Location management for GPRS

Computer Networks 50 (2006) 2888–2901 www.elsevier.com/locate/comnet

Location management for GPRS Ning Chai

a,b

, Boon Sain Yeo

a,*

, Yong Huat Chew

a

a

b

Institute for Infocomm Research, Agency for Science Technology and Research, 21 Heng Mui Keng Terrace, Singapore 119613, Singapore Department of Electrical and Computer Engineering, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Singapore Received 2 September 2004; received in revised form 8 September 2005; accepted 25 October 2005 Available online 7 December 2005 Responsible Editor: W. Wang

Abstract In cellular wireless networks, location management is an important mechanism that enables network to discover the current attachment point of a mobile so as to facilitate successful information delivery. Although the design of optimal location management has been studied extensively for GSM, it is surprising that little, or possibly no, attention has been given to the consideration of location management design for General Packet Radio Service (GPRS), given that it is fast becoming a de facto system. Unlike GSM, the tracking of mobiles (MS) in the GPRS is made through routing area (RA) and location area (LA). For the first time, the mode of operation of MS, mobility management of MS and the network operation mode are considered as part of the proposed location management design model. The objective of the paper is to study in detail the impacts of the various varying parameters have on the performance of location management in GPRS. Two schemes, namely, greedy algorithm and optimal algorithm, are proposed and the mathematical models are developed in this paper. Comparative studies of the two schemes are carried out and discussed.  2005 Elsevier B.V. All rights reserved. Keywords: General Packet Radio Service (GPRS); Location management; Location update; Paging; Location area (LA); Routing area (RA)

1. Introduction In cellular wireless networks location management is an important mechanism that enables the network to discover the current attachment point of a mobile so as to facilitate successful information delivery. Location information about mobiles is main-

*

Corresponding author. Tel.: +65 68748535. E-mail address: [email protected] (B.S. Yeo).

tained by registration [1,2] and mobiles update their registration area(s) information with the HLR and the VLR, in the event of changes to the registration areas(s) [3]. A registration area comprises of a set of cells and may be static [4] or dynamic [5–8]. A static registration area is comprised of a set of cells permanently assigned and is fixed for all mobiles, whilst, dynamic registration areas [5–8] are made to vary in accordance to the traffic conditions of each mobile and its surrounding users so as to achieve optimality of a predefined objective. Although optimality is

1389-1286/$ - see front matter  2005 Elsevier B.V. All rights reserved. doi:10.1016/j.comnet.2005.10.015

N. Chai et al. / Computer Networks 50 (2006) 2888–2901

generally achieved through the use of dynamic registration areas, this scheme imposes a higher computational complexity and incurs more data storage capacity. As a result, most of the existing cellular systems use static registration areas. The current location management scheme, GSM Mobile Application Parts (MAP) or IS-41, is based on partitioning the cells into static registration areas, known as location areas (LAs), as shown in Fig. 1. As discussed, location updates are to be performed when mobiles cross the partitioning of LA so that upto-date location information for each mobile is stored in the respective HLR and VLR. It is to be noted that the location information of each mobile is tracked on a resolution that is dependent on the size of the LA. Hence, to facilitate a successful data delivery, all the cells within the LA have to be paged concurrently. The processes of performing location update and paging are illustrated in Fig. 1. It is also worth noting that both the updating traffic and paging traffic are inversely proportional to one another with respect to the size of the location area, i.e. updating load decreases whilst paging load increases for increasing sizes of LA, and vice versa. As a result, many works have been dedicated in finding optimal sizing [4,9–11] of the LA in GSM. It is, however, surprising that little, or possibly no, attention has been given to the consideration of location management design for General Packet Radio Service (GPRS), given that it is fast becoming a de facto system. The objective of this paper is to address this issue.

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GSM provides only circuit-switched (CS) services, while GPRS provides both packet-switched (PS) services and CS services. In view of its ability to accommodate both bursty packet data services and traditional voice data services, the location management design for GPRS is to be considerably more complex, as compared to GSM. In GSM, the tracking of the location information of mobile stations (MS) is only made in the LA; whilst, GPRS tracks the mobile in three different registration areas, namely, cell area (CA), routing area (RA) and LA. The tracking of mobile location information within the various registration areas is decided upon three parameters, notably, network operation mode, MS mobility management (MM) states and the MS mode of operation [12]. These parameters will be discussed in greater details later. This complexity stems from the need to optimize the increased signaling traffic that arises from providing both PS and CS services. It is therefore vitally important to consider an optimal location management design for GPRS systems. The paper continues in Section 2 with a description of the GPRS architecture which highlights the additional components that were previously not available in GSM. Section 3 describes the location management procedure as defined in GPRS, and states the key parameters that are vitally important in an optimum design. Section 4 presents the signaling traffic and model for an optimal location management design. Section 5 provides two approaches for GPRS RA/LA design problem,

Fig. 1. Current GSM location management scheme.

