reducing location update cost in a pcs network

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IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 5, NO. 1, FEBRUARY 1997 25 Reducing Location Update Cost in a PCS Network Yi-Bing Lin, Senior Member, IEEE Abstract—Location tracking operations in a personal communi- cations services (PCS’s) network are expensive. Several strategies have been proposed to reduce the location update cost. This paper studies a special case of a location tracking algorithm called the alternative location algorithm. This special case is referred to as the two location algorithm (TLA). An analytical model is proposed to compare the performance of TLA and the IS-41 protocol. Our study indicates that the performance of TLA is significantly affected by the user moving patterns and the call traffic. If the user mobility is higher than the call frequency or the user tends to move back to the previously visited registration areas, then TLA may significantly outperform IS-41. We also observe that the variance of the portable residence times in registration areas has impact on the performance of TLA (i.e., better performance is expected for larger variance). Index Terms— Home location register, mobility management, personal communications services, roaming management, visitor location register. I. INTRODUCTION I N a personal communications services (PCS’s) system, the location of a called portable must be determined before the connection can be established. Due to the mobility of portables, a database called home location register (HLR) is required to store the location of a portable. The location record is modified when the portable moves to another location. A procedure to locate a portable is specified in IS-41 [1]. This procedure is referred to as the basic find operation in this paper. In IS-41, call termination consist of two parts. In the first part, the basic find operation is performed. In the second part, the trunk is set up for the conversation. The basic find operation is described below. We assume that the calling party is a wireline user. Step 1) The incoming call to a portable is initiated at a switch called the originating switch. Step 2) The originating switch queries the HLR for the portable’s current location. Step 3) The HLR queries the visitor location register (VLR) where was last registered. Step 4) The VLR queries the mobile switching center (MSC) where is located to determine whether is capable of receiving the call. If so, the Manuscript received July 2, 1993; revised August 20, 1996; approved by IEEE/ACM TRANSACTIONS ON NETWORKING Editor C.-L. I. This work was supported by the National Science Council under Grant NSC 86-2213-E-009- 074. The author is with the Department of Computer Science and Information Engineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C. (email: [email protected]). Publisher Item Identifier S 1063-6692(97)01704-4. MSC returns a routable address Temporary Local Directory Number (TLDN) to the VLR. The VLR sends the TLDN back to the HLR. Step 5) The HLR forwards the TLDN to the originating switch. After the originating switch has received the TLDN, it routes the call to the MSC where is located. We assume that every VLR serves a registration area (RA) which consists of one or more radio port coverage areas. When a portable moves from one RA to another, it registers at the VLR of the new RA, and its new location is reported to the HLR. This action is referred to as the registration operation. The registration operation may be followed by a deregistration (or cancellation) operation to remove the obsolete record in the old VLR. (This is referred to as explicit deregistration [2].) In IS-41, HLR sends a deregistration message to the old VLR. In [3], the deregistration message is sent directly from the new VLR to the old VLR. The deregistration operation may not be performed immediately after a registration operation. In timeout deregistration, the obsolete entries are cancelled periodically [2]. In implicit deregistration, no deregistration operation is performed. An old VLR record is replaced to accommodate a newly arrived portable when the resource such as TLDN is used up [2], [4]. The advantage of implicit deregistration is that no deregistration message is required to cancel an obsolete record. To simplify our analysis, implicit deregistration is assumed in this study. Studies [5]–[7] indicated that the message traffic due to the find and registration operations is significant. When the frequency of the incoming calls is high with respect to the portable mobility (i.e., the rate that a portable moves to new RA’s), the location cache scheme [8], [9] was proposed to reduce the traffic (i.e., to reduce the number of the find operations). When the call frequency is low with respect to the mobility, the number of the registration operations increases which significantly degrades the performance of the location cache scheme. Several algorithms such as the pointer forwarding algorithm [3], [7] and the alternative location algorithm (ALA) [10]–[12] have been proposed to reduce the registration cost. This paper studies a special case of ALA called the two lo- cation algorithm (TLA). In TLA, we consider two locations to track the location of a portable. On the other hand, ALA allows more than two user locations in the profile. The performance of ALA has been studied in [10]–[12]. These studies focused on the cost analysis for the paging operations in call termination, and provided the mean analysis of the user mobility. 1063–6692/97$10.00 1997 IEEE

