Wirel. Commun. Mob. Comput. 2003; 3:311– 327 (DOI: 10.1002/wcm.90)
A batch-update strategy for the distributed HLRs
architecture in PCS networks
Hang-Wen Hwang, Chien-Chao Tseng*,† and Ming-Feng Chang
Department of Computer Science and Information Engineering, National Chiao-Tung University, Hsinchu, Taiwan, Republic of China
Summary
Owing to the increasing population of mobile subscribers, the rapidly expanding signaling traffic has become a challenge to the mobility management in PCS networks. Multiple database schemes to reduce signal traffic and to solve the bottleneck problem of the single home location register (HLR) architecture have been proposed by many
researchers. However, in most of the multiple location databases or HLR systems, extra signaling is required for the multiple database updates. We propose a batch-update strategy, instead of the immediate update method, for the location-tracking schemes with replication to reduce the signaling overhead. In this paper, we first introduce a
distributed HLRs architecture in which each HLR is associated with a localized set of VLRs and the location registrations and queries are processed locally. Then we propose our batch-update strategy and present two pointing schemes for inter-HLR call deliveries. The numerical result shows that our approach can effectively decrease the signaling cost of location registration and call delivery compared with the IS-41 standard. Copyright 2002 John Wiley & Sons, Ltd.
KEY WORDS distributed HLRs mobility management location registration call delivery batch update mobile terminal
Published online: 3 September 2002
ŁCorrespondence to: Professor Chien-Chao Tseng, Department of Computer Science and Information Engineering, National
Chiao-Tung University, Hsinchu, Taiwan 300, Republic of China.
†E-mail: cctseng@csie.nctu.edu.tw
1. Introduction
The personal communication service (PCS) is a sys-tem that provides wireless telecommunication to the subscribers with mobile terminals (MTs). To enable the mobile subscribers to communicate with a remote terminal (static or mobile) regardless of its current location, the PCS network must implement the mobil-ity management function to keep track of the MTs and locate the called MT when a call is initiated. The two most commonly used mobility management standards are EIA/TIA IS-41 [1] and ETSI GSM MAP [2].
The PCS mobility management has two basic oper-ations, location registration and location tracking. The former is the process that an MT informs the net-work of the location changes when it moves and the latter is required when the network attempts to deliver a call to a target MT. Both IS-41 and GSM standards employ a two-level database architecture, which con-sists of the home location register (HLR) and the
visitor location registers (VLRs). The HLR contains
the profiles of the users who have subscribed to the services. When the MT moves into a new registration area (RA), a temporary record is created in the visited VLR. The VLR then sends a message to the HLR for location registration. As described in Reference [3], in IS-41 Revision B, the registration message is first forwarded to a signal transfer point (STP) through Signaling System no. 7 (SS7) for global title transla-tion (GTT). After the HLR address of the MT is found via the GTT procedure, the message is forwarded to the HLR. Similarly, if the network wants to deliver a call to an MT from a VLR or originating switch (initiated by a static terminal), a GTT procedure is required to access the HLR. Then the HLR sends a query to the serving VLR of the MT. The serving VLR returns a routable address called a temporary-location directory number (TLDN) to the calling VLR or originating switch through the HLR. On the basis of the TLDN, a trunk is established from the calling switch to the called MT.
Because of the heavy traffic generated by PCS loca-tion registraloca-tion and tracking, the HLR may become bottlenecked. To reduce the traffic to an HLR, one natural solution is to distribute the HLR function in several locations. Under the distributed architec-ture, we assume that each distributed HLR (DHLR) is nearby or is collocated with the GTT STP, so that the signaling for GTT can be neglected or avoided [3]. However, for consistency of the location information among HLRs, extra traffic is generated for multiple HLR updates. Therefore, in this paper we propose
a batch-update strategy to reduce the overhead for the multiple HLR updates. This batch-update strategy could make the DHLR architecture more feasible.
2. Related Research
Owing to the increasing population of mobile sub-scribers, the signaling traffic of the PCS network is expanding rapidly. So the mobility management for a huge number of the MTs becomes more impor-tant. In addition to the studies [4– 9] for reducing the paging delay, many schemes have been proposed to improve the location management [3,10–18]. These schemes aim to reduce the signaling traffic gener-ated by location registration and/or to make the call delivery more efficient.
A fully distributed strategy for location registration is proposed in Reference [18]. Under this scheme, all the location databases are organized as a tree struc-ture. Each database (node of the tree) contains the location information of the MTs that reside in its subtree area. So the processing of the location reg-istration and tracking is effectively localized. How-ever, an MT’s movement or call between large sub-tree areas will cause location updates or queries in many databases.
A location forwarding strategy is first proposed in Reference [14] to reduce the signaling cost for location registration. When an MT moves to a new registration area, a pointer is set up from the previ-ous VLR and the location registration to HLR is no longer needed. As a call is generated, the HLR can find the current VLR of the called MT by following the chain of forwarding pointers. In Reference [3], a DHLR architecture is further suggested to solve the bottleneck problem of the single HLR. The incoming calls are distributed to their closest HLRs for loca-tion queries. As a result, the calls can be delivered efficiently. In Reference [15], the authors proposed a modification to limit the forwarding pointers to one step at the most. However, both the above location forwarding schemes pose reliability problem since a failure in one VLR can result in the loss of the track of all MTs that are currently visiting other VLRs but their forwarding pointer chains pass across the mal-functioned VLR.