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In the CN, GPRS introduces a new set of switching nodes, also known as the GPRS support nodes (GSN), and a set of supporting interfaces to enhance the integration with GSM. The GSN that is capable of routing PS data into a separate network contains internet protocol (IP) or other routing functionalities. There are two main functional entities to be considered, as noted in Fig. 2. The first is the access point for an external data network and is known as the gateway GPRS support node (GGSN). It contains the routing for GPRS-attached users. With this information, GGSN is capable of delivering the packet data units (PDU) to the user’s current point of attachment. The location information can be obtained from the HLR via the optional Gc interface, as shown in Fig. 2. The second is the serving GPRS support node (SGSN) that serves the need of mobile users. When a user is GPRS-attached, the SGSN establishes an MM context containing information pertaining to routing, security and mobility, such as, among others, the identity of the RA and the LA, in which the MS is residing, and the MS’s MM state. The SGSN also ciphers PS traffic, given that the BTS is only responsible to cipher CS traffic [13]. From the specification [12], it is noted that both the GGSN and the SGSN are collectively known as the GSN, and they can either be combined into one physical node or be separated and reside in the same or different networks, of which the latter is to be linked via the Gn interface. Critical to an optimal GPRS LM design is the optional Gs interface, as shown in Fig. 2. The Gs interface allows the SGSN to forward the MS’s location information to the MSC/VLR and relay the CS paging message generated by MSC to the BSSs (Base Station Subsystem, i.e. a BSC and the

together with the simulation results and discussions. Some conclusions are given in Section 6. 2. GPRS architecture As discussed, GPRS is an upgraded version of GSM and is designed to support both PS and CS services. Fig. 2 illustrates the GPRS system architecture with the additional key components highlighted. There are two notable add-ons and/or differences, in addition to the changes in the ways some protocols and signalings are being implemented to the GSM system, namely, the MS and the core network (CN). An MS comprises of user equipment (UE), typically a handset, and a subscriber identity module (SIM). A GSM UE is able to establish both speech and data connections using circuit switching. However, a GPRS UE has to be equipped with packet transmission abilities [13], and operates in one of the three modes of operation: • Class-A: an UE is both GPRS and IMSI (international mobile subscriber identities) attached, i.e. being attached to both PS and CS services, and supports simultaneous PS and CS connections; • Class-B: an UE is both GPRS and IMSI attached but provides either PS or CS connection at one time. It has the capability of holding a PS transfer when receiving a CS paging which is generally more delay sensitive; • Class-C: an UE is exclusively GPRS attached [12]. Evolving from GSM, GPRS continues to serve the GSM (i.e. IMSI-attached only) MSs with CS services. Only GPRS-attached MSs can get PS services.

PSTN

Gc

HLR

Gr

Gn

Gr

Core Network

Gn

MSC/ VLR

SGSN1

Gn

GSN

Gb

BSC

Um

SGSN2

Gs

A

Um BTS BTS

BTS GSM MS

Data Network (IP)

GGSN

BTS

UE SIM GPRS MSs

Fig. 2. GPRS system architecture.

N. Chai et al. / Computer Networks 50 (2006) 2888–2901

respective BTSs). The above procedures are socalled combined RA/LA update and coordinated paging respectively. The presence of Gs interface and the assignment of packet paging channel determine the network operation mode: • Mode I: The Gs interface exists and the packet paging channel may be assigned in the cell that supports GPRS. In this mode, the PS paging is meant for either PS connections or CS connections because the network in this mode provides coordinated paging for class-A/-B MSs. • Mode II: The Gs interface does not exist and combined updates and coordinated paging is not allowed. • Mode III: This is similar to Mode II, i.e. without the Gs interface. The difference between Mode II, is the ways with which the paging channel is being allocated. This is not relevant to the discussion of location management, and will not be considered further. Therefore, in the context of location management, Mode III and Mode II can be considered to be similar.

3. Location management in GPRS Location management contains two basic processes: paging for information delivery and location update to facilitate the system keeping track of MSs. For paging, PS paging message will be generated by SGSN once there is an incoming PS data. It will

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be broadcast within the RA where the MS last updated its location. Meanwhile, MSC generates CS paging message for incoming CS data. If the network is in mode II/III, this paging message will be transmitted from MSC directly to the BSSs which govern the LA where the desired MS last updated. If the network is in mode I, coordinated paging is available, i.e. SGSN converts the CS paging message for class-A/B users into a PS paging message and broadcast it in RA instead of LA. For location update, the MS executes the procedure under two circumstances: • Periodic location update: the MS reports its presence to the network on a periodic basis, despite having sojourned in a registration area for a prolonged period of time. • Normal location update: the MS performs when it detects that the residential registration area has changed by comparing the cell identity stored in the MS with that broadcast by the network. For the normal location update, unlike GSM registration area which comprises of only LA, in view of GPRS add-ons which are designed to accommodate PS services, the LA of a GPRS is further divided into the routing area (RA) and the cell area (CA) to accommodate the parallel bursty PS services, as noted in Fig. 3. A CA is a cell, and an RA is a group of cells, which is a subset of an LA. When a GPRS MS moves to a new RA, it updates its location information stored at the system by performing an RA

Fig. 3. Three types of registration areas for GPRS: CA, RA and LA.

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update. When moving to a new LA, given being GPRS/IMSI attached, the MS performs either separate LA and RA updates (if the network is in mode II/III) or a combined RA/LA update (if the network in mode I). RA update and combined RA/LA update are charged by SGSN. A GSM MS (i.e. IMSI-attached only) will perform LA update once changing the residential LA and LA update is governed by MSC. The CA update happens when an MS in PS connection changes its residing cell since GPRS never support handover for PS connections. A third parameter that impacts MSs’ execution of location update is the MS’s MM states. In CS domain GPRS retains GSM states, i.e., an IMSIattached MS can either be idle or in CS-connection. An idle IMSI-attached MS updates its location either periodically or when it changes LA. Once it is in CS-connections, it performs handover proce-

GPRS Idle

*

Ready

MS initiated GPRS attach MS initiated GPRS dettach

LA update *

dures. In PS domain, GPRS characterizes an MS’s MM activities into three states: • GPRS Idle: the MS is not available for PS services, so it never performs RA or combined RA/LA update. It may perform LA update, provided it is IMSI-attached. The MS must initiate a GPRS attachment procedure in order to access PS services. • Ready: the MS is in PS connection. It is the only state where packet data units (PDU) are allowed to be delivered to the MS. A valid MM context is established and is hold by the MS and the corresponding SGSN. The MS executes CA update and is tracked at cell level by SGSN. The state transits to Standby if no PDU is transmitted before a ready timer expires. It transits to GPRS Idle when the MS or network initiates a GPRS detachment.

