Combinatorial Mobile IP: A New Efficient Mobility Management Using Minimized Paging and Local Registration in Mobile IP Environments

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1 Wieless Netwoks 0, 3 32, Kluwe Academic Publishes. Manufactued in The Nethelands. Combinatoial Mobile IP: A New Efficient Mobility Management Using Minimized Paging and Local Registation in Mobile IP Envionments TAEHWAN CHOI, LAEYOUNG KIM, JEONGEUN NAH and JOOSEOK SONG Depatment of Compute Science, Yonsei Univesity, Seoul, 20-79, Koea Abstact. Combinatoial Mobile IP, a new mobility management scheme fo Mobile IP, is poposed and analyzed. We pesent how to adopt mobility management schemes on cellula netwoks and adapt them in Mobile IP without disupting the natue of the Intenet. We apply widely used mobility management schemes such as hieachical achitectue and paging in cellula netwoks to Mobile IP. We estict paging to the aea that has to be paged using local egistations. In this way, we show that the total signaling costs of Combinatoial Mobile IP ae educed compaed to othe mico-mobility potocols such as Mobile IP Regional Registation and P-MIP. Random walk on a connected gaph is used to analyze the pefomance of Combinatoial Mobile IP. Keywods: mobile IP, mobility management, mico-mobility potocol, andom walk model on a connected gaph. Intoduction Wieless access to the Intenet is becoming pevasive. Recent eseach on mobility management on the Intenet has focused on Mobile IP [0]. Mobile IP suppots the mobility of teminals simply and scalably, and is well suited fo macomobility but not fo mico-mobility [0]. Mobility management on the Intenet is a difficult poblem since location infomation is distibuted aound the Intenet. Mobility management of cellula netwoks is moe natual than on the Intenet since cellula netwoks ae centalized systems. In cellula netwoks, mobility management uses two schemes: location updates and paging. On the othe hand, Mobile IP uses egistation only. Cuently, a lot of eseach effots ae being made to impove Mobile IP mobility management. Paging and hieachical achitectue have been poposed in most mobility management schemes in Mobile IP envionments. Paging and hieachical achitectue ae not newly developed techniques fo Mobile IP. They have been widely used in telephone netwoks. Thus, the gap between mobility management in Mobile IP and cellula netwoks is disappeaing. Cellula netwoks ae commecially implemented and seve uses with eliable, obust and seamless mobility. Compaed with cellula netwoks, Mobile IP is a latecome. Howeve, the Intenet is eve-gowing and Mobile IP would be a good solution fo mobility management in the next geneation netwok. Registation in Mobile IP coesponds to location updates on cellula netwoks. Howeve, egistation in Mobile IP is diffeent fom location updates on cellula netwoks, in that egistation costs in the fome ae distibuted at the leaf nodes such as Home Agent (HA) and Foeign Agent (FA), while location update costs in the latte ae centalized at the top level such as the Mobile Switching Cente (MSC). Since mobility management in Mobile IP depends on egistation only, Mobile IP does not sufficiently povide mobility management compaed with cellula netwoks. Adding paging schemes is not a sufficient condition fo efficient mobility management, since signaling ovehead by paging is significant while it educes location update costs. Thus, intewoking between paging and egistation is the keyissueofimplementationinealwoldnetwoks. Since location databases ae distibuted and managed on leaf-level nodes in Mobile IP, paging costs can be educed by using that infomation. A Regional Aea (RA) o a Location Aea (LA) is a goup of Paging Aeas (PAs) that manage and contol use mobility in the zone-based location management scheme [,]. The zone-based location management scheme is a widely deployed scheme in the eal wold of cellula netwoks. In the zone-based location management scheme, the RA concept was adopted to educe location update costs. Uses do not have to update thei locations wheneve they move away fom PAs but they do location updates when they move away fom RAs. Registation costs in Mobile IP ae highe than location update costs on cellula netwoks. The Home Netwok (HN) size in Mobile IP is much smalle than that in cellula netwoks. Theefoe, if we assume the same mobility ate fo Mobile IP and cellula netwoks, the tansition pobability fom a HN to a Foeign Netwok (FN) in Mobile IP is highe than that in cellula netwoks. When a Mobile Node (MN) moves away fom its HN, it egistes with its FA and then the FA egistes with the MN s HA. Registation costs in a FN ae at least twice as much as those in a HN. Moeove, egistation costs incease geatly if the FA and the HA ae distant fom each othe. The way that Mobile IP and cellula netwoks exchange messages is diffeent. Message exchanges ae asymmetic on Mobile IP. In Mobile IP, a MN eceives