In Reference [17], the authors propose a
dynami-cally hierarchical database architecture. A level of
database, called directory register (DR), is imple-mented between the HLR and VLR. The DRs deter-mine the distribution strategy of location informa-tion for each of their associated MTs based on their
mobility and call arrival parameters. Basically, the location registrations of all MTs are distributed to the DRs and the DRs could deliver a call with the already set up location pointer. This implementation effectively reduces the signal traffic in most cases. However, extra signaling is needed for multiple DR updates. Besides, a call delivery initiated by a static terminal does not benefit from this architecture but spends time in routing through the DR.
For the data consistency of the MT’s location information in distributed databases, the scheme in Reference [17] normally sends messages to update the location information in the associated DRs as soon as the MT’s location changes. In this paper, we propose a batch-update method that can significantly reduce the signaling traffic for location management by allowing temporary inconsistency of the MT’s location information among DHLRs. Our analysis shows that the impact of this temporary inconsistency of MT’s location is negligible on the call delivery in our architecture. In Section 3 we describe how the batch-update strategy is applied in the DHLR architecture, and then evaluate its performance and present the numerical results in Section 4.
3. Distributed HLRs Architecture
In this section, we describe the DHLR/VLRs archi-tecture and the proposed scheme in detail. Figure 1 shows that several HLRs are distributed in the PCS network and that each DHLR serves a number of VLRs. The DHLRs communicate with each other and
with their associated VLRs by SS7 network, which is responsible for routing of signaling messages based on their destination addresses. The area covered by a VLR is called the registration area (RA) and the area covered by a DHLR is called the distributed area (DA).
Under the DHLR structure, the location registration for each MT is performed in its local DHLR. The signaling messages for the registration process are no longer sent to the unique HLR located far away. Thus, the traffic on the network will be effectively reduced. However, for the registration of an MT, it is required to update all the DHLRs. Extra signaling messages are needed to complete the updating. We observe that among the DHLRs there exist many movements of the MTs. Each movement requires inter-DHLR messages to complete the registration process. If we exploit these inter-DHLR messages to convey the updating information by batch, the extra update messages are no longer needed. In Section 3.2 an example will be presented to describe the detailed operation of the batch-update strategy. As for call delivery, the location query for a call is always served at the local DHLR. The DHLR can lead the call to the target MT by using a well-updated location pointer. Obviously, this localization of the service for a call delivery lowers the searching cost and also shortens the setup delay for a connection.
As shown in Figure 2(a), an MT currently resides under VLR1, which is managed by DHLR1. DHLR1 locates the MT with a local pointer. Meanwhile, in DHLR2 (a remote DHLR) there is a direct remote
DA2 DHLR2 DHLR1 DA1 DHLR3 DA3 VLR PSTN VLR VLR VLR VLR VLR VLR VLR VLR VLR VLR VLR VLR VLR VLR VLR VLR VLR VLR VLR VLR
(a) DHLR1 VLR1 DHLR2 DHLR1 Local pointer VLR1 DHLR2 Remote direct pointer Remote indirect pointer
Mobile terminal 1 Mobile terminal 1
Local pointer
Distributed area 1
(b) Distributed area 1
Fig. 2. (a) Configuration under the direct remote pointing scheme and (b) Configuration under the indirect remote pointing scheme.
pointer used to lead to the serving VLR of the
MT. As for Figure 2(b), the direct remote pointer in DHLR2 is replaced with an indirect remote pointer. By using the indirect remote pointer, DHLR2 locates the currently serving DHLR (DHLR1) of the MT. Then DHLR1 finds the MT with the local pointer. Although we cannot directly locate the VLR in which the target MT currently resides, we need not update the location changes happening within a DA under the indirect remote pointing scheme. This is a trade-off between the direct and indirect remote pointing schemes. Later, we will analyze the performance of each scheme.
3.1. Location Registration
When an MT is initialized in some RA, an initial-ization message is sent to its local DHLR to create a local pointer that leads to the serving VLR of the MT. At the same time, the local DHLR informs each of the remote DHLRs of this initiation to create a remote pointer for the MT.
As soon as an MT moves to another RA, the MT registers with the DHLR. The registration procedures for an intra-DA movement and an inter-DA move-ment are depicted in Figures 3 and 4, respectively. The steps shown in Figures 3 and 4 are described as follows:
Step 1. The MT sends a location registration message to the new VLR.
Step 2. The new VLR records the MT and forwards the location registration message to update the local pointer in the associated DHLR. Then the DHLR sends an acknowledgement message back to the VLR.
Step 3. The new VLR sends a successful registration message to the MT.
Step 4. If the movement is an intra-DA movement, we have the following:
– The DHLR sends a location cancellation message to the old VLR to cancel the record of the MT.
– The old VLR sends an acknowledgement message back to the DHLR.
Otherwise, if the movement is an inter-DA movement, we have the following:
– The new DHLR sends a location update message to the old DHLR.