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Page 1: Reducing location update cost in a PCS network

IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 5, NO. 1, FEBRUARY 1997 25

Reducing Location Update Costin a PCS Network

Yi-Bing Lin, Senior Member, IEEE

Abstract—Location tracking operations in a personal communi-cations services (PCS’s) network are expensive. Several strategieshave been proposed to reduce the location update cost. This paperstudies a special case of a location tracking algorithm called thealternative location algorithm. This special case is referred toas the two location algorithm (TLA). An analytical model isproposed to compare the performance of TLA and the IS-41protocol. Our study indicates that the performance of TLA issignificantly affected by the user moving patterns and the calltraffic. If the user mobility is higher than the call frequency orthe user tends to move back to the previously visited registrationareas, then TLA may significantly outperform IS-41. We alsoobserve that the variance of the portable residence times inregistration areas has impact on the performance of TLA (i.e.,better performance is expected for larger variance).

Index Terms—Home location register, mobility management,personal communications services, roaming management, visitorlocation register.

I. INTRODUCTION

I N a personal communications services (PCS’s) system, thelocation of a called portable must be determined before

the connection can be established. Due to the mobility ofportables, a database called home location register (HLR) isrequired to store the location of a portable. The location recordis modified when the portable moves to another location. Aprocedure to locate a portable is specified in IS-41 [1]. Thisprocedure is referred to as the basicfind operation in thispaper. In IS-41, call termination consist of two parts. In thefirst part, the basicfind operation is performed. In the secondpart, the trunk is set up for the conversation. The basicfindoperation is described below. We assume that the calling partyis a wireline user.

Step 1) The incoming call to a portableis initiated at aswitch called theoriginating switch.

Step 2) The originating switch queries the HLR for theportable’s current location.

Step 3) The HLR queries thevisitor location register(VLR) where was last registered.

Step 4) The VLR queries themobile switching center(MSC) where is located to determine whether

is capable of receiving the call. If so, the

Manuscript received July 2, 1993; revised August 20, 1996; approved byIEEE/ACM TRANSACTIONS ON NETWORKING Editor C.-L. I. This work wassupported by the National Science Council under Grant NSC 86-2213-E-009-074.

The author is with the Department of Computer Science and InformationEngineering, National Chiao Tung University, Hsinchu, Taiwan, R.O.C.(email: [email protected]).

Publisher Item Identifier S 1063-6692(97)01704-4.

MSC returns a routable addressTemporary LocalDirectory Number(TLDN) to the VLR. The VLRsends the TLDN back to the HLR.

Step 5) The HLR forwards the TLDN to the originatingswitch.

After the originating switch has received the TLDN, it routesthe call to the MSC where is located.

We assume that every VLR serves aregistration area(RA)which consists of one or more radio port coverage areas. Whena portable moves from one RA to another, it registers at theVLR of the new RA, and its new location is reported to theHLR. This action is referred to as theregistration operation.Theregistrationoperation may be followed by a deregistration(or cancellation) operation to remove the obsolete record in theold VLR. (This is referred to asexplicit deregistration[2].) InIS-41, HLR sends a deregistration message to the old VLR.In [3], the deregistration message is sent directly from thenew VLR to the old VLR. The deregistration operation maynot be performed immediately after aregistration operation.In timeout deregistration, the obsolete entries are cancelledperiodically [2]. In implicit deregistration, no deregistrationoperation is performed. An old VLR record is replaced toaccommodate a newly arrived portable when the resourcesuch as TLDN is used up [2], [4]. The advantage of implicitderegistration is that no deregistration message is required tocancel an obsolete record. To simplify our analysis, implicitderegistration is assumed in this study.