2 32 T. CHOI ET AL. Table Compaison between cellula netwoks and Mobile IP on mobility management. Cellula netwoks Mobile IP Netwok system Centalized Distibuted Achitectue Hieachical Flat Mobile equipment side Location update Registation System side Paging None Message exchange Symmetic Asymmetic data fom a Coespondent Node (CN) though its FA and via its HA when the MN moves away fom its HN while the MN sends diectly data to the CN. In cellula netwoks, message exchanges ae symmetic in that the outes to send and eceive messages ae the same. A compaison between cellula netwoks and Mobile IP is summaized in table. In this pape, we will pesent a new efficient mobility management scheme fo Mobile IP. We will adopt paging and hieachicalachitectuein cellula netwoks, but adapt them to Mobile IP consideing the diffeences between the telephone netwok and the Intenet. We will use minimized paging and local egistation to manage mobility in Mobile IP envionments. This pape is stuctued as follows. Section 2 shows the elated wok and section 3 pesents an oveview of Combinatoial Mobile IP. Section descibes the detailed opeation of the potocol. Section analyzes and evaluates Mobile IP, Mobile IP Regional Registation [], P-MIP [], and Combinatoial Mobile IP. Section concludes the pape. 2. Related wok Mobile IP is not only the de facto but also the de jue standad fo maco-mobility on the IP netwok. Mobile IP is suitable fo maco-mobility but not fo mico-mobility. Theefoe, a lot of eseach has been conducted to povide mico-mobility. Cellula IP [], Mobile IP Regional Registation [], HAWAII [], Mobile IP Regional Paging [], and P-MIP [] ae pesented as mico-mobility potocols. Cellula IP suppots local mobility by adopting passive connectivity and paging. Diffeentiating active and idle modes of mobile nodes enables passive connectivity. This is a useful featue fo minimizing battey consumption. Cellula IP adopts semi-soft and had handoff fo suppoting fast handoff. A Base Station (BS) in Cellula IP is the univesal component, since it functions not only as a wieless access point but also as a oute fo IP packets. Theefoe, it is completely diffeent fom the BS in cellula systems. Routing in Cellula IP plays an impotant ole fo mobility management and handoff suppot. Location infomation is maintained by outing and paging caches in Cellula IP. Cellula IP bings cellula system design pinciples to IP design pinciples. Mobile IP Regional Registation [] educes the numbe of signaling messages to the HN, and the signaling delay, by pefoming egistation locally. It uses egistation and the hieachical model to suppot mobility management. Thee ae two types of FAs, such as the Gateway Foeign Agent (GFA) at the top of the hieachical model, and the Regional Foeign Agent (RFA) beneath the GFA. Since a GFA cae-of addess is egisteed at the HA, a MN does not have to notify its HA of its point of attachment when the MN moves fom one RFA to anothe RFA unde the same GFA. Refeence [7] shows that 9% of a use s mobility is local. Theefoe, detaching local mobility fom global mobility is desiable. In Mobile IP, global mobility and local mobility ae teated in the same way. Because of this, egistation costs incease as a MN becomes moe distant fom its HN. The sepaation of global mobility and local mobility is the pactice that handles mobility moe efficiently. In this way, the popagation of local egistation to a coe netwok is eliminated. In ode to sepaate local mobility and global mobility, hieachical achitectue is needed fo Mobile IP. Mobile IP Regional Registation [] is a good candidate fo solving this poblem. It guaantees that a MN does not have to egiste wheneve it moves. It only egistes when it moves away fom the aea that a GFA contols. Howeve, since Mobile IP Regional Registation only depends on egistation, it lacks the function of fast handoff. In addition, though Mobile IP Regional Registation is successful in sepaating global mobility fom local mobility, egistation costs ae still high, since a MN has to send a egistation equest to its FA and the FA elays this equest to its GFA. Theefoe, an appopiate use of paging and egistation is the key to success in mobility management fo Mobile IP envionments. HAWAII is a domain-based system that povides fast handoff by passive connectivity and paging. In P-MIP, paging costs ae consideable since it pages all the PAs that a MN is pedicted to exist. In ovelapping PAs, the PAI (Paging Aea Identification) is made up of the entie lists of FA IP addesses. Though it suppots ovelapping PAs, scalability is limited if the numbe of FAs inceases, since it wastes a lot of bandwidth. Mobile IP Regional Paging [] is an extension to Mobile IP, with Regional Registations to suppot powe-constained opeation. Since it uses time slot-based paging within a PA, it is intefeence-fee. In addition, a MN does not have to powe up its eceive fo evey advetisement slot, but it may powe up its eceive only fo evey Nth advetisement slot. The achitectue of the paticula netwok influences location management. In cellula netwok achitectue, since it is a centalized netwok, location infomation is centally managed by stoing data on the Home Location Registe (HLR). In Mobile IP achitectue, location infomation is managed in a HA and a FA. Theefoe, it is impotant to utilize the chaacteistics of its paent netwok. P-MIP [] and Mobile IP Regional Paging [] adopt a paging scheme. Howeve, they adopt paging schemes in cellula netwoks without consideing thei paent netwoks. As a esult, they have add-on signaling costs since the egistation costs ae inceased if we assume paging costs ae appoximately the same. Among the above pesented mico-mobility schemes, Cellula IP [], HAWAII [] and Regional Paging [] use paging and egistation, and Mobile IP Regional