– The old DHLR replaces the invalid local pointer by a new remote pointer and sends an acknowledgement message back to the new DHLR.
Step 5. If the movement is an inter-DA movement, we have the following:
– The old DHLR sends a location cancellation message to the old VLR to cancel the record of the MT.
– The VLR sends an acknowledgement mes-sage back to the old DHLR
3.2. Batch-update Strategy for Remote Pointers When an MT moves to a new RA, the local pointer and the remote pointers for that MT must be updated. The local pointer will be updated naturally during the location registration. However, the updating of the
1 2 3 4 RA3 RA1 RA2 RA4 VLR VLR VLR VLR VLR VLR VLR VLR DHLR1 DHLR2 PSTN RA8 RA5 RA6 RA7 DA1 DA2 MT1
Fig. 3. Registration for an intra-DA movement.
1 2 3 4 RA3 RA1 RA2 RA4 VLR VLR VLR VLR VLR VLR VLR VLR DHLR1 DHLR2 PSTN RA8 RA5 RA6 RA7 DA1 DA2 MT 5
Fig. 4. Registration for an inter-DA movement. remote pointers must be done explicitly. Therefore,
we propose a batch-update method to reduce the cost of updating the remote pointers. In our method, remote pointers are always updated in a batch fashion only when an inter-DA movement occurs. Figure 5 shows an example of how the DHLRs update the remote pointers for each other. We assume that two
MTs, MT2 and MT3, have changed their locations in DA1 and MT5 has moved to DA1 since the last inter-DA movement between DHLR1 and DHLR2. When MT1 moves to DA1, MT1 initiates an inter-DA registration procedure. In Step 4 of the procedure, in addition to the location of MT1, the new locations of MT2, MT3 and MT5 are sent in the update message
RA3 RA1 DHLR2 DHLR1 RA2 RA11 DA1 DA3 DA2 RA4 MT1 MT2 MT3 RA12 RA13 MT4 DHLR3 RA21 RA5 MT5
For the direct remote pointing scheme, the contents in the messages are Update message :
HEADER
Acknowledgment message: HEADER
For the indirect remote pointing scheme, the contents in the messages are Update message : HEADER Acknowledgment message: HEADER MT1 : VLR4 MT2 : VLR2 MT3 : VLR3 MT5: VLR5 MT4: VLR13 MT1 : DHLR1 MT5 : DHLR1 Update message Ack. message
Fig. 5. Update strategy for remote pointers (through an inter-DA location registration). to DHLR2. DHLR2 will change the remote pointers
for MT2, MT3 and MT5 as well as the one for MT1. Similarly, the location change of MT4 will be added to the corresponding acknowledgement message to update the remote pointer for MT4 in DHLR1. As for the indirect remote pointing scheme, the operation for updating indirect remote pointers is similar to that for the direct remote pointing scheme, except for the MT’s location information. However, the update or acknowledgement messages must contain the location pointers to the new serving DHLRs, instead of the serving VLRs, of the MTs.
The remote pointers may be temporarily obsolete in our batch-update strategy. If an MT’s location is queried when the corresponding remote pointer is obsolete, we call it a query miss; otherwise it is a query hit. However, by following these obsolete
remote pointers, we still can find out the correct location of the target MT. In general, the number of MTs is so huge that the inter-DA movement could be frequent, and almost all the remote pointers could be updated in time for the location queries for the mobile terminating calls. In the next section, we evaluate the average update rate of the remote pointers and show that a very high hit ratio of a location query can be achieved with our proposed update strategy. This effectively reduces the setup time for call delivery without extra update messages.
In order to append the location changes to the update message as soon as possible, each DHLR maintains a table to record the location changes of the MTs. Table I, for example, is the update table for the DHLR2. DHLR1 and DHLR3 are two neighbor-ing DHLRs of DHLR2. For each neighborneighbor-ing DHLR,
Table I. The update table for the remote pointers. DHLR1 MT5 MT6 . . . . VLR10 VLR12 . . . . DHLR3 MT1 MT5 MT6 . . . VLR11 VLR10 VLR12 . . . . . . .
Table II. The relay table for the remote pointers.
From DHLR1 to DHLR3 MT10 MT3 . . . VLR16 VLR18 . . . From DHLR3 to DHLR1 MT2 MT7 . . . VLR13 VLR14 . . .
there is an entry in the location changes table. An entry will be sent to its corresponding DHLR during the next location registration for an inter-DA move-ment between these two DHLRs. As soon as it is sent out, the entry has to be cleared for collecting the next batch of the changed locations of the MTs.
For those nonneighboring pairs of DHLRs, we can choose a unique relay DHLR between them to relay the update of the remote pointers in both directions. As shown in Figure 6, DHLR2 can relay the location changes for the nonneighboring pair (DHLR1, DHLR3). Whenever DHLR2 receives the location changes of the MTs from either DHLR1 or DHLR3, it will record the location changes in a relay table for each as shown in Table II.
3.2.1. Hit ratio for a query of the remote pointer
As described above, a remote pointer for a target MT is updated by a batch-update method instead of an immediate-update method. As a consequence, a remote pointer may be obsolete when it is accessed for a call connection. Therefore, we would like to evaluate the probability that a remote pointer is
always updated in time for a location query initiated by a call.