Ready timer expires /no PDU transferred

Standby

MS responses to a page from SGSN CA update *

details in Table 1 *

MS's probable location update procedures.

Fig. 4. Mobility management states of GPRS MS.

Table 1 Update procedures performed by GSM GPRS MSs

RA00 an RA location update procedure; LA00 an LA location update procedure; RA/LA00 a combined RA/LA location update procedure.

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• Standby: This packet idle state is similar to GSM idle. An MS is GPRS-attached, and both MS and SGSN have established MM contexts. The MS is tracked by SGSN at RA level and performs RA or combined RA/LA update. The SGSN may perform paging procedures. The MS in this state transits to Ready state upon a successful response to a page from SGSN. The MS’s MM states model and state transitions, as described above, are depicted in Fig. 4. Given the current MS’s mobility management (MM) state, the network operation mode and MS modes of operation, the types of update to be performed are summarized in Table 1. It details the different update procedures performed by the MS of different state combinations in PS and CS domain. 4. GPRS location management signaling traffic Location management design focuses on minimizing the signaling traffic for location management. On account of the antagonistic nature between the paging traffic and the location update traffic with respect to the registration areas, this work aims to find out the optimal RA/LA configuration so as to minimize the total signaling load on the Um interface. It stems from the fact that RA/ LA configuration affects the number of cells to be paged and the frequency with which a roaming MS has to perform location updates. Therefore, in GPRS location management design, three types of normal location update, which are associated with the RA/LA configuration, will be examined: LA update, RA update and combined RA/LA update. For any pair of cells, i and j, in the service area which contains K cells (1 6 i < j 6 K), we first define the following notations: mi: This parameter distinguishes the network operation mode of cell i. mi = 1 if cell i indicates the network operation mode I; mi = 0 if the cell i indicates mode II/III. The vector mij ¼ ½ mi mj ð1  mi Þð1  mj Þ mi ð1  mj Þ þ mj ð1  mi ÞT is a 3-tuple vector with only one element taking a value of 1. The 3 elements represent whether two cells i and j are both of mode I (i.e. mimj = 1), or both of mode II (i.e. (1  mi)(1  mj) = 1), or each of different modes (i.e. mi(1  mj) + mj(1  mi) = 1), respectively.

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tQij : Represents the MSs’ crossing rate between cell i, j (MSs/h), with the superscript Q 2 {I, Ac, Cs, Gi, At, Bt} indicates various MM state combinations and MS mode of operation. I: GPRS standby and GSM idle class-A/B MSs. Ac: GPRS standby class-A MSs during CSconnections. Cs: GPRS standby class-C MSs. Gi: GSM idle MSs, which access to CS services only. At(Bt): GPRS standby class-A (B) MSs with the CS-connections when roaming between cells i and j. The MS initiates a CS connection when it was in cell i and terminates the connection when it moves into cell j (or in the opposite direction). Here cells i and j may or may not be adjacent. h iT The vector tij ¼ tIij tAijc tCij s tGij i tAijt tBijt

Ccu: Cpu:

Ccp: Cpp:

is a bi-directional, MSs crossing rate. It represents the mobile location update frequency (MSs/h/boundary). In a unit of time, it extracts the number of MSs that perform RA, LA or combined RA/LA updates from all cell-boundary-crossing MSs. It is set to be zero when i P j, and 0.5tij represents a unidirectional MSs crossing rate. Cost on the Um interface when an MS performs an LA update to MSC; Cost on the Um interface when an MS performs an RA or combined RA/LA update to SGSN; Cost on Um interface for a CS paging message sent directly from the MSC; Cost on Um interface for a paging message transmitted via the SGSN.

To simplify the computation in this paper, it is assumed that the bandwidth-cost is always the same regardless of the network operation mode. 4.1. Location update signaling traffic The MSs’ inter-cell crossing rate, T = {tij, 1 6 i < j 6 K}, relates to the location update frequency if the considered cell boundary is chosen to be an LA and/or RA boundary. Meanwhile, if a cell boundary is selected, the generated location updates traffic will terminate at either MSC/VLR or SGSN.

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Therefore, based on Table 1, we will group the location update traffic into two possible cases: 4.1.1. LA-associated update traffic It represents, if the considered boundary is chosen to be an LA boundary, the number of updates generated per unit time by the MSs that cross this boundary. In this case, the possible types of procedure include LA updates to MSC/VLR and combined RA/LA updates to SGSN: (a) LA-associated updates to MSC/VLR. The MSs of the group f tIij tAijt tBijt g perform LA updates if the new resided cell is in mode II/III. The MSs of ftGij i g always performs LA updates regardless of the network mode. This portion of the updating process can be expressed mathematically as: T #LA MSC;ij ¼ mij Ptij ;

ð1Þ T

where P ¼ ½ r2 0 0 r1 r2 r2 , r1 ¼ ½ 1 1 1  , T T r2 ¼ ½ 0 1 0:5  , 0 ¼ ½ 0 0 0  . The matrix P extracts out the relevant MS groups, assesses the impact of the network operation mode, and evaluates the total number of MSs that update to the MSC/ VLR per unit time. (b) LA-associated updates to SGSN. Table 1 shows that, if the termination cell is in mode I, MSs of ftAijt g perform combined RA/LA update. This part of update frequency is given by: At #LA SGSN;ij ¼ t ij ½ 1

0 0:5 mij .