Studies [5]–[7] indicated that the message traffic due tothe find and registration operations is significant. When thefrequency of the incoming calls is high with respect to theportable mobility (i.e., the rate that a portable moves to newRA’s), the location cache scheme[8], [9] was proposed toreduce the traffic (i.e., to reduce the number of thefindoperations). When the call frequency is low with respectto the mobility, the number of theregistration operationsincreases which significantly degrades the performance of thelocation cache scheme. Several algorithms such as thepointerforwarding algorithm [3], [7] and thealternative locationalgorithm (ALA) [10]–[12] have been proposed to reduce theregistration cost.

This paper studies a special case of ALA called thetwo lo-cation algorithm(TLA). In TLA, we consider two locations totrack the location of a portable. On the other hand, ALA allowsmore than two user locations in the profile. The performance ofALA has been studied in [10]–[12]. These studies focused onthe cost analysis for the paging operations in call termination,and provided the mean analysis of the user mobility.

1063–6692/97$10.00 1997 IEEE

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26 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 5, NO. 1, FEBRUARY 1997

(a) (b) (c) (d)

Fig. 1. The two location algorithm.

This paper analyzes the SS7 traffic cost of registration andcall delivery for a basic scheme based on IS-41 and theTLA. We also consider the impact of the portable movementdistributions, which provides important insight to complementthe performance studies in [10]–[12].

TLA and ALA can be integrated with the cache schemeto further reduce the location update/tracking costs for allincoming call frequencies and mobility patterns.

II. THE TWO LOCATION ALGORITHM

In the TLA, a portable has a small built-in memory tostore the addresses for the two most recently visited RA’s.The record of in the HLR also has an extra field to store thecorresponding two locations. The first memory location (seeFig. 1) stores the most recently visited RA. The algorithmguarantees that the portable is in one of the two locations.Fig. 1 illustrates a sequence of’s movements

. When joins the network, the location is stored inits memory, and aregistrationoperation is required to modifythe HLR record as shown in Fig. 1(a). Whenmoves to anew location, it checks if the new location is in the memory.If the new location is not found, the address for the RAjust left is kept, and the other address is replaced by theaddress for the new RA [see Fig. 1(b) and 1(c)]. Aregistrationoperation is required to make the same modification in theHLR record. If the address for the new location is already inthe memory, no action is taken in the HLR record. In otherwords, noregistration operation is performed [see Fig. 1(d);

moves back to the previously visited registration area].Note that in TLA, the portable always has the correct viewof the “latest visited RA.” On the other hand, the HLR mayhave an “incorrect view.” In Fig. 1(a)–(c), both the portableand the HLR have the consistent view of the latest visited RA[which is in Fig. 1(a), in Fig. 1(b), and in Fig. 1(c)].At Fig. 1(d), the HLR considers as the latest visited RA,which is incorrect.

When a phone call arrives, the two addresses are used to findthe actual location of the portable. The order of the addressesselected to locate the portable affects the performance of thealgorithm. If the portable is located in the first try (this is

referred to aslocation hit), then thefind cost for TLA is thesame as the IS-41 algorithm. Otherwise, extra penalty incurs inTLA to locate the portable for the second try (this is referred toaslocation miss; note that the second try is always successful).After the second try, the HLR identifies the RA where theportable is visiting.

There are several alternatives to select the address forthe first try. An obvious heuristic is to select the locationrandomly. Another heuristic is thelatest-RA-first strategywhere the latest visited RA address (in the HLR’s view) isselected. We have observed that the latest-RA-first strategy isbetter than the random selection algorithm in all cases studiedin this paper. We only present the results for the latest-RA-firststrategy.

III. M OVEMENTS BETWEEN TWO PHONE CALLS

This section studies the patterns of the incoming calls andthe portable movement. We derive the probability thata portable moves across RA’s between two phone calls.Assume that the incoming calls to a portable are a Poissonprocess, and the time the portable resides in an RA has ageneral distribution. We show that for a portable, differentmoving patterns result in different distributions.