In general, only a few HLRs are enough to achieve a good performance under the two-level (HLR/VLR) database architecture with multiple HLRs. Therefore, we assume that there are a few DHLRs deployed and their covering areas are fully neighbored in the following analysis. Under such an assumption, a DHLR can directly use our batch-update method to update the remote pointers in every DHLR.
We define the following parameters used for analysis:
D the number of DHLRs
N the average number of MTs within a DA 1/a the average RA residence time of an MT q the probability that the movement of an
MT is an inter-DA movement
Furthermore, we assume the network as a homoge-neous system. Under this assumption, we can focus our analysis on a single DHLR. In unit time, an MT in a DHLR will take aq/D 1 movements into one of the neighboring DAs. For a DHLR with N MTs, there will be Naq/D 1 movements into a neigh-boring DA. Similarly, there will be Na q/D 1 incoming movements from a particular neighboring DA. As mentioned above, a DHLR can update the remote pointers in a neighboring DHLR by the loca-tion registraloca-tion procedure stimulated by an MT arriv-ing or leavarriv-ing the neighborarriv-ing DA. So we can cal-culate the average update rate for a remote pointer as follows:
R D 2Naq D 1
A location query for an inter-DA call delivery will be missed if the remote pointer for the target MT cannot be updated in time as shown in Figure 7(a). To evaluate the probability of a query miss, pm, we first assume the movements for a target MT as a Poisson
DHLR2 DHLR1 DHLR1 DA3 DHLR3 DA1 DA2
Location changes inside
Location changes inside DHLR2 and DHLR3
Location changes inside DHLR3 Location changes inside DHLR2 and DHLR1
Move Move (a) (b) Sobs R Obsolete periods
Updates for a remote pointer Time
Supd λm
Fig. 7. (a) Illustration for the update timing of a remote pointer and (b) validity state diagram of a remote pointer. process with rate m, while the updates for a remote
pointer of the target MT are also a Poisson process with rate R since an MT’s residence time could also be assumed to be an exponential distribution with rate a, and then use a simple Markov chain as shown in Figure 7(b) to model the validity status of a remote pointer. In the Markov chain, the Sobs and Supd, respectively, represent the remote pointer for an MT that is obsolete and updated. The steady state probabilities of Sobs and Supd, which stand for the probabilities of a query miss and a query hit (pmand ph, can be obtained as follows:
pm DobsD m mCR , phDupdD R mCR We can expect a high probability of ph since the average number of MTs, N, is normally large. 3.3. Call Delivery
Similar to location registration, call delivery can be classified into intra-DA and inter-DA types. On receiving a call, the DHLR uses the local pointer to deliver the call to the serving VLR of the MT for the former type and uses the remote pointer for the latter. Figure 8 shows the normal operations of call deliv-ery. The steps, as shown in Figure 8, are described as follows:
Step 1. A call is initiated by an MT (or a Fixed Terminal) and forwarded to the VLR (or the Public switched telephone network (PSTN) switch).
Step 2. The VLR (or the PSTN switch) sends a location request message to the local DHLR. Step 3. When the callee and caller are within the
same DA, we have the following:
(a) The DHLR sends a location request to the local VLR that serves the called MT. (b) The VLR assigns a TLDN to the called MT and sends this TLDN to the DHLR. If the callee and caller are not in the same DA, as mentioned above, we have two cases of remote pointing.
A: direct remote pointing scheme
(c) The DHLR sends a location request to the remote VLR that serves the called MT.
(d) The VLR assigns a TLDN to the called MT and sends this TLDN to the call-ing DHLR.
B: indirect remote pointing scheme
(e) The local DHLR sends a location request to the DHLR that serves the called MT. (f) The called DHLR forwards the location
request message to the VLR that serves the called MT.
(g) The VLR assigns a TLDN to the called MT and sends this TLDN to the call-ing DHLR.
Step 4. The calling DHLR forwards the TLDN to the calling VLR.
Step 5. The calling mobile services switching center (MSC) (or the calling PSTN switch) sets up a connection to the called MSC using this TLDN.
Because the remote pointers are not updated imme-diately after location changes of the corresponding
Called DHLR Called VLR/MSC For intra-DA call delivery For inter-DA call delivery (1) (2) (3.a) (3.b) (3.c) (3.d) (3.e) (3.f) (3.g) (5) (4)
Under the direct remote pointing scheme
Under the indirect remote pointing scheme Calling MT (or FT) Calling VLR/MSC (or PSTN Switch) Local DHLR
Fig. 8. Normal operations of call delivery. MT, it is possible that a remote pointer fails to point
directly to the right serving VLR or DHLR of the tar-get MT. However, by following the obsolete remote pointers, we can still find out the correct location of the target MT. Figure 9 sketches some worse cases for an inter-DA call delivery under the direct remote pointing scheme. In Figure 9(a), for the called MT, DHLR1 has a pointer that leads to VLR5. After fail-ing to find the MT in the VLR5 pointed out by the obsolete remote pointer, VLR5 forwards the location query to DHLR2. The DHLR then uses the local pointer to find out the serving VLR of the called MT. As described in Section 3.2, under the present scheme the miss ratio for location queries is very low. So the case with two consecutive failures in querying the tar-get MT’s location would take place with an extremely low probability. In the following section we neglect the call delivery cases with more than one query of the target MT’s location in our analysis.