ð2Þ

The use of 0.5 is based on the assumption that there is an equal probable number of MSs moving from mode I to mode II and vice versa, while only those MSs that move into the cell in mode I perform T updates to SGSN. If we denote r3 ¼ ½ 1 0 0:5  , T 0 ¼ ½ 0 0 0  , it can be expressed as: T #LA SGSN;ij ¼ mij ½ 0

0

0 0

r3

0 tij .

ð2aÞ

4.1.2. RA-associated update traffic Similarly, it describes the number of location update traffic per unit time generated by the crossing MSs when the boundary (i, j) is selected to be an RA boundary. It includes RA and combined RA/LA updates performed by MS groups f tIij tAijc tCij s tBijt g, regardless of the network operation mode of cells i and j. Recall that a combined RA/LA update is a relayed RA update [12], and their radio consumptions should be the same. Hence we are able to group them into the same class. These

updates terminate only at SGSN. The frequency can be expressed mathematically by: T #RA SGSN;ij ¼ r tij .

ð3Þ T

The vector r ¼ ½ 1 1 1 0 0 1  is to extract the relevant groups of MSs from tij that perform updates via the SGSN. Using the definition of unit cost, we can express the costs of RA-associated and LA-associated location update signaling traffic per unit time as follows: RA eRA ij ¼ C pu #SGSN;ij ;

eLA ij

¼

C pu #LA SGSN;ij

þ

ð4Þ C cu #LA MSC;ij .

ð5Þ

4.2. Paging signaling traffic The paging signaling traffic per unit time is related to the packet and call arrival rates of cell i, which are denoted by pi (packets/h/cell) and ci (calls/h/cell), respectively. ki is considered to be the fraction of the calls of GPRS-attached MSs for calls arriving into cell i. 4.2.1. LA-associated paging traffic The paging message that will be sent within the LA that contains cell i must have been transmitted directly from MSC but the amount per unit time depends on the network operation mode of cell i. It can be expressed as follows: dLA MSC;i ¼ mi ð1  ki Þci þ ð1  mi Þci ¼ ð1  mi ki Þci . ð6Þ 4.2.2. RA-associated paging traffic Based on the preceding discussion, the paging traffic in this case is initially generated by either SGSN or MSC then transmitted via SGSN and broadcast in the RA containing cell i. It can be expressed mathematically as: dRA SGSN;i ¼ pi þ mi ki ci .

ð7Þ

By the definition of unit cost on performing paging procedures, we further express the costs of RA-/ LA-associated paging signaling traffic as follows: nLA ¼ C cp dLA MSC ¼ C cp ð1  ki mi Þci ; i nRA i

¼

C pp dRA SGSN

¼ C pp ðpi þ ki mi ci Þ.

ð8Þ ð9Þ

Starting with the average MS crossing rate in area and packet/call arrival rates in cell i, we express the cost of signaling for GPRS location manage-

N. Chai et al. / Computer Networks 50 (2006) 2888–2901 LA RA ment on the Um interface by eRA and nLA ij , eij , ni i . We classify the signaling traffic as RA or LA associated because the essential of GPRS location management design is to select the RA and LA boundaries from all the cell boundaries properly. In addition, since the GPRS core network governs the PS and CS services by different entities (i.e. SGSN and MSC/VLR), we have to distinguish the destination or the source of the signalings.

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LA. Compared with GSM graph partitioning problem which has been NP-complete, the GPRS graph partitioning is more complex since it has two sets of node and edge. It consists of RAs and LAs with each RA having a size smaller or equal to an LA. In addition, the location management has to obey the procedure set in Table 1. In the next two subsections, we present two approaches for GPRS graph partition. One is the optimal approach whilst the other is heuristic.

5. Problem statement and solutions 5.2. Solution from branch and bound algorithm 5.1. Problem statement Given a network comprising of K cells with the following parameters {mij, tij, ci, pi, ki} (1 6 i < j 6 K), our problem is to partition the K cells into M disjoint RAs and N disjoint LAs (1 6 N 6 M 6 K) such that the signaling traffics for LM are optimal. With the interpretation and expressions in SecLA RA tion 4, we can compute eRA and nLA from ij , eij , ni i the given parameters and then describe the problem of GPRS location management design by a graph, G = (V, E), shown in Fig. 5, where the node set, V = {1, 2, . . . , K}, denotes the cells in the area. E is the set of edges, (i, j), between cells i and j (1 6 i < j 6 K). Compared with GSM graph in [9], there are two weights attached with each edge for the GPRS graph: (1) eRA is RA-associated update cost and ij (2) eLA ij is the LA-associated update cost. Each node also has two weights: (1) nRA is the cost of paging an i MS in an RA, these paging messages transmits via SGSN and (2) nLA is the cost of paging the desired i MS in an LA, these paging messages are issued directly by the MSC. This classification is necessary because GPRS tracks an MS in both PS and CS domain so as to provide PS and CS services. The location management design for GPRS is to partition the cells of graph G into subsets of RA and

#i

niRA / niLA RA LA {e ij , e ij } #j LA n RA j / nj

# i : cell idex

Fig. 5. Graph for GPRS networks.