Consider the timing diagram in Fig. 2. Let be the intervalbetween two consecutive phone calls to a portable. Supposethat the portable resides in an RA when the previous phonecall arrived. After the phone call, visits another RA’s, and

resides in the th RA for a period ( ). Letbe the interval between the arrival of the previous phone calland the time when moves out of . Let be the intervalbetween when the portable entersand when the next phonecall arrives. Let be independent identically distributedrandom variables with a general distribution , thedensity function and the Laplace–Stieltjes Transform

(1)

Note that it is possible that the next phone call arrives whilethe previous call is still in progress. The phenomenon is calledbusy lineeffect. In this case, the portable cannot initiate/acceptthe next call and the assumption of Poisson process for calls

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LIN: REDUCING LOCATION UPDATE COST IN A PCS NETWORK 27

Fig. 2. The timing diagram.

is no longer valid. Thebusy lineeffect was studied in [13]. Tosimplify and strengthen our results, we assume that the busyline effect is insignificant. This assumption is justified whenthe inter-call arrival times are more than 10 times longer thanthe call holding times.

Let and be the density function of and ,respectively. Let and . Since theincoming phone calls are a Poisson process, we have

From the memoryless property of the exponential distribution,have the same exponential distributions asfor all .

Also from the random observer property [14], [15]

(2)

(the detailed derivation can be found in [15, pp. 67–69], andis referred to as theexcess life theorem). The Laplace–StieltjesTransform for the distribution is

(3)

The probability that moves across RA’s betweentwo phone calls is derived in two cases. For

(4)

where is the call-to-mobility ratio defined in [8].

For

(5)

, , and are derivedas follows:

(6)

From (6),

(7)

From (4),

(8)

From (4)–(8), we have

(9)

We assume that the portable residence times have a Gammadistribution. Most studies use the exponential distribution forits simplicity. Exponential is a special case of Gamma. In thispaper, the Gamma distribution is selected for three reasons.Firstly, the Gamma distribution does not have a specific distri-bution shape, and it has the desirable property to fit an arbitrarydistribution by setting appropriate parameters [16]. Secondly,the Gamma distribution has a simple Laplace–Stieltjes Trans-form format which simplifies the calculation of (9). Thirdly,with Gamma, the impact of variance of the residence times canbe conveniently studied. With mean and variance , theLaplace–Stieltjes Transform of a Gamma random variable isexpressed as

where

Fig. 3 plots for Gamma portable residence time distri-butions with different Variance values. The figure indicatesthat the distribution is significantly affected by the varianceof the residence times. The next section will show that thevariance of the distribution may have a significant impact onthe performance of TLA.

IV. PERFORMANCE OF THELOCATION UPDATE STRATEGIES

This section studies the performance for TLA and IS-41.We first estimate the costs of thefind and theregistration

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28 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 5, NO. 1, FEBRUARY 1997

Fig. 3. �(K) for Gamma portable residence time distribution with differentvariance values (�c = 0:5�m.

operations, then derive the number of operations performed inthe two algorithms.

For a particular PCS system, economic analysis is requiredto estimate the costs for thefind/registrationoperations. Forthe demonstration purpose, we give a simple cost analysis asfollows.

The basicfind operation consists of two parts. The firstpart includes the interactions between the originating switchand the HLR [Steps 1), 2), and 5) in thefind operation;see Fig. 4(a)]. We assume that the PCS messages are sentthrough the signaling system no. 7 (SS7) network in thepublic switched telephone network (PSTN). (A tutorial forPCS signaling using SS7 can be found in [17].) Upon thereceipt of the dialed number (the mobile identification number(MIN) of the portable), the originating switch is not capableof associating this number with the physical address of theHLR. Instead, it forward the message to a signal transfer point(STP). The STP uses a table lookup technique called globaltitle translation (GTT) to identify the HLR address. Thenthe message is forwarded from the STP to the HLR. (GTTis needed because nongeographic numbering is assumed [1],[18].) Note that several SS7 network elements may be visitedbefore the STP and the HLR are reached. The second partincludes the interactions between the HLR, the VLR, the MSC,and the portable [Steps 3) and 4) in thefind operation; seeFig. 4(a)]. For systems such as PACS [2], in the second partof thefind operation the MSC pages the portable to make surethat the portable is in its area before the VLR sends the TLDNto the HLR. The design of the PACS alerting protocol allowsa large paging capacity with low cost (the alerting capacity ofPACS [19] is ten times larger than DECT [20] and 1000 timeslarger than CT2 [21], [22]). Note that for other systems suchas AMPS [23], the paging cost is high and the portable is notpaged during the VLR query. The portable is paged duringtrunk setup.