4. Performance Analysis
Our proposed architecture aims to reduce the signal-ing cost for location registration and call delivery. However, it should be noted that, our scheme will
not incur extra database access compared with the single HLR architecture. Therefore, we just evaluate the performance of our scheme in terms of the sig-naling cost. The sigsig-naling cost could be measured by the bandwidth required to complete the signal transmission. In the following analysis, we use an embedded Markov chain [19] to model the behavior of the MT’s movement with respect to its incom-ing calls from each individual DHLR. The signalincom-ing cost for location registration and call delivery will be evaluated separately.
4.1. The Analytical Model
As mentioned in Section 3.2.1, we assume that all DAs are fully neighbored. For a particular DHLR, the location pointer to a target MT may be local or remote. If the pointer is a remote one, a move-ment of the MT will make it temporarily obsolete under the batch-update strategy. In order to rep-resent different conditions of the location pointers, we model the activity of a particular MT using an embedded Markov chain in which the states, with respect to a call originated from DAi, are defined as follows:
1 2 3 4 RA3 RA1 RA2 RA4 VLR VLR VLR VLR VLR VLR VLR VLR DHLR1 DHLR2 PSTN RA8 RA5 RA6 RA7 DA1 DA2 MT1 MT2 5 1 2 3 RA3 RA1 RA2 RA4 VLR VLR VLR DHLR1 DA1 DA2 MT1 4 VLR VLR VLR VLR VLR DHLR2 PSTN RA8 RA5 RA6 RA7 MT2 5 VLR VLR RA12 VLR RA9 VLR RA10 RA11 DHLR3 DA3 1 V 2 3 RA3 RA1 RA2 RA4 VLR VLR VLR DHLR1 DA1 DA2 MT1 4 VLR VLR VLR VLR DHLR2 PSTN RA8 RA5 RA6 RA7 MT2 5 VLR VLR RA12 VLR RA9 VLR RA10 RA11 DHLR3 DA3 6 7 VLR (a) (b) (c)
Fig. 9. (a) A remote call delivery with one remote and one local pointer tracing; (b) A call delivery with two remote pointers tracing; and (c) A remote call delivery with two remote and one local pointer tracing.
SiLC the call is a local one to the MT. Si
RC the MT has made an inter-DA movement from DAi but its location information in DHLRi, a remote DHLR, is still valid. Therefore, a call to the MT from DAi is a remote one and will be delivered in exactly one step from DHLRi. If a remote call originates from DAi, in which the location pointer is obsolete, the delivery will be completed with one remote and one local pointer tracing. Si
RLC the MT has further made an intra-DA movement after leaving DAi and its location information in DHLRi, a remote DHLR, may be obsolete.
Si
RrplusC the MT has made more than two inter-DA movements to a new DA, which is different from DAi. Similar to SiRLC, the MT’s location information in DHLRi, a remote DHLR, may be obsolete. If a remote call originates from DAi, in which the location pointer is obsolete, the delivery will be completed with not less than two remote pointers tracing. We also assume, for a target MT, that the inter-RA movements are a Poisson process with rate m, while the arrivals of its incoming calls from DAi are a Poisson process with rate i. State transi-tions of the embedded Markov chain occur right
after the movement of the MT to one of the adja-cent RAs or the arrival of a call from DAi. We assume that a target MT starts moving in its local DA, DAi. For each movement, the MT moves out of DAi with the probability qi. Once the MT leaves DAi, it moves back to its local DA with the prob-ability iki in each movement. The parameter ki is the inter-DA movement probability for the MT outside DAi, and i is the move –back probabil-ity that the MT moves back to DAi in each inter-DA movement. A high value of i means a high locality of the MT to DAi. The state transition dia-grams for the embedded Markov chain are given in Figure 10.
Let i
LC, RCi , iRLCand iRRplusCdenote the steady state probabilities of being Si
LC, SiRC, SiRLC and Si
RrplusC, respectively. We further assume that from each adjacent DA of the DAi an MT moves to DAi with equal probability. Therefore, we can derive the following equations:
D iD1,i6Dj
ikiDqj, for 1 j D
Then, we have the balance equations as follows: LCi CRCi CRLCi CiRRplusCD1 1 iRCmDiLCqimCRLCi C i RRplusCi 2 iLCqimDikimRCi C i RLCC i RRplusC 3 mi ki lm mi ki lm li+(1−qi) lm mi ki lm (1−mi)ki lm (1−ki ) lm (1−ki ) lm (1−mi)ki lm (1−mi)ki lm+(1−ki ) lm Si RC li li li Si RRplus Si RLC SiLC qi lm 1 = i = D< <
RLCi kimCi D RCi 1 kim 4 RRplusCi ikimCi D 1 ikimRCi C
i RLC
5 After simple derivation, we have
iLCD iki qiCiki 6 iRCD qiikimCi qiCikimCi 7 iRLCD 1 kiqimikimCi kimCiqiCikimCi 8 iRRplusCD 1 ikiqim qiCikikimCi 9 The average inter-DA movement probability, q, for the MT can be calculated as follows:
q D D
iD1 qiiLC
In the next subsection, we use the above steady state probabilities and average inter-DA movement probability to evaluate the signaling costs.