3 COMBINATORIAL MOBILE IP 33 Table 2 Compaison of mico-mobility potocols. Mico-mobility potocols Hieachical achitectue Paging Mobile IP Regional Registation Yes No Mobile IP Regional Paging Yes Yes P-MIP No Yes Cellula IP Yes Yes HAWAII Yes Yes Table 3 Compaison between cellula netwoks and Mobile IP on netwok elements. Components Cellula netwoks Mobile IP Mobile equipment Cellula phone Mobile node Paging equipment BS PFA Paging equipment contolle BSC CFA HN location infomation HLR HA s use lists FN location infomation VLR FA s visito lists Registation [] depends on egistation only. A compaison among mico-mobility potocols accoding to hieachical achitectue and paging is summaized in table 2. Hieachical mobility is categoized by two styles of mico-mobility, such as Hieachical Tunnelling and Mobile- Specific Routing [2]. Hieachical Tunnelling uses distibuted location databases, and Mobile IP Regional Registation and Mobile IP Regional Paging ae examples using the technique. Mobile-Specific Routing uses the home addess inside the access netwok, whee Cellula IP and HAWAII ae good examples. 3. Potocol oveview In this section, we pesent Combinatoial Mobile IP, a new mobility management scheme using minimized paging and local egistation. Befoe we discuss Combinatoial Mobile IP, some assumptions ae pesented as follows. 3.. Basic assumptions Two-level hieachy. Multi-level hieachy could possibly be constucted, but twolevel hieachy is sufficient. If multi-level hieachy is constucted, mobility management is complicated and signaling loads fo egistation incease. Paging and egistation ae suppoted. All FAs suppot paging and egistation Basic components Cellula netwoks ae the benchmak models fo Mobile IP. In cellula netwoks, a PA is contolled by a BS and a goup of BSs ae managed by a Base Station Contolle (BSC). A MSC is in chage of call contol and switching, and it has an HLR, a location database. As a BS manages a PA, Paging Foeign Agent (PFA) manages a FN. The PFA, FA which manages a PA, has a paging function in addition to the function of a FA. Likewise, a Contolling Foeign Agent (CFA) coesponds to a BSC. The CFA, FA which manages a RA, has a paging function in addition to the function of a FA. It is the bidge between the HA and PFAs and is not involved diectly with MNs. In cellula netwoks, location update costs ae citical since signaling loads will be conveged to a centalized location database. Thus the capacities of databases ae impotant fo the scalability of cellula netwoks. In addition, inte-msc taffic is ovewhelming and inceases 30% of signaling taffic []. Howeve, this is not the case in Mobile IP. Since location databases in Mobile IP ae distibuted and localized, the capacities of databases ae not an issue in Mobile IP. The compaison of netwok components between cellula netwoks and Mobile IP is summaized in table Basic achitectue If a MN is in its HN, it opeates though conventional Mobile IP. Howeve, if a MN moves away fom its HN, it must egiste with its PFA and the PFA must egiste with its CFA. The CFA must elay the infomation to the MN s HA. When a MN egistes with its PFA and CFA, the PFA and the CFA must set the time fo active mode. Fo the duation of an active time session, if a MN has data to send o eceive, active mode will be extended. Howeve, if a MN does not send o eceive data fo a cetain peiod of time, the active time will expie and the MN will evet to idle mode. If a MN moves away fom its PA in active mode, it must egiste its location with its PFA and the PFA must egiste the infomation with its CFA. If a MN moves away fom its PA in idle mode, it must egiste with its new PFA. Howeve, the PFA does not egiste the MN s location infomation with its CFA. Since the MN and the PFA ae close to each othe, egistation costs ae not consideable. Since egistations ae localized, signaling costs will not affect the coe netwok. If a MN moves away fom its CFA, it must egiste with its new CFA, and the CFA notifies the HA of the new location of the MN. When thee is data fo a MN in idle mode, the CFA sends Paging Requests to its PFAs. The PFA seaches its visito lists and then it boadcasts Paging Requests to its PA if it finds the MN s home addess in its location database. If the PFA does not find the MN s home addess in its visito lists, it assumes that the MN is not in its PA and it does not boadcast Paging Requests to its PA. Paging in Combinatoial Mobile IP is used fo bidging between the CFA and the PFA. If the CFA pages the entie netwok, paging is ovewhelming. If the PFA egistes with its CFA wheneve a MN moves, as in [], the egistation costs ae consideable. Since paging taffic is less citical than location update taffic [], Combinatoial Mobile IP will incu a smalle amount of taffic than Mobile IP Regional Registation []. The basic achitectue of Combinatoial Mobile IP is illustated in figue and explained as follows.

