departure times of a user at an LA are available in the cellular systems. These data can be approximated by a general

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Fig. 9. The call termination operation (overflow).

density function using the standard statistic methods.

Assumption III. Let the call arrivals to a user be a Poisson distribution with the arrival rate . The Poisson call arrivals are a widely used assumption in telecommunication modeling, which has been validated in PSTN.

Assumption IV. Let be the size of the VLR.

Assumption V. Assume that during the short periods (i.e., the residence time of a user) the population is stationary. We will ad-dresses the mobility effect through the population distribution (1). This tech-nique significantly reduces the com-plexity of the analytic analysis, which has been shown reasonable in perfor-mance [6].

Assumption VI. If a registered mobile user (a nonoverflow user) leaves the VLR, there are two approaches to handle the cancellation procedure. In the first ap-proach, the HLR selects an overflow user (if any) and sends its informa-tion to the VLR through the cancellainforma-tion message ( 's deregistration). The VLR then creates the VLR record for using the storage for . Thus, if the

number of users in the VLR is larger than , we guarantee that the VLR is always full. The advantage is that when call origination/termination occurs to , Algorithm III/IV is used without overflow handling cost.

In the second approach, the VLR simply deletes the record for without further action. When the next new user ar-rives, the VLR creates a VLR record for using the reclaimed storage. The ad-vantage of this approach is that the VLR may not be considered overflow even if the number of user in the area is larger than . In the following analysis, the first approach is considered.

A. Issue I: Derivation for

A VLR area overflows if the number of users in the area is larger than the size of the VLR database. The probability was computed in our previous work [6]–[8]. Specifically, we de-rived the LA population distribution or the probability that there are users in the LA. The probability is derived as fol-lows. In the steady state, the rate that mobile phones move into a cell equals to the rate that they move out of the cell. The arrivals of mobile phones to an LA can be viewed as being generated from input streams that have the same general distribution

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(2)

Based on (2), Fig. 10 plots as a function of for dif-ferent values. The figure indicates that is large if

and % if . The figure also shows that for the same value, larger results in smaller .

B. Issue II: Derivation for

The probability (i.e., the probability that the VLR record of a mobile user is never replaced due to VLR overflow) is derived as follows. We make an approximation assumption that during the short periods (i.e., the residence time of a user) the popula-tion is stapopula-tionary and then address the mobility effect through the population distribution (1). This technique significantly re-duces the complexity of analytic analysis and has been shown reasonably accurate [6]. Suppose that there are users in the LA. Suppose that the VLR records are randomly selected for replacement at Steps 1) and 2) in Algorithm O-I. Then the probability that a VLR record is selected for replacement is

From Assumption III, the rate of the calls that result in VLR record replacement is

(3) Let be the probability that there are call ar-rivals with VLR record replacement during a period . From As-sumption III, has a Poisson distribution

Let be the probability that a VLR record is not selected for replacement during the period . Then

Fig. 10. The stationary probabilityp for VLR overflow.

Let be the probability that the VLR record for a user is not replaced (under the condition that (3) holds). Since the LA residence time of a user has a general density function (As-sumption II), can be derived as follows:

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From (3), . From (1)

and an argument similar to the one for deriving (2), we have

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If is an exponential density function, then

(6) and (5) is rewritten as

(7)

Based on (7), the solid curves in Fig. 11 illustrates as a func-tion of . Fig. 11(a) plots the curves when

and (i.e., 10, 1, and 0.1 calls for a mobile user are expected during the user's stay in an LA), respectively.

In this figure, . The figure indicates that increases as increases. This result is consistent with our intuition that if call arrivals are infrequent, the VLR records are unlikely to be replaced. We also observe that % when .

Fig. 11(b) plots the curves for , and , respectively. In this figure, . The figure shows that for a fixed value, increases as increases.

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Fig. 11. The probability that the VLR record of a mobile user is never replaced due to VLR overflow.

C. Issue III: Derivation for

The probability (i.e., the probability that the call activities of a user is not affected by VLR overflow) is derived as follows. Suppose that there are users in the LA. Starting from time , let be the density function that a VLR record is replaced at time , and there are replacements to other VLR records during the period . Then

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On the right-hand side of (8), the term means that the first replacements are made to other VLR records. The th replacement is made to record with probability . From Assumption III, the interarrival times for calls (that will result in VLR record replacements) have an exponential distribution with rate [cf., (3)], and the sum of the call interarrival times has an Erlang density function given in the remaining part of the right-hand side of (8).