In order to calculate the total cost of signaling traffic for location management, we first introduce two decision variables, xij, yij. We denote:  1 if cell i and cell j are in the same RA; xij ¼ 0 otherwise;  1 if cell i and cell j are in the same LA; y ij ¼ 0 otherwise. They are for selecting RA and LA boundaries among cell boundaries. Within the entire service area, xij = 0 implies that the boundary between cell i and cell j is an RA boundary. Similarly yij = 0 implies an LA boundary. Therefore the cost of location update signaling within a unit of time can be expressed mathematically as: U¼

K 1 X K X

LA ½eRA ij ð1  xij Þ þ eij ð1  y ij Þ

i¼1 j¼iþ1

¼

K 1 X K X

½C pu #RA SGSN;ij ð1  xij Þ

i¼1 j¼iþ1 LA þ C cu ð#LA SGSN;ij þ #MSC;ij Þð1  y ij Þ.

ð10Þ

The number of cells in the RA that contains cell i is given by the following mathematical expression  PK Pi1  1 þ j¼iþ1 xij þ l¼1 xli . The cost of RA-associated paging traffic is therefore expressed by: ! K K i1 X X X RA RA ni 1þ xij þ xli . P ¼ i¼1

j¼iþ1

ð11Þ

l¼1

The that contains celli comprises the number  LA PK Pi1 of 1 þ j¼iþ1 y ij þ l¼1 y li cells including cell i. Hence, on the Um interface, the cost of LA-associated paging traffic can be expressed by the following formulation:

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P

LA

N. Chai et al. / Computer Networks 50 (2006) 2888–2901

¼

K X

nLA i

K X

1þ

i¼1

y ij þ

j¼iþ1

i1 X

! y li .

ð12Þ

l¼1

The cost of paging signaling traffic is the sum of the above two parts. And the total cost of signaling traffic for the location update and the paging is computed by summing the results given by (10)– (12). By grouping terms that carry xij and yij together, the total signaling cost can be shown by: K 1 X K h  X nRA þ nRA  eRA Constant þ xij i j ij i¼1 j¼iþ1

  i LA þ nLA þ nLA y ij . i j  eij

ð13Þ

Since the Constant plays no further role in the optimizing problem, it is not considered later. We LA rewrite (13) by using the expressions of eRA ij , eij , RA LA ni and ni , and then simplify it by defining: cpcu = Cpu/Ccu, cppu = Cpp/Cpu, ccpu = Ccp/Ccu and Dij=mikici + mjkjcj. The problem of static GPRS location management design can be formulated as: Objective function min

C cu

K1 X K X

cpcu fcppu ðpi þ pj þ Dij Þ

i¼1 j¼iþ1

 ½ 1 1 1 0 0 1tij gxij þ fccpu ðci þ cj  Dij Þ  mTij ½ r2 0 0 r ðr2 þ cpcu r1 Þ r2 tij gy ij

ð14Þ

Subject to jmi  mj jxij ¼ 0; jmi  mj jy ij ¼ 0 xij 6 y ij

81 6 i < j 6 K

ð15Þ ð16Þ

81 6 i < j 6 K

xij þ xjk  xik 6 1; xij  xjk þ xik 6 1; 81 6 i < j 6 K

ð17aÞ

xij þ xjk þ xik 6 1 y ij þ y jk  y ik 6 1; y ij  y jk þ y ik 6 1; 81 6 i < j 6 K y ij þ y jk þ y ik 6 1 xij ;y ij ¼ f0; 1g

81 6 i < j 6 K.

ð17bÞ ð18Þ

Constraints (15) and (16) are specific for GPRS location management design. Constraint (15) implies that the cells within the same registration area should be set to be the same network operation mode. That is, if xij = 1, constraint (15) becomes jmi  mjj = 0, forcing mi = mj. Constraint (16) ensures the RA is the subset of the LA. This implies that if xij = 1, constraint (16) becomes yij P 1, forcing yij = 1. The group of constraints given by (17a) and (17b), called triangle-inequalities for a cell triangle

{i, j, k}, translates the logical induction of combination, which ensures that if some two cells i and cell j belong to the same registration area as cell k, they must also be in the same registration area. For instance, if xik = 1 and xjk = 1, the constraint xij + xjk + xik 6 1 becomes xij P 1, forcing xij = 1. The proposed solution scheme was encoded in C++ using the branch and bound library available in ILOG CPLEX 8.1 [14]. It ran on a 2.8 GHz Dell Optiplex System. We tested the computation time for the algorithm. The CPU time is less than 1 s when it attempts to solve an RA/LA design for a network of 6 · 6 cells (Fig. 6). The total signaling costs before/after the design is 36968.8/29387.8 Ccu-bits/h, 20.5% decrease is achieved compared to the one cell per LA and one cell per RA configuration. The data used is similar to the one given by [15] and cell 1  20 are in network mode I, the remaining are in mode II. The objective function (13) is a typical graph partitioning problem which is NP-complete. The time complexity of exhaustive search is O(2K(K1)). We propose an approximate method which can be applied to the area of a large topology. It has been generally accepted that, in GSM network, the user in connection is normally the minority, hence the MSs crossing the cell boundary can be treated as in idle state [4]. Since GPRS network is an upgraded version of GSM, it is reasonable to make the assumption that the MSs that cross the cell boundary are in GPRS Standby and/or GSM idle state. Under such assumption, we develop the following heuristic algorithm. 5.3. Solution using greedy algorithm The algorithm will be looking into merging cells into RAs and LAs to fulfill the preset objective function. We first present a useful lemma. Lemma. Given the graph G = (V, E) for a GPRS network, we define the gains of merging two cells i and j as   RA RA GRA þ nRA ; ð19Þ j ij ¼ eij  ni   LA LA LA GLA ¼ e  n þ n . ij ij i j

ð20Þ

LA 1. If GRA ij < 0 and Gij > 0, then merge the two cells into an LA but the different RAs. LA RA 2. If GRA ij > 0 and Gij þ Gij > 0, then merge the two cells into an RA.