Note that the global title translation (and visits to severalextra STP’s) is performed in Part 1 but is not performed inPart 2, and the paging operation performed in Part 2 is notperformed in Part 1. Without loss of generality, we normalizethe cost of the basicfind operation to one. We assume that thecost for Part 1 is , where . For systems with lowpaging cost such as PACS, a large(e.g., ) isappropriate. For systems with high paging cost such as AMPS,a low (e.g., ) is expected. (A detailed pagingcost analysis can be found in [10]–[12].)

In TLA, if the HLR selects the right location at the firsttime (a location hit), then the TLAfind operation is exactlythe same as the basicfind operation. If the first try fails (alocation miss), then the HLR tries the second location [seeSteps 3a, 3b, 3, and 4 in Fig. 4(b)]. The extra cost (for Steps3a and 3b) is the same as the cost for Part 2 of the basicfindoperation.

Fig. 4(c) illustrates theregistration operation. Similar toPart 1 of the basicfind operation, a global title translationis required to access the HLR. Also, a deregistration operationis required to delete the obsolete record in the old VLR. Tosimplify our analysis, we assume that the cost for registrationis the same as the cost for Part 1 of the basicfind operation(without considering the authentication procedure [6]).

Based on our simple cost analysis we have the followingestimation.

1) The cost for the basicfind and the TLAfind (locationhit) operations are one.

2) The cost for theregistration is where .3) The cost for the TLAfind (location miss) operation is

.

The numbers of operations for TLA and IS-41 are derivedas follows. Suppose that the portable moves acrossRA’sbetween two phone calls. Let be the number ofregistrationoperations performed among the moves. From (9), the cost

for the IS-41 algorithm is

-

and the cost is

- (10)

Consider TLA. Suppose that the portable moves acrossRA’s between two phone calls. The conditional probability

that registration operations are performedamong the moves has a Bernoulli distribution:

where is the probability that when a portablemoves, thenew RA address is in the portable memory [i.e., the probabilitythat Fig. 1(d) occurs]. Since there are only two addressesstored in a portable, is the probability that moves back

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LIN: REDUCING LOCATION UPDATE COST IN A PCS NETWORK 29

(a)

(b)

(c)

Fig. 4. Cost estimations for different operations. (a) The basic find operation or the MLA find operation (location bit) (b) The MLA find operation(location miss). (c) The registration operation.

to the RA where it came from.The number for TLA is

and the cost is

(11)

Let be the number offind operations performed to locate aportable. The number and the cost for IS-41 are

-

and

- (12)

For TLA, the number is derived in the Appendix.The probability that the HLR has a location miss in a calltermination is given in (21)

The number and the cost for TLA is

and

(13)

Define as the net cost ofregistration and findoperations performed between two phone calls, then from(10)–(13) we have

-

(14)

Figs. 5 and 6 plot - and . These figures indicate thatwhen the call-to-mobility ratio is small, TLA outperforms IS-41 even if the user movement exhibits low locality (is small)and theregistration cost is low. For example, when ,

, and , TLA reduces 16% of the cost overIS-41 [see Fig. 5(a)]. When the user movement exhibits highlocality ( ), TLA significantly outperforms IS-41 when

is small. The improvements of TLA over IS-41 are 31% to50% [for a low registration cost ; see Fig. 5(b)], 51% to58% [for a moderate registration cost ; see Fig. 6(a)],and 65% to 67% [for a large registration cost ; seeFig. 6(b)].