4.2. Cost Evaluation
Under our architecture, the signaling cost comes from three parts, location registration, batch-update of remote pointers and call delivery. The costs for a registration after an RA movement and an inter-DA movement are denoted as cirand cid, respectively. The cost for a call delivery depends on where the call is from and whether the location pointer is up-to-date or not. Table III groups the call delivery costs under various situations. In the table, the lowercase sub-scripts ‘r’ and ‘l’, respectively, indicate ‘remote’ and ‘local’ with respect to the called MT. For example, DHLRl indicates the local DHLR for a target MT, while DHLRr1and DHLRr2 are two remote DHLRs.
Location registration cost. As assumed above, an MT makes mmovements per unit time, and each
movement is of inter-DA type with probability q. Let ˛denote the average registration cost for an MT, then ˛ D 1 qmcirCqmcid 10
Update cost. Because two types of remote point-ing schemes are proposed, the update cost for differ-ent schemes will be evaluated, respectively.
1) Direct remote pointing scheme: Under this scheme, for each intra-DA movement of a particular MT, we need to update D 1 remote pointers in the D 1 neighboring DHLRs. However, for each inter-DA movement we only need to update D 2 remote pointers since the location pointers of the MT in the other DHLRs are naturally updated in the registra-tion process. The number of locaregistra-tion updates for an MT per unit time could be [1 qD 1 C qD 2]m. The total update cost for an MT could be normalized, with respect to the update cost in the immediate update scheme, as
ˇ1 D[1 qD 1 C qD 2]mcD2D l L 11 where l is the length of location information data for an MT in our scheme and L is the average length of an update message in the immediate update scheme. Besides, cD2D is the average signaling cost for transmitting an update message sent from one DHLR to the other.
2) Indirect remote pointing scheme: As mentioned earlier, an indirect remote pointer is used to point to the serving DHLR of a target MT instead of the serving VLR. The remote pointers are updated only when an inter-DA movement occurs. So we can easily obtain the update cost, ˇ2, as follows.
ˇ2DqD 2mcD2D l
L 12
Call delivery cost. The call delivery costs for the two proposed schemes are as follows:
Table III. The various costs for a call delivery.
Cost parameter Finding operation clc MT ! VLRcalling!DHLRl!VLRcalled crc1 MT ! VLRcalling!DHLRr!VLRcalled crc2 MT ! VLRcalling!DHLRr!VLR ! DHLRl!VLRcalled crc3 MT ! VLRcalling!DHLRr1!VLR ! DHLRr2!VLRcalled crc10 MT ! VLRcalling!DHLRr!DHLRl!VLRcalled crc20 MT ! VLRcalling!DHLRr!DHLRr!DHLRl!VLRcalled
1) Direct remote pointing scheme: For a target MT, a call from DAimay be classified into four cases with the following probabilities:
LCi the probability that a call originated from DAi under the state SiLC.
RCi the probability that a remote call originated from DAi under the state Si
RC.
RLCi the probability that a remote call originated from DAi under the state Si
RLC.
RRplusCi the probability that a remote call originated from DAi under the state SiRRplusC.
Then, the total call delivery cost due to the calls from all DAs is computed as
1D D iD1 i[LCiclcCRCicrc1 CRLCicrc1phCcrc2pmph CRRplusCicrc1phCcrc3pmph Cfp2mph, p3mph, . . .] 13 where fp2
mph, p3mph, . . .) represents the summation of all other terms with a parameter pmand the order of pm is not less than 2. In the steady state of our model, we have lim t!1LCi D i LC,t!1limRCiDiRC, lim t!1RLCiD i
RLC and limt!1RRplusCiDiRRplusC Because the cost function fp2mph, p3mph, . . .) with parameters of high order pmis much smaller than the former term, we can neglect it to obtain a simple form in terms of crc1, crc2 and crc3, as shown in Table III.
2) Indirect remote pointing scheme: Following a similar approach, we can derive the total delivery cost of indirect remote pointing scheme as
2D D iD1 i[LCiclcCRCiCRLCicrc10 CRRplusCicrc10phCc rc20pmph Cf0p2mph, p3mph, . . .] 14 The intra-DA movement of the MT does not change the cost of searching the target MT. Therefore, the cost of the remote call delivery under the states Si
RC
and Si
RLC are the same, that is, crc10. Similarly, the cost function, f0p2
mph, p3mph, . . .), is too small to be taken into account. The costs crc10 and c
rc20 are also shown in Table III.