Consider the timing diagram in Fig. 12. Suppose that a user enters the LA at time zero and leaves the LA at time . The VLR record of the user is replaced at time . After , the first call to/from the user occurs at time . The call setup procedure for this call is not affected by VLR overflow if . Suppose that there are record replacements in the VLR during the period . Let be the probability that the call

Fig. 12. The timing diagram for deriving.

setup procedure will be affected by VLR overflow (i.e., ). From Appendix A, we have

(9) and

(10)

For exponential LA residence times, in (9) is replaced by (6) to yield

(11) Substituting (11) into (10), we have

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Based on (12), Table I lists as a function of for various and values. The figure indicates that under the range of input parameters considered in our study, % for . In other words, the results indicate that even if the VLR overflow probability is high (e.g., % for

in Fig. 10), the call setup procedure is only slightly affected ( %) when the VLR overflow algorithm is exercised.

V. CONCLUSION

This paper studied the mobility database overflow problem in a cellular system. If the mobility database (specifically, the VLR) for a cellular service LA is full, the incoming mobile users cannot receive services under the existing cellular phone technology. To allow these “overflow” users to receive cellular services, we proposed a VLR overflow control scheme. The scheme can be easily adopted in the existing cellular systems such as GSM and AMPS with only minor modifications. Partic-ularly, no modifications are made to the mobile phones.

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We also studied three performance issues for VLR overflow. Let be the expected number of mobile users in an LA and be the size of the corresponding VLR. Under the range of input parameters we considered, the following results were observed.

• The VLR overflow probability is less than 0.2% for .

• When the overflow control scheme is exercised, a mo-bile user's VLR record may be replaced. We showed that this “replacement” probability is less than 0.4% for

.

• In the VLR overflow control scheme, the call activities of a “replaced” user are affected (and extra effort is required in the call setup procedure) if, after the VLR record re-placement, the user has call activity before moving out of the LA. Our study indicated that the call activities of a mo-bile user is unlikely to be affected (e.g., a user is affected with probability less than 0.4% if ).

The last observation merits further discussion. When , about 50% of the incoming users to the LA cannot receive ser-vice under existing cellular technology. By exercising the over-flow control scheme, all the mobile users in the LA continue to receive the service. The extra overhead for the scheme is very low: most of the call setups (with a probability larger than 99.6%) to a user is not affected by the overflow control scheme. This work assumed that every VLR is associated with an LA and the replacement policy is uniformly random. One of the re-search directions is to extend the analytic model for the system with multiple LA’s per VLR and to consider various replace-ment policies.

APPENDIX I THEDERIVATION FOR

Consider the timing diagram in Fig. 12. Suppose that a user enters the LA at time zero and leaves the LA at time . The VLR record of the user is replaced at time . After , the first call to/from the user occurs at time . The call setup procedure for this call is not affected by VLR overflow if . Suppose that there are record replacements in the VLR during the period . Let be the probability that the call setup procedure will be affected by VLR overflow (i.e.,

(14) where and Thus (15) and (16)

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Substituting (15) and (16) into (14), we have

(17)

From (13) and after rearrangement

(18)

Substituting (17) and (18) into (13), we have

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ACKNOWLEDGMENT

The author would like to thank the anonymous reviewers for their valuable comments which significantly improved the quality of this work. Specifically, Assumption VI was established with the assistance of the reviewers.

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Yi-Bing Lin (S'80–M'96–SM'96) received the B.S.E.E. degree from National Cheng Kung Uni-versity, Taiwan, R.O.C., in 1983 and the Ph.D. degree in computer science from the University of Washington, Seattle, in 1990.

From 1990 to 1995, he was with the Applied Re-search Area, Bell Communications ReRe-search (Bell-core), Morristown, NJ. In 1995, he was appointed as a Professor in the Department of Computer Science and Information Engineering (CSIE), National Chiao Tung University (NCTU), Hsinchu, Taiwan. In 1996, he was appointed as Deputy Director of the Microelectronics and Information Systems Research Center, NCTU. Since 1997, he has been Chairman of CSIE, NCTU. His current research interests include design and analysis of personal communications services network, mobile computing, distributed simulation, and performance modeling. He is an Associate Editor of the IEEE NETWORK. He was a Guest Editor of the IEEE TRANSACTIONS ONCOMPUTERSSpecial Issue on Mobile Computing.

Dr. Lin is an Associate Editor of SIMULATION Magazine, an Area Editor of the ACM Mobile Computing and Communication Review, a Columnist of ACM

Simulation Digest, a member of the editorial board of the International Journal of Communications Systems, a member of the editorial board of ACM/Baltzer Wireless Networks, a member of the editorial board of Computer Simulation Modeling and Analysis, Guest Editor for the ACM/Baltzer MONET Special Issue

on Personal Communications, and an Editor of the Journal of Information

Sci-ence and Engineering. He was the Program Chair for the 8th Workshop on

tributed and Parallel Simulation, General Chair for the 9th Workshop on Dis-tributed and Parallel Simulation, Program Chair for the 2nd International Mobile Computing Conference, and Publicity Chair of ACM Sigmobile. He received the 1997 Outstanding Research Award from the National Science Council, Taiwan, and the Outstanding Youth Electrical Engineer Award from CIEE, Taiwan.