When is large, the performance of TLA is significantlyaffected by the portable’s RA residence time distribution(specifically, the variance of the Gamma distribution). Fora reasonable large variance (e.g., ), TLA outper-forms IS-41 for the ranges of all input parameters consideredin our study (when is large, 5% to 20% improvementsare observed in Figs. 5 and 6). On the other hand, IS-41outperforms TLA when and are small, and is large

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30 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 5, NO. 1, FEBRUARY 1997

(a) (b)

Fig. 5. The costs for IS-41 and TLA. (a)� = 0:25; � = 0:2: (b)� = 0:75; � = 0:2:

(a) (b)

Fig. 6. The costs for IS-41 and TLA.� = 0:75; � = 0:4: (b)� = 0:75; � = 0:4:

(see Fig. 5). From (21), it is not difficult to see thatis adecreasing function of . Consider the cases whenand :

(15)

From (13), also is a decreasing function of andthe performance of TLA degrades as the varianceof the

(a)

(b)

Fig. 7. The effects of the call-to-mobility ratio�. � = 0:6; � = 0:6: (b)� = 0:2; � = 0:2:

RA residence time distribution decreases (see Figs. 5 and 6).When is small, in (13) has more effect on the cost

, and IS-41 has a better chance to outperform TLA whenis small.

Fig. 7 indicates that - is either an increasingfunctions of [see Fig. 7(a)] or a convex function [see thecurve for in Fig. 7(b)], -

, the value will approach to one). From (21),is a decreasingfunction of , and

Since

-

We have

- (16)

That is, for all and values, TLA is the same as IS-41 whenis large (i.e., - in Fig. 7). In this

case, there are many call terminations between two portablemovements. For these call terminations the HLR always haslocation hits (except for the first one that may or may not havea location miss), the basicfind operation is performed in TLA.

When , we have

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LIN: REDUCING LOCATION UPDATE COST IN A PCS NETWORK 31

(a)

(c)

(c)

Fig. 8. Situations when the HLR has the correct view of the latest visited RA. (a) Case I: No move between two phone calls. (b) Case II: The last registrationfollowed by an even number of moves. (c) Case III: No registration between two phone calls.

and

-

(17)

That is, for all values and all , TLA is much betterthan IS-41 when is small. In this case, the portables movewithout receiving any phone call. It is clear that the move costfor TLA is always cheaper than IS-41 if . When ,

-

That is, if a portable never moves back to the previously visitedRA, then TLA behaves exactly the same as IS-41 does.

Our analysis indicated that TLA may underperform IS-41when the variance of the RA residence times is small. In thiscase, it is desirable to disable TLA when the cost of the TLAis higher than IS-41. Heuristics similar to the ones proposedin [8] and [9] can be used to dynamically disable/enable TLA.

V. CONCLUSION

This paper studied the performance of a PCS locationtracking strategy called the TLA. TLA is a variation (and aspecial case) of the alternative location algorithm proposedin [10]. We studied how the incoming call rate, the portablemobility, and the portable locality affect the performance ofTLA. Our study indicated that TLA significantly outperformsIS-41 when the call-to-mobility ratio is low (i.e., the usermoves more frequently than to receive calls) or when theregistration cost is large. We also showed that the variance

of the portable residence times (in registration areas) mayaffect the performance of TLA when the registration cost islow. The performance of TLA degrades whenis small.

TLA can be easily implemented by modifying the existingIS-41 based systems. The modifications are done in twoplaces. Firstly, one more field should be added to the portablelocation record in the HLR to hold the address of the secondportable location. A few lines of code are added to the HLRregistration/call delivery procedures to exercise TLA. TheHLR modifications can be easily done by using the userfriendly tools with graphical inputs such as ISCP SPACESystem [24]. Secondly, a few lines of code should be added tothe micro kernel of the protable to exercise TLA. Note that wemay need to slightly modify the SS7 TCAP message format,but no hardware modifications are necessary.