Total cost. Summing the Equations (10), (11) and (13), we obtain the total cost under the direct remote pointing scheme C1 D˛ C ˇ1C1. Similarly, we obtain the cost under the indirect remote pointing scheme C2 D˛ C ˇ2C2. Besides, we also derive the total cost under the immediate update method that is given by C3D˛ C[1 qD 1 C qD 2]mcD2D C D iD1 i[LCiclcC1 LCicrc1] 15 4.3. Numerical Results
In this section, we present the numerical results based on our analytical model. The signaling costs are con-stituted from the following elementary cost parame-ters and can be calculated from the expression shown in Table IV.
cLD2V the average signaling cost of a message transmission between a VLR and its local DHLR
cRD2V the average signaling cost of a message transmission between a VLR and a remote DHLR
cD2D the average signaling cost of a message transmission between two DHLRs cSH2V the average signaling cost of a message
transmission between a VLR and the single HLR under IS-41 standard cV2G the average signaling cost of a message
transmission between a VLR and the
GTT STP under IS-41 standard
cG2SH the average signaling cost of a message transmission between the GTT STP and the single HLR under IS-41 standard Besides, we assume that the signaling cost is pro-portional to the routing distance and the message load transmitted between the two communicating sites, obtaining the following relation:
cV2G cG2SH cSH2V½cRD2V½cD2D½cLD2V The cost values we use in the performance evalu-ation are shown in Table V.
Table IV. Cost expressions for the location regist-ration and call delivery operegist-rations.
Cost parameter Expression cir 4cLD2V cid 4cLD2VC2cD2D clc 4cLD2V crc1 2cLD2VC2cRD2V crc2 4cLD2VC2cRD2V crc3 3cLD2VC3cRD2V crc10 3cLD2VCcD2DCcRD2V crc20 3cLD2VC2cD2DCcRD2V
Table V. Cost sets.
Set cLD2V cD2D cRD2V cV2GDcG2SHDcSH2V
1 1 1.5 1.5 1.5
2 1 2.5 2.5 2.5
3 1 5 5 5
The total cost of the proposed location management scheme is measured as the ratio of the total cost per unit time for the proposed scheme to that of the IS-41 standard, C/CIS-41. We can express the total cost of IS-41 standard, CIS-41, as
CIS-41DmCc3cSH2VCcV2GCcG2SH 16 where c is the total call arrival rate to the target MT. An extra visit to the GTT STP costs cV2G and cG2SH. In the registration operation, we need cSH2V to send an acknowledgment message to the new VLR, and 2cSH2V are to inform the old VLR of canceling the obsolete record. As for the call delivery operation, 3cSH2Vis needed to complete the necessary signaling. In our analysis, we assume that there are four DHLRs (D D 4) deployed and each DHLR serves an average of one hundred thousand of users (N D 100 000), while the data length ratio, l/L, in Equations (11) and (12) is set to be 0.1. The comparisons of numerical results are discussed as follows:
Figure 11 shows the relative cost for the direct and indirect remote pointing schemes under the batch-update strategy. The vertical axis represents the rela-tive cost C/CIS-41 and the horizontal axis is the ratio of the call arrival rate to the mobility rate (CMR), c/m, varies from 0.01 to 100. The numerical result for the immediate update strategy is also provided. As mentioned before, the immediate update strategy needs a lot of signaling to complete the multiple HLR updates. When users move frequently, it is not worthy to adopt the distributed HLRs architecture if the immediate update strategy is used. Figure 11 also
illustrates that the batch-update strategy reduces the update overhead when the CMR is low. Since the
indirect pointing scheme only needs to update the
remote pointer in each DHLR due to the target MT’s inter-DA movement, this further results in significant cost savings for the indirect pointing scheme. How-ever, when the CMR is high, the call delivery cost dominates. The extra cost for indirect pointing obvi-ously degrades the performance. Therefore, the best policy is to adopt the direct remote pointing scheme for the MT with a high CMR and adopt the other one for the MT with a low CMR. It should be noted that if each signaling to a VLR is always routed through the STP to which the local DHLR is connected, the indirect remote pointing scheme is undoubtedly the best choice.
Figure 12(a) and (b) show the effect of the inter-DA movement probability, q, on the direct and indi-rect remote pointing schemes, respectively. Because an inter-DA registration process needs more signals than an intra-DA registration one, the smaller the inter-DA movement probability, the lower the rel-ative cost. In general, we can increase the size of the DA to obtain a lower inter-DA movement proba-bility [17]. However, the enlarged DA lengthens the routing distance between the local DHLR and VLR, and thus the signaling cost of the local transmis-sion also increases. Consequently, the relative cost is unavoidably increased.
From Equation (13), the total local call arrival rate for a target MT is determined by the summation term,DiD1iLCi. The LCi is further affected by the locality parameter, i. A high value of i implies that the target MT tends to move back to DAi once it moves. Therefore, a high value of i and a high probability of i represent a high total local call
10−2 10−1 100 101 102 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 ∗: Immediate update + : Batch-update/direct pointing o : Batch-update/indirect pointing CMR
Relative total cost C/C
IS-41
Fig. 11. The relative total costs for the batch-update and immediate update schemes with Cost Set 2.
(a) Direct pointing scheme
(b) Indirect pointing scheme
10−2 10−1 100 101 102 10−2 10−1 100 101 102 0.4 0.42 0.44 0.46 0.48 0.5 0.52 ∗ : q = 0.357 o : q = 0.214 + : q = 0.071 CMR CMR 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 ∗ : q = 0.357 o : q = 0.214 + : q = 0.071
Relative total cost C/C
IS-41
Relative total cost C/C
IS-41
Fig. 12. Comparison of different inter-DA movement probabilities.
arrival rate. The higher the total local call arrival rate is, the less the call delivery cost will be. Figure 13(a) and (b) obviously shows this phenomenon.