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#1

#2

#14

#19

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LA and RA boundary; RA 18 groups, LA 16 groups.

RA boundary;

Fig. 6. A illustrative result of branch and bound algorithm.

3. Otherwise, each cell remains in different RA and LA. These conditions ensure that if such merging is performed, the total signaling cost for GPRS location management will be reduced. Proof. Before we group the two cells into RA or LA, the total signaling cost for location management can be expressed mathematically as: LA RA T before ¼ eRA þ nRA þ nLA þ nLA ij þ eij þ ni j i j .

ð21Þ

If we group cells i and j into the same RA, the signaling cost for location management after grouping can be expressed as: RA LA T RA þ nRA þ nLA after ¼ 2  ðni j Þ þ 2  ðni j Þ.

ð22Þ

If we group cells i and j into the same LA but different RA, the signaling cost for location management after the grouping can be expressed as: RA RA T LA þ nRA þ 2  ðnLA þ nLA after ¼ eij þ ni j i j Þ.

ð23Þ

We denote the differences between the signaling cost before and after grouping as DRA ¼ T before  T RA after ;

ð24Þ

DLA ¼ T before  T LA after .

ð25Þ

By using (21)–(23), we can express these differences as

  RA LA RA RA ¼ e þ e  n þ n DRA ¼ T before  T RA after ij ij i j   LA þ nLA ð26Þ  nLA ¼ GRA ij þ Gij ; i j   LA LA DLA ¼ T before  T LA þ nLA ¼ GLA ij . after ¼ eij  ni j ð27Þ Hence DRA is the gain of merging cells i and j into the same RA, and DLA is the gain of merging cells i and j into the same LA but different RA. LA When GRA ij < 0 and Gij > 0, from (26) and (27), RA it implies DLA > DRA and DLA > 0, i.e. T LA after < T after LA and T after < T before . This suggests that cells i and j should be in the same LA but different RAs since it then will have lower location management signaling load. LA RA When GRA ij > 0 and Gij þ Gij > 0, it implies RA LA DRA > DLA (because DRA ¼ GLA ij þ Gij > Gij ¼ RA RA DLA if Gij > 0Þ and DRA > 0, i.e. T after < T LA after and T RA < T . Using the same argument, cells i before after and j should be in the same RA. This proves the lemma. h RA RA Note that we employ GLA ij þ Gij rather than Gij as the criteria for testing whether any two cells should be in the same RA, because an RA should be the subset of an LA [12]. Since the optimal GPRS RA/LA design is NP-complete, the heuristic algorithm (Fig. 7) put forward starts with each RA subset and LA subset containing only one cell. In order to apply the lemma to our algorithm at all step, we

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Fig. 7. Greedy algorithm.

first extend (19) and (20) to a more general case where each RA/LA may contain more than one cells. Given the graph G = (V, E) for a GPRS network, "i, j 2 V and (i, j) 2 E, i 2 Rs, La and j 2 Rt, Lb (1 6 s,t 6 M and 1 6 a, b 6 N), where Rs, Rt and La, Lb represent the set of cells in the sth, tth RA and the ath, bth LA, respectively, then LA 1. If s ¼ t GRA ij ¼ 0, Gij ¼ 0; 2. If s 5 t and a = b, then

GRA ij

¼

X

eRA ij



k2Rs ;l2Rt

X

nRA k

þ

k2Rs

X

! nRA l

l2Rt

ð28Þ

 ðjRs j þ jRt jÞ; GLA ij ¼ 0. 3. If s 5 t and a 5 b, then GRA ij

¼

X

eRA ij



k2Rs ;l2Rt

X

nRA k

þ

k2Rs

X

! nRA l

l2Rt

 ðjRs j þ jRt jÞ; GLA ij

¼

X

eLA ij



k2La ;l2Lb

X k2La

nLA k

þ

X

!

ð29Þ

nLA l

k2Lb

 ðjLa j þ jLb jÞ. Eqs. (28) and (29) are to replace (19) and (20) to calculate the gain of merging two cells of edge (i, j), where cells i and j are in the same or different subsets which may contain more than one cell. The notation jRj denotes the number of cells in the set R. The developed algorithm is shown in Fig. 7. For every edge (i, j), the network modes of both cells are first check. If they have different mode, the gains are