Our future research directions include modeling the generalalternative location strategy by combining our model and themodels proposed in [10]–[12], and comparing TLA with thepointer forwarding scheme [3]. Also, it is possible that IS-41may outperform TLA in certain conditions. We are developingan adaptive mechanism (similar to the one described in [8])to dynamically switch between IS-41 and TLA based on theuser mobility.

APPENDIX

DERIVATION FOR

We first consider the probability that the HLR hasthe correct view of the latest visited RA when a call arrives

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32 IEEE/ACM TRANSACTIONS ON NETWORKING, VOL. 5, NO. 1, FEBRUARY 1997

(i.e., a location hit occurs and thefind cost for TLA is thesame as IS-41).

If the HLR has the correct view of the current RA of theportable when a call arrives, one of the following situationsholds.

1) Case I: The portable has not moved since the last callarrival [see Fig. 8(a)]. After a call termination, the HLR alwaysidentifies the current RA of the portable. Thus, location hitoccurs when the second call arrives. The probabilityofCase I is

(18)

2) Case II: Suppose that the portable visits RA’sbetween two phone calls andregistration operations are per-formed during some of the moves. If the HLR has thecorrect view of the latest RA at the next call arrivals, thenduring the moves, the lastregistrationoperation performedin TLA is followed by even number of portable movements(and noregistrationoperations are performed in these move-ments) as shown in Fig. 8(b). Note that at timein Fig. 8(b),the HLR’s view of the current RA is the same as the portable(which is ). After four moves (without any registration),the portable moves back to , and the HLR’s view for thelatest visited RA is correct. Let be the probability of CaseII, and be the conditional probability of Case II whenthe portable makes moves between two phone calls. Sincethe probability of a move with registration is ( ) and theprobability of a move without registration is, we have

for

Note that for . The probabilityis

(19)

3) Case III: Suppose that the portable visits RA’sbetween two phone calls and noregistration operation isperformed during the moves. If the HLR has the correctview of the latest visited RA at the next call arrival, thenmust be an even number as shown in Fig. 8(c). In this figure,the HLR has the correct view of the latest visited RA (whichis ) immediately after the previous call termination. Afterfour moves without registration, the portable moves back to

when the next call arrives. The probability of Case III is

(20)

From (18) to (20), the probability that the HLR has alocation miss in a call delivery is

(21)

REFERENCES

[1] EIA/TIA, “Cellular radio-telecommunications intersystem operations.”EIA/TIA, Tech. Rep. IS-41 Revision B, 1991.

[2] Bellcore, “Generic criteria for version 0.1 wireless access communica-tions systems (WACS) and supplement,” Bellcore, Tech. Rep. TR-INS-001313, Issue 1, 1994.

[3] R. Jain and Y.-B. Lin, “Performance modeling of an auxiliary userlocation strategy in a PCS network,”ACM-Baltzer Wireless Networks,vol. 1, no. 2, pp. 197–210, 1995.

[4] Y.-B. Lin and A. Noerpel, “Implicit deregistration in a PCS network,”IEEE Trans. Veh. Technol.,vol. 43, pp. 1006–1010, 1994.

[5] C. N. Lo et al., “An estimate of network database transaction volumeto support universal personal communication services,” presented at the8th ITC Specialist Seminar on Universal Personal Telecommunications,1992.

[6] K. S. Meier-Hellstem and E. Alonso, “The use of SS7 and GSM tosupport high density personal communications,” presented at the IEEEICC, 1992.

[7] T. Imielinski and B. R. Badrinath, “Querying in highly mobile dis-tributed environment,” inProc. 18th VLDB Conf.,1992.

[8] R. Jain, Y.-B. Lin, C. N. Lo, and S. Mohan, “A caching strategy toreduce network impacts of PCS,”IEEE J. Select. Areas Comm.,vol. 12,no. 8, pp. 1434–1445, 1994.

[9] Y.-B. Lin, “Determining the user locations for personal communicationsnetworks,” IEEE Trans. Veh. Technol.,vol. 43, pp. 466–473, 1994.