4 3 T. CHOI ET AL. Figue 2. PAI extension. conseves powe. Combinatoial Mobile IP uses a PAI extension fo Agent Advetisements like P-MIP but it is moe scalable than that in P-MIP. The PAI extension in P-MIP consists of the entie lists of FA IP addesses while that in Combinatoial Mobile IP consists of a CFA IP addess and a PFA IP addess. Thus, as the numbe of FAs inceases, the length of the PAI extension in P-MIP also inceases while that in Combinatoial Mobile IP is fixed... Paging Figue. Basic achitectue of Combinatoial Mobile IP. Global egistation scenaio. A MN moves into a new RA fo the fist time. In this scenaio, a MN moves fom its HN to RA o a MN moves fom RA to RA 2. The MN must egiste with its PFA o PFA and PFA o PFA must egiste with its CFA o CFA 2, espectively. CFA o CFA 2 must egiste with the MN s HA. Regional egistation scenaio. A MN moves fom a PA to anothe PA within the same RA in active mode. In this scenaio, a MN moves fom PFA to PFA 2. The MN must egiste with PFA 2 and PFA 2 must egiste with CFA. Local egistation scenaio. A MN moves fom a PA to anothe PA within the same RA in idle mode. In this scenaio, a MN moves fom PFA to PFA 2. The MN must egiste with PFA 2 but does not egiste with CFA.. Potocol detail In this section, we show the detail opeations of Combinatoial Mobile IP. Combinatoial Mobile IP has seveal benefits by educing the oveall signaling costs. It is notable that a eduction in signaling costs of Combinatoial Mobile IP guaantees the obustness and scalability of netwoks. Thus, Combinatoial Mobile IP ealizes a obust, scalable, and low-cost signaling scheme fo wieless access to the Intenet using the diffeentiated egistations accoding to the level of movement, and the minimized paging with the intewoking between PFAs and thei CFA. The egistation scheme in Combinatoial Mobile IP is distinct fom that in cellula netwoks since a MN egistes with its HA, PFA, o CFA accoding to the level of movement. Thus, the egistation costs ae significantly educed. The paging scheme in Combinatoial Mobile IP is diffeent fom that in cellula netwoks since paging does not incu the paging stom in RA. The paging costs ae also educed since paging is esticted within PA. Moeove, paging A PA is identified by its CFA and PFA IP Addesses. A PAI is constucted by appending its PFA IP Addess to its CFA IP Addess. As a netwok pefix distinguishes a netwok, a PAI is used fo identifying a PA in a paticula RA. In this way, each PA is uniquely identified by using a small amount of bandwidth. PAI extension is shown in figue 2. PAIs ae distibuted by Agent Advetisements with a PAI extension. Theefoe, MNs detect thei PA by eceiving Agent Advetisements. (a) When a CFA eceives packets fom the HA sent to an idle MN, it sends Paging Requests to all PFAs in its RA. (b) All PFAs will not elay Paging Requests to all MNs in thei PAs. Befoe elaying Paging Requests to thei MNs, PFAs seach thei visito lists to find out the MN in idle mode. Only the PFA which has the MN s home addess in its visito lists will send Paging Requests to its PA. (c) When a MN finds its home addess in the Paging Request, the MN sends a Paging Reply to its PFA. The MN changes its mode to active and stats its active time. (d) When the PFA eceives the Paging Reply, it sends a Regional Registation Request to its CFA. (e) The CFA sends back a Regional Registation Reply to the PFA. (f) The PFA sends a Paging Reply to its CFA. Paging pocedue is shown in figue Registation In Mobile IP, egistation does not guaantee a signaling delay when a MN is emote fom its HA. In addition, a MN tigges egistation wheneve it moves fom one FA to anothe FA. In Combinatoial Mobile IP, egistation in the FN is elaboately contolled by using a CFA cae-of addess in a RA, and egistation costs ae educed compaed to Mobile IP. Afte eceiving a egistation eply, a MN and a FA enew the MN s status by setting the MN s mode to active mode and stating the active time.