Figure 14 shows the comparison of the improve-ments under different sets of the elementary costs as shown in Table V. We can expect that the more localized the processing of the network is, the lower the ratio of the local signaling cost to the remote signaling cost (LRCR), cLD2V/cRD2V, will be. There-fore, the performance improves proportionally as the LRCR decreases. More improvement can be achieved when both the LRCR and the CMR are low. This phe-nomenon implies that we can benefit more from the property of frequent movements in a local area by our approach compared with the single HLR one.
Finally, Figure 15 shows the comparison of the call delivery performance. As we analyzed before, the batch-update strategy for the direct remote pointing scheme does not incur significant impact on signaling.
(a) Direct pointing scheme
10−2 10−1 100 101 102 0.38 0.4 0.42 0.44 0.46 0.48 0.5 0.52 0.54 0.56
∗ : Local call probability = 0.7 o : Local call probability = 0.423 + : Local call probability = 0.146
CMR
(b) Indirect pointing scheme
10−2 10−1 100 101 102
CMR
∗ : Local call probability = 0.7 o : Local call probability = 0.423 + : Local call probability = 0.146
Relative total cost C/C
IS-41
Relative total cost C/C
IS-41 0.6 0.55 0.5 0.45 0.4 0.35 0.3
Fig. 13. Comparison of the costs among various local call arrival rates.
By using our approach, a call delivery can be com-pleted in the direct remote pointing scheme as well as in the immediate update scheme.
5. Conclusion
In this paper, we introduce a distributed HLRs archi-tecture. Under this architecture, each MT only makes location registration to its serving DHLR, and each DHLR is responsible for updating the MT’s location change in other DHLRs. A batch-update strategy is proposed to significantly reduce the heavy traffic that the immediate update method in most replication sys-tems could generate. In our batch-update strategy, the remote pointers (pointing to the MTs residing in other DHLRs) are always updated in a batch fashion only when an inter-DA registration process occurs. So the signaling overhead for updating the remote pointers
(a) Direct pointing scheme 10−2 10−1 100 101 102 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65 0.7 ∗ : LRCR =1/5 (Set 3) o : LRCR = 1/2.5 (Set 2) + : LRCR = 1/1.5 (Set 1) CMR
(b) Indirect pointing scheme
10−2 10−1 100 101 102
CMR
∗ : LRCR =1/5 (Set 3) o : LRCR = 1/2.5 (Set 2) + : LRCR = 1/1.5 (Set 1)
Relative total cost C/C
IS-41
Relative total cost C/C
IS-41 0.7 0.65 0.6 0.55 0.5 0.45 0.35 0.25 0.4 0.3 0.2
Fig. 14. Comparison of the improvements among different sets of the elementary costs.
10−2 10−1 100 101 102 0.45 0.46 0.47 0.48 0.49 0.5 0.51 ∗ : Immediate update + : Batch-update/direct pointing o : Batch-update/indirect pointing CMR
Relative delivery cost C/C
IS-41
Fig. 15. Comparison of the call performance.
can be avoided. Our analysis shows that most of the location changes of the MTs will be updated in time
and that the delivery of the remote calls could be performed as well as the replication systems do. In PCS networks, distributed mobility schemes seem to be a trend to reduce the signaling overhead caused by the increasing number of subscribers. Our approach makes the multiple HLRs architecture feasible.
We also analyze the properties of both the direct and indirect remote pointing schemes used in the DHLR network. There exists a trade-off between them. However, on the basis of the MT’s mobility and call arrival patterns, we can dynamically switch the pointing method between these two schemes to obtain a better performance. Therefore, developing an adaptive algorithm to get an optimal result will be our future work.
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Authors’ Biographies
Hang-Wen Hwang received the M.S. degree in Control Engineer-ing from National Chiao-Tung Uni-versity, Hsin-Chu, Taiwan, in 1987. He is currently a specialist in the Chung Shan Institute of Sci-ence and Technology, Taiwan, and working toward Ph.D. degree with the Department of Computer Sci-ence and Information Engineering at National Chiao-Tung University. His research interests include Personal Communication Sys-tems and Mobile Computing.
Chien-Chao Tseng is currently a professor in the Department of Computer Science and Information Engineering at National Chiao-Tung University, Hsin-Chu, Taiwan. He received his B.S. degree in Indus-trial Engineering from National Tsing-Hua University, Hsin-Chu, Taiwan, in 1981; M.S. and Ph.D. degrees in Computer Science from the Southern Methodist University, Dallas, Texas, USA, in 1986 and 1989, respectively. His research interests include Mobile Computing, and Wire-less Internet.
Ming-Feng Chang received the Ph.D. degree in computer science from the University of Illinois at
Urbana-Champaign in 1991. He
is currently a Professor in the
Department of Computer Science and Information Engineering, Chiao-Tung University, Taiwan, R.O.C. His research interests include Internet Communication, Mobile Computing and VLSI system design. Current research projects include VoIP for wireless networks, internetworking of VOIP protocols and cache model for WAP applications.