set to zero since no merging should be made. OtherRA and GLA are computed wise, the gains GLA ij þ Gij ij using (28) and (29), and maintained in two separate tables. In every iteration, we always select the pair RA or of cells with maximum gain (either GLA ij þ Gij LA LA Gij ). For "(i, j) 2 E, suppose maxfGij g ¼ GLA kl LA RA LA and maxfGRA þ G g ¼ G þ G , where (p, q), ij ij pq pq (k, l) 2 E, p, q, k, l 2 V, here (k, l) and (p, q) may or may not be the same edge. Below we show that the condition given in step III of Fig. 7 is sufficient. LA LA LA When GRA pq þ Gpq P Gkl , since Gkl is the largest LA LA in the list (i.e. Gkl > Gpq ), this implies LA LA RA GRA pq þ Gpq > Gpq , which implies Gpq > 0, then rule 2 in Lemma can be applied and we will merge two cells (p, q) into an RA. Similarly, when GLA kl > LA LA þ G , it implicitly indicates that G GRA pq pq kl > LA RA GRA kl þ Gkl which implies Gkl < 0, hence rule 1 in Lemma applied. While running the proposed greedy algorithm on the network mentioned in Section 5.2, this algorithm achieves similar RA/LA layout as shown in Fig. 6, of which is the optimal solution solved analytically. We have repeated the design by varying the mobile traffic in the cells and the call/packet arrival rates [16] to demonstrate the effectiveness of our proposed greedy algorithm. In Table 2, we compare the results obtained optimally with the results obtained by using the greedy algorithm. It can be seen that the designed costs obtained are very close to the optimal design and at a much reduced computational time. Furthermore, the number of LAs and RAs required are also tabulated. In all our examples, the greedy algorithm always achieves the same number of RAs and LAs as that obtained from optimal solution. Given that our proposed scheme is a heuristic approach, the objective function does vary slightly from the optimal one (highlighted entries in Table 2). This indicates that the actual grouping of cells in LAs and RAs might be slightly different, but yet effective, as shown in the cost value achieved. This shows that our algorithm can obtain close to optimal solution. We further apply the greedy algorithm to a larger network of size 10 · 10. Fig. 8 shows the graphical representation of the obtained RA/LA design where there are 53 RAs and 28 LAs. The data used in this design are as follows: (1) the average MSs moving speed in the considered area is m = 30 km/h, (2) the call arrival rate per MS in cell i is c = 0.6 calls/h/MS, (3) a fraction k = 0.5 of the incoming

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Table 2 Comparison of the greedy algorithm results with the optimal solutions

a

Optimal number of RAs/LAs. Objective value obtained by the optimal solution. c Objective value obtained by the greedy algorithm. b

LA boundary RA containing only one cell

Cells in the same RA

Fig. 8. Solution to RA/LA design for a GPRS network of size 10 · 10.

calls to cell i will be terminated at class-A/B MSs, (4) the ratio of the packet arrival rate to the call arrival rate in cell i is c = 1, (5) a fraction lPS = 0.5 of all crossing MSs are PS users who have been GPRS-attached. 90% of the PS users is GPRS standby GSM idle class-A/B users and the rest 10% is GPRS standby class-C users, and (6) we also assume cpcu = 1, cppu = 0.1, and ccpu = 0.1. The above parameters can be modified according to the actual environment. (7) All the cells in the network is operated in mode I. The total signaling costs before/after design are 2684.5/1370.3 Ccu-bits/h,

and 49% decrease has been achieved. Optimal solution in this case cannot be obtained due to the large number of unknown constraints and variables that need to be solved on account of the large cell size. However, by using the proposed greedy algorithm, the computer running time is less than 10 s. 5.4. Discussions Eq. (15) suggests that the network mode for the cells, which can be set by the operator, provides another way to reduce the amount of signaling load

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to be incurred. It is because the network operation mode I is more radio efficient than mode II/III. Coordinated paging makes the SGSN to share the MSC’s paging load (the amount depends on ki, the percent of calls terminated to class-A/B users, given by Dij = mikici + mjkjcj), and hence to page over a smaller area (i.e. RA) rather than over the LA; On the other hand, combined update refreshes MS’s location information at both SGSN and MSC/VLR after a single update. For the network shown in Fig. 8, the total signaling cost after design would be 1714.5 Ccu-bits/h if it is operated in mode II. Although the MS coordination saves radio resources, it incurs additional signal processing in the core network. The operator therefore has to find a compromise between their core network processing capability and their radio resources. Other factors that could affect the design will not be illustrated here in detail, due to space limitation. For example, in the event that pi is larger than ci (e.g. there are more users who surf the internet than those who make voice call), enlarging RA could lead to a dramatic increase in paging traffic, given that the SGSN has to page over a larger area. For the network shown in Fig. 8, if the RA takes the layout of LA which is obtained from the optimal RA/ LA design, the total signaling cost would be 1501.3 Ccu-bits/h, which is 9.6% higher than the optimal RA/LA layout. On the other hand, reducing the size of LA could cause the updating traffic to increase. For the same network, if LA takes the layout of RA which is obtained from the optimal RA/LA design, the total cost would be 1450.5 Ccu-bits/h, 5.9% higher. Such an observation is not surprising as there will be certain MSs traffic distribution resulting in LA equal to RA in the design. Finally, from the operators’ point of view, the ratios of single performance cost, cpcu, cppu, ccpu, which are assumed to be equal to 1, 0.1, 0.1 respectively in the analysis, are also having impact on the design and may affect the application to the practical system. In our previous approach, we assume that network operation mode of all the cells are known. Alternatively, the scheme can be tailored for the optimal SGSN or MSC/VLR allocation, or the distribution of network operation mode for the cells in the service area to achieve a good balance between the network signal processing capability in the core network and the signaling load on the Um interface.