5 COMBINATORIAL MOBILE IP 3 Figue 3. Call flow of paging. Figue. Call flow of the egional egistation. Figue. Call flow of the global egistation. Registation equests and egistation eplies ae involved in egistation pocedues. The global egistation pocedue is as follows when a MN initially visits a RA. (a) A MN sends a Global Registation Request to the PFA in its PA. (b) The PFA pocesses the Global Registation Request and elays the Global Registation Request to its CFA. (c) The CFA pocesses the Global Registation Request and elays the Global Registation Request to the HA. (d) The HA sends a Global Registation Reply to the CFA to accept o eject the Global Registation Request. (e) The CFA elays the Global Registation Reply to the PFA. (f) The PFA pocesses the Global Registation Reply and elays it to the MN to acknowledge the esult of the Global Registation Request. The global egistation pocedue is illustated in figue. Though the egistation pocedue equies two moe steps than that on Mobile IP, it guaantees the eduction of egistation costs in oveall egistation pocedues. The egional egistation pocedue when an active MN moves fom one PA to anothe PA without changing its RA is as follows. Figue. Call flow of the local egistation. (a) A MN sends a Regional Registation Request to the PFA in its PA. (b) The PFA pocesses the Regional Registation Request and elays the Regional Registation Request to its CFA. (c) The CFA sends a Regional Registation Reply to the PFA. (d) The PFA pocesses the Regional Registation Reply and elays it to the MN. The egional egistation pocedue is illustated in figue. The local egistation pocedue when an idle MN moves fom one PA to anothe PA without changing its RA is as follows. (a) A MN sends a Local Registation Request to the PFA in its PA. (b) The PFA sends a Local Registation Reply to the MN. The local egistation pocedue is illustated in figue. When a MN moves between PAs in idle mode, the egistation pocedue is simplified since the MN only egistes with its PFA. In ode to suppot the authentication pocess, Mobile IP contol messages contain Mobile Home Authentication (32),

6 3 T. CHOI ET AL. Mobile Foeign Authentication (33), and Foeign Home Authentication (3) [0]. In Combinatoial Mobile IP, Mobile Foeign Authentication will be used between the MN and the PFA. Theefoe, PFA and CFA need an authentication extension in Mobile IP contol messages. Foeign Foeign Authentication must be defined to suppot a mobility secuity association fo mobile entities. In Combinatoial Mobile IP, egistation pocedues occu when: An idle MN detects that it has moved to a new PA in the same RA, a local egistation pocedue follows. An active MN detects that it has moved to a new PA in the same RA, a egional egistation pocedue follows. A MN detects that it has moved to a new RA, a global egistation pocedue follows. A MN s egistation lifetime is about to expie. A MN detects that its PFA o CFA has ebooted. A MN is paged, a egional egistation pocedue follows. An idle MN is about to tansmit data..3. Movement detection In Mobile IP [0], two mechanisms ae povided fo movement detection. They use the Lifetime field in the Agent Advetisement and netwok pefixes. Howeve, the movement detection of Mobile IP does not suppot the level of movement. In Combinatoial Mobile IP, PAI extension is used to distinguish the level of movement. Movement detection algoithms Movement detection by the Advetisement Lifetime Step. A MN eceives an Agent Advetisement fom agents. Step 2. The MN pocesses the Agent Advetisement and keeps the Advetisement Lifetime. Step 3. If the MN fails to eceive anothe Agent Advetisement fom the same agent within the specified Advetisement Lifetime, go to step. Othewise, go to step. Step. If the MN has peviously eceived an Agent Advetisement fom anothe agent fo which the Advetisement Lifetime has not yet expied, go to step. Othewise, the MN sends an Agent Solicitation, and go to step. Step. If a new PAI is diffeent fom the cuent PAI, go to step. Othewise, go to step. Step. If the IP Addess of CFA in the new PAI is diffeent fom that in the cuent PAI, the MN assumes that it moves fom one RA to anothe RA and the global egistation pocedue occus. Othewise, go to step 7. Step 7. The MN assumes that it moves fom one PA to anothe PA within the same RA and local o egional egistation pocedue occus accoding to idle o active mode, espectively. Movement detection by the netwok pefixes Step. A MN eceives an Agent Advetisement fom agents. Step 2. The MN pocesses the Agent Advetisement and obtains the netwok pefix. Step 3. If a new PAI is diffeent fom the cuent PAI, go to step. Othewise, go to step. Step. If the IP Addess of CFA in the new PAI is diffeent fom that in the cuent PAI, the MN assumes that it moves fom one RA to anothe RA and the global egistation pocedue occus. Othewise, go to step. Step. The MN assumes that it moves fom one PA to anothe PA within the same RA and local o egional egistation pocedue occus accoding to idle o active mode, espectively... Data handling Step. When a HA eceives data destined to a