[10] S. Tabbane, “Comparision between the alternate location strategy andthe classic location strategy,” WINLAB, Rutgers University, Tech. Rep.WINLAB-TR-37, 1992.

[11] G. P. Pollini and S. Tabbane, “The intelligent network signaling andswitching costs of an alternate location strategy using memory,”IEEETrans. Veh. Technol.,vol. 42, 1993.

[12] H. Xie, S. Tabbane, and J. D. Goodman, “Dynamic location areamanagement and performance analysis,”IEEE Trans. Veh. Technol.,vol.42, 1993.

[13] Y.-B. Lin and W. Chen, “Impact of busy lines and mobility on callblocking in a PCS network,”Int. J. Commun. Syst.,vol. 9, pp. 35–45,1996.

[14] W. Feller, An Introduction to Probability Theory and Its Applications,Vol. I. New York: Wiley, 1966.

[15] S. M. Ross,Stochastic Processes.New York: Wiley, 1983.[16] N. L. Johnson and S. Kotz,Distributions in Statistics: Continuous

Multivariate Distributions. New York: Wiley, 1972.

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[17] Y.-B. Lin and S. K. DeVries, “PCS network signaling using SS7,”IEEEPersonal Commun. Mag.,pp. 44–55, June 1995.

[18] EIA/TIA, “Cellular intersystem operations–Baseline text draft 3 9-2-94(IS-41 Rev. C),” EIA/TIA, Tech. Rep. PN-2991, 1994.

[19] A. R. Noerpel, L. F. Chang, and Y.-B. Lin, “PACS contention algorithmfor initial access and handoff,” inProc. 5th WINLAB Workshop,1995,pp. 217–226.

[20] ETSI, Digital European Cordless Telephone Common Interface, Version05.03, 1991.

[21] Radio Advisory Board of Canada,CT2Plus class 2: Specification for theCanadian Common Air Interface for Digital Cordless Telephony, Includ-ing Public Access Services, Annex 1 to Radio Standards Specification130, 1992.

[22] ETSI,Common Air Interface Specification to be ued for the InterworkingBetween Cordless Telephone Apparatus in the Frequency Band 864.1MHz, Including Public Access Services, I-ETS 300 131:1990,June 1991.

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[24] Bellcore, “ISCP SPACE System Service Creation Guide,” Bellcore,Tech. Rep. BR-780-003-124, 1993.

Yi-Bing Lin received the B.S.E.E. degree fromNational Cheng Kung University, R.O.C., in 1983,and the Ph.D. degree in computer science from theUniversity of Washington, Seattle, in 1990.

Between 1990 and 1995, he was with the AppliedResearch Area at Bell Communications Research,Morristown, NJ. In 1995, he was appointed FullProfessor of the Department of Computer Scienceand Information Engineering, National Chiao TungUniversity, Hsinchu, Taiwan, R.O.C. In 1996, hewas appointed as Deputy Director of Microelectron-

ics and Information Systems Research Center, NCTU. His current researchinterests include design and analysis of personal communications servicesnetwork, mobile computing, distributed simulation, and performance model-ing. He is an Associate Editor of theACM Transactions on Modeling andComputer Simulation, a Subject Area Editor of theJournal of Parallel andDistributed Computing, an Associate Editor of theInternational Journal inComputer Simulation, an Associate Editor of IEEE NETWORKS, an AssociateEditor of Simulation magazine, an Area Editor ofACM Mobile Computingand Communication Review, and a columnist ofACM Simulation Digest.He is a member of the Editorial Board of the International Journal ofCommunications, a member of the Editorial Board of Computer SimulationModeling and Analysis, Program Chair for the 8th Workshop on Distributedand Parallel Simulation, General Chair for the 9th Workshop on Distributedand Parallel Simulation. Program Chair for the 2nd International MobileComputing Conference, the publicity chair of ACM Sigmobile, Guest Editorfor the ACM/Baltzer WINET special issue on Personal Communications, andGuest Editor for the IEEE TRANSACTIONS ON COMPUTERS special issue onMobile Computing.