6. Conclusion This paper provides a detailed study of GPRS location management (LM) design and proposes a practical scheme to minimize the total signaling traffic for paging and location updating. The three parameters, which are crucial for an optimal GPRS LM design, are detailed in Table 1 and Section 4. Their effects on the signaling traffics for LM are discussed in details and are expressed by using matrix/ vectors, tij, mij, P. Other parameters that affect the design, such as ki, pi, ci, etc., are also identified and included in our model. The objective function is formulated as a 0–1 programming model with the aim of minimizing the total signaling traffic by selecting RA/LA boundaries appropriately. The constraints formulated enforce the compulsory relationship, as discussed, between the RA and the LA. A heuristic algorithm using the Greedy approach is also proposed. The examples provided illustrates that the proposed scheme is able to solve GPRS RA/LA configuration optimization problem effectively. The scheme should be readily adapted for other GPRS RA/LA optimization goals. References [1] I.F. Akyildiz, J.S.M. Ho, On location management for personal communications networks, IEEE Commun. Mag. (1996) 138–145. [2] V.W.-S. Wong, V.C.M. Leung, Location management for next-generation personal communications networks, IEEE Network Mag. (Sep./Oct.) (2000) 18–24. [3] Y.-B. Lin, Y.-R. Haung, Y.-K. Chen, I. Chlamtac, Mobility management: from GPRS to UMTS, Wireless Commun. Mobile Comput. 1 (4) (2001) 339–360. [4] E. Cayirci, I.F. Akyildiz, Optimal location area design to minimize registration signaling traffic in wireless systems, IEEE Trans. Mobile Comput. 2 (1) (2003) 76–85. [5] I.F. Akyildiz, W. Wang, A dynamic location management scheme for next-generation multitier PCS system, IEEE Trans. Wireless Commun. 1 (1) (2002) 178–189. [6] K. Wang, J.-M. Chen, Intelligent location tracking strategy in PCS, IEEE Proc. Comm. 147 (1) (2000) 63–68. [7] L.P. Araujo, J.R.B. de Marca, Paging and location update algorithms for cellular systems, IEEE Trans. Vehicular Technol. 49 (5) (2000) 1606–1614. [8] S. Tabbane, An alternative strategy for location tracking, IEEE J. Select. Areas Commun. 13 (5) (1995) 880–892. [9] S.Z. Ali, Design of location areas for cellular mobile radio network, in: IEEE Vehicular Technology Conference, vol. 3, May 2002, pp. 1106–1110. [10] J. Plehn, The design of location areas in a GSM network, in: The 45th IEEE Vehicular Technology Conference, vol. 2, 1995, pp. 871–875. [11] H. Xie, S. Tabbane, D. Goodman, Dynamic location area management and performance analysis, in: Proceedings of

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the 43rd IEEE Vehicular Technology Conference, 1993, pp. 536–539. 3GPP, Technical Specification Group Services and Systems Aspects; General Packet Radio Service (GPRS); Service Description; Stage 2 (Release 1999), 3GPP TS 23.060 version 3.16.0 (2003-12). G. Sanders, L. Thorens, M. Reisky, O. Rulik, S. Deylitz, GPRS Networks, John Wiley & Sons, 2003. ILOG Inc. ILOG Software Components, ILOG CPLEX 8.1, December 2002. R. Subrata, A.Y. Zomaya, A Comparison of three artificial life techniques for reporting cell planning in mobile computing, IEEE Trans. Parallel Distribut. Syst. 14 (2) (2003) 142– 153. N. Chai, Location Management for GPRS, M.Eng. dissertation, National University of Singapore, 2005.

a course on Wireless Network Protocols. He is actively involved in research and development in the areas of wireless communication systems, network management of wireless communication systems, internetworking of hybrid communication systems and operation research. He is currently the deputy director for technology and development for Wavex Technologies, a fast growing start-up company in Singapore specializing in RFID and wireless communication systems. He is also actively involved in conferences, both technical and organizational aspects, whereby he is the organizing chair for IEEE MWCN 2002, technical co-chair of IEEE GLOBECOM 2004 Wireless Communications, Networks and Systems Symposium, IFIP MWCN 2003, GLOBECOM 2005 General Symposium and GLOBECOM 2006 Wireless Symposium, and the general co-chair for ISWCS, of which he is also the co-initiated. HE also serves as an editorial board member for a couple of journals.

Ning Chai obtained her bachelor degree from the Northwestern Technological University, Xian, China, in 1996. She then joined Liming Aero Engine Manufacture Co., China as an Assistant Engineer. She received her first MS degree in Engineering from the Beijing University of Aeronautic and Astronautic, China, in 1999. Since 2002, she was a research scholar in National University of Singapore, Singapore. She was conferred with MS degree in Electrical and Electronic Engineering from the National University of Singapore.

Yong Huat Chew received the B.Eng., M.Eng. and Ph.D. degrees in electrical engineering from National University of Singapore (NUS), Singapore. He has been with the Institute for Infocomm Research (formerly also known as Centre for Wireless Communications, NUS and Institute for Communications Research), an institute under Agency for Science, Technology and Research, where he is presently a lead Scientist, since 1996. He is also holding an adjunct position in the Department of Electrical and Computer Engineering, NUS, since 1999, and he is currently an adjunct associate professor. His research interests are in technologies related to high spectrally efficient wireless communication systems.

[12]

[13] [14] [15]

[16]

Boon Sain Yeo ([email protected]) received the B.Eng. (Hons) and Ph.D. in Electrical Engineering from University of Glasgow and Imperial College, respectively. He was an R&D engineer in Siemens from 1996 to 1998 before pursuing his Ph.D. Since 2001, he has been working in Institute for Infocomm Research (I2R), Singapore, as a research scientist. He also holds an adjunct appointment in the Department of Electrical and Computer Engineering in NUS where he lectures in