MN, it detemines whethe the MN is in the HN. Step 2. If the MN is in the HN, the HA simply fowads the data to the MN. If the MN is in the FN, go to step 3. Step 3. The HA fowads the data to the egisteed CFA. Step. When the CFA eceives the data, it seaches its location database. If the MN is in active mode, incoming data ae sent to the MN though its PFA. If the MN is in idle mode, go to step. Step. The CFA pages all PFAs in its RA and then the PFAs seach thei visito lists. Step. If any PFA identifies the MN, the PFA pages all MNs in its PA. When the MN that is the destination of data eceives a Paging Request fom the PFA, it eplies to the PFA. The MN activates its active time and evets to active mode. Step 7. Afte eceiving a Paging Reply, the PFA egistes the MN with its CFA. Step 8. Afte finishing the egistation pocedue, the CFA sends the data to the MN though its PFA.. Pefomance analysis In cellula netwoks, paging taffic, which aises in all cells of the RA, is popotional to the numbe of mobile teminating calls diected to all subscibes in the RA, and location update taffic, which aises only in bode cells of the RA, is popotional to the numbe of subscibes cossing the RA bode in the paticula cell []. Since egistation taffic is elated with the cell cossing ate, it is impotant to find a ealistic cell stuctue. In [3], a andom walk on a connected gaph model is used to analyze the netwok pefomance of cellula netwoks. Since the netwok model is not assumed to have any stuctued topology o geomety, it is moe ealistic

7 COMBINATORIAL MOBILE IP 37 than the othe netwok models such as a hexagonal o squae aea model. Theefoe we will take the modelling technique fom [3] and apply it to analyze the signaling costs of Combinatoial Mobile IP. In this section, we pove that Combinatoial Mobile IP is obust fo the distance between a HA and a FA, the efesh ate of egistation, and paging costs. Since Combinatoial Mobile IP is obust fo the distance between a HA and a FA, a MN is fee to move egadless of the distance between a HA and a FA and the data can be tansmitted without the latency due to the egistation when the MN moves within a RA. Although a MN efeshes its location fequently, the data can be tansmitted quickly and coectly. The incement of the efesh ate of egistation lagely inceases signaling oveheads in the case of Mobile IP, while in the case of Combinatoial Mobile IP signaling oveheads is not vey affected by that. Thus, Combinatoial Mobile IP is scalable fo the size of RA and the movement of MNs. As the numbe of MNs gows, the signaling costs will incease. Thus the signaling costs ae the key issues of scalability... Netwok model A numbe of mobility management schemes depend on a fixed shape to model a wieless netwok. Hexagonal o squae shape aeas ae widely used in netwok models. Howeve, those netwok models ae athe unealistic and have theoetical values. We will have no assumptions fo the cellula topology but the existence of cells. In ou model, each PA is epesented with a node V and the inteconnection between PAs is epesented with an edge E. Since cell shapes ae vaying and the numbe of neighbo is andomly decided, a connected gaph model is moe ealistic and applicable to a netwok of the eal wold. This connected gaph model is a bounded-degee G = (V, E), wheen = V is the numbe of PAs and M = E is the numbe of paths..2. Mobility model A andom walk model is applied to detemine the connectivity of gaphs [9]. A andom walk on a connected and undiected gaph is a stochastic pocess which occus in a sequence of discete steps [9,2]. If G = (V, E) is a connected, nonbipatite, undiected gaph whee V =Nand E =M, it induces a Makov chain M G as follows [9]: the states of M G ae the nodes of G and fo any two nodes, i, j V,the tansition pobability between i and j is as follows: if (i, j) E, P i,j = d(i) 0 othewise, whee d(i) is the degee of node i. The Makov chain, M G, is ieducible, finite and apeiodic [3]. Theefoe, thee is a unique stationay pobability distibution vecto π such that, fo i N, π i > 0. If the tansition pobability distibution is known, the location pobability of a use in any PA can be calculated by using the andom walk model. The aival pocess is assumed to be Poisson with mean ate λ. Thus, the inte-aival time is exponentially distibuted with this ate. The sevice time of a data packet is assumed to be exponentially distibuted with ate µ..3. Signaling costs We will analyze signaling costs of Mobile IP, Mobile IP Regional Registation, P-MIP and Combinatoial Mobile IP, and then compae one anothe. An analysis is done fo a MN which is located in a FN since signaling costs in a HN ae the same fo Mobile IP, Mobile IP Regional Registation, P-MIP and Combinatoial Mobile IP. Following is the notations fo analysis: P j,i is the tansition pobability fom PA j to PA i. C (j, i) is the egistation cost when a MN moves fom PA j to PA i. C p (i) is the paging cost in PA i. i is the location pobability of a use in PA i. α is the atio of active time to the total time. λ is the incoming data ate fo a MN and the paging ate fo amn. R is the efesh ate that a MN enews its location. t i is the time duation that a MN stays in a PA. C FA-HA C FA-GFA C GFA-HA C PFA-CFA C CFA-HA is the egistation cost between a FA and a HA. is the egistation cost between a FA and a GFA. is the egistation cost between a GFA and a HA. is the egistation cost between a PFA and a CFA. is the egistation cost between a CFA and a HA..3.. Mobile IP In Mobile IP, signaling costs consist of only egistation costs, such that the fist tem is the aveage egistation costs with a new FA and the second tem is the aveage egistation costs with MN s HA in equation (). Signaling costs in Mobile IP depend on the distance between the FA and the HA. Theefoe, if the distance between the FA and the HA is fixed, signaling costs ae constant egadless of the mobility and call aival patten. C MIP = N N i= j=,j i j P j,i C (j, i)+ i C FA-HA } R t i. ().3.2. Mobile IP Regional Registation In Mobile IP Regional Registation [], signaling costs only depend on egistation costs like Mobile IP, but it is deployed on a hieachical achitectue. Thee ae two independent events as follows: (i) the fist egistation in a new RA, and (ii) the subsequent egistation within the same RA.

8 38 T. CHOI ET AL. The fist egistation costs in a new RA ae deived in equation (2). C init = j C (k, j) + C FA-GFA + C GFA-HA }, (2) whee PA k and PA j ae located in diffeent RAs. The subsequent egistation costs ae deived in equation (3). The fist tem is the egistation costs fom a MN to its FA and the second tem is the egistation costs fom the FA to its GFA in equation (3): N N } C REG = j P j,i C (j, i) + i C FA-GFA R t i. i= j=,j i.3.3. P-MIP In P-MIP [], signaling costs consist of egistation and paging costs. In active mode, P-MIP opeates the same as Mobile IP. In idle mode, paging is used fo locating uses in PAs. PAs in P-MIP consist of two o moe netwoks. Accodingly, PAs in P-MIP can be epesented as RAs in ou pape. The fist egistation costs in a new RA ae given by C init = j C (k, j) + C FA-HA }, () whee PA k and PA j ae located in diffeent RAs. The fist tem in equation () is the aveage egistation costsfoamn smovementfompak to PA j. The second tem in equation () is the aveage egistation costs fom a FA to MN s HA. The subsequent signaling costs in active mode at a new PA within the same RA ae } N C active = j=,j i j P j,i C (j, i) + i C FA-HA (3) R t i. () The fist tem in equation () is the aveage egistation costsfoamn smovementfompaj to PA i in active mode. The second tem in equation () is the egistation costs fom afatomn shaatpai. The subsequent signaling costs in idle mode at a new PA within the same RA ae N C idle = i λt i we[pagingcost], () j=,j i whee w is the numbe of PAs since paging is boadcast to all the PAs in the RA. Note that the signaling costs in idle mode only consist of paging costs in equation (). If we assume that MNs ae equally distibuted in a RA, the paging costs become constant fo this model: E[PagingCost] =C p (i) = C p. (7) Theefoe, the subsequent egistation costs ae deived in equation (8): N } C P-MIP = αcactive + ( α)c idle. (8) i=.3.. Combinatoial Mobile IP Signaling costs in Combinatoial Mobile IP consist of egistation and paging costs. Thee ae thee independent events as follows: (i) the fist egistation in a new RA, (ii) the subsequent egistation in active mode at a new PA within the same RA, and (iii) the subsequent egistation in idle mode at a new PA within the same RA. The fist egistation costs in a new RA ae given by C init = j C (k, j) + C PFA-CFA + C CFA-HA }, (9) whee PA k and PA j ae located in diffeent RAs. The fist tem in equation (9) is the aveage egistation costsfoamn smovementfompak to PA j and the second tem is the aveage egistation costs fom a PFA to its CFA. The thid tem in equation (9) is the egistation costs fom the CFA to MN s HA, and it is constant if the distance between the CFA and the HA is detemined. Note that this egistation cost only happens when a MN moves into a new RA whethe it is in idle o active mode. The subsequent egistation costs in active mode at a new PA within the same RA ae } N C active = j=,j i j P j,i C (j, i) + i C PFA-CFA R t i. (0) The fist tem in equation (0) is the aveage egistation costsfoamn smovementfompaj to PA i in active mode. The second tem in equation (0) is the egistation costs fom a PFA to its CFA at PA i. The subsequent egistation costs in idle mode at a new PA within the same RA ae N C idle = j P j,i C (j, i)+ i λt i E[PagingCost]. () j=,j i The fist tem in equation () is the aveage egistation costsfoamn smovementfompaj to PA i in idle mode. The second tem in equation () is the aveage paging cost in PA i. If we assume that MNs ae equally distibuted in a RA, the paging costs become constant fo this model: E[PagingCost] =C p (i) = C p. (2) Theefoe, the subsequent egistation costs ae deived in equation (3): C C-MIP = N } αcactive + ( α)c idle. (3) i=.. Netwok model example In ode to calculate the signaling costs fo Mobile IP, Mobile IP Regional Registation, P-MIP and Combinatoial Mobile IP, the netwok model example is pesented in figue 7.

9 COMBINATORIAL MOBILE IP 39 Table Paametes fo analysis. Paametes Values α % λ (/sec) [] R /30 (/sec) [] t i 00 (sec) [3] Figue 7. Netwok model example. Table Tansition pobability matix and steady-state pobabilities. PAs Tansition pobability Steady-state PA PA 2 PA 3 PA PA PA PA 7 PA 8 pobability PA PA PA PA PA PA PA PA Note that the nodes and edges epesent PAs and the inteconnections between PAs, espectively. The tansition pobability depends on the degee of nodes such that if j Ɣ(i), P i,j = d(i) + () 0 othewise, whee Ɣ(i) is the neighboing nodes of i. If the tansition pobability is known in equation (), thee exists a unique steady-state pobability distibution vecto = (, 2,..., N ), such that i > 0fo i N. The steady-state pobability vecto can be obtained by solving = P fo [8]. Fom ou netwok model example, the tansition pobability matix and the steady-state pobability vecto ae calculated in table... Signaling costs evaluation To simplify the evaluation of signaling costs fo Mobile IP, Mobile IP Regional Registation, P-MIP and Combinatoial Mobile IP, it is assumed that a MN has egisteed with its HA peviously. The initial egistation costs of Mobile IP Regional Registation, P-MIP and Combinatoial Mobile IP, i.e., equations (2), () and (9), will be excluded in evaluation. Theefoe, equations (), (3), (8) and (3) will be used fo analyzing signaling costs fo Mobile IP, Mobile IP Re- Figue 8. Total signaling costs accoding to the distance fom the HA. gional Registation, P-MIP and Combinatoial Mobile IP, espectively. The paametes used fo the analysis ae tabulated in table. Figue 8 shows how the total signaling costs ae affected by the distance between HA and FA when C p /C is fixed at. As a MN is distant fom its HA, signaling costs ae much affected in Mobile IP. Signaling costs incease linealy as the distance between the HA and the FA inceases in figue 8. Since Mobile IP Regional Registation and Combinatoial Mobile IP sepaate global egistation fom egional egistation, egistation costs do not popagate to its HA while a MN is in the same RA. Signaling costs in Mobile IP Regional Registation and Combinatoial Mobile IP ae steady and do not change in the same RA. The benefits of signaling costs in Combinatoial Mobile IP esult fom the sepaation of local egistation and egional egistation and the use of paging. If we conside that mico-mobility is moe widespead than maco-mobility, Combinatoial Mobile IP deceases unnecessay signaling costs. Figue 9 shows how the total signaling costs ae affected by the incement of the efesh ate of the local egistation. As the efesh ate of the local egistation inceases, the total signaling costs ae much influenced in the cases of Mobile IP and Mobile IP Regional Registation. Howeve, Combinatoial Mobile IP is much moe steady than the othe potocols. Figue 9 indicates the impotance of the sepaation of the level of movement and the MN modes. Figue 0 shows that P-MIP and Combinatoial Mobile IP function the same as Mobile IP and Mobile IP Regional

10 320 T. CHOI ET AL. Registation, espectively, when the ate of active MNs appoaches to. P-MIP and Combinatoial Mobile IP educe the total signaling costs by sepaating the active and idle modes of MNs. If we assume that MNs ae usually in idle mode, Combinatoial Mobile IP is moe scalable than Mobile IP o Mobile IP Regional Registation. Figue shows how C p /C affects the total signaling costs. As the atio of paging costs to egistation costs inceases, the total signaling costs incease linealy in the cases of P-MIP and Combinatoial Mobile IP, and the total signaling costs of Mobile IP and Mobile IP Regional Registation ae constant. Howeve, P-MIP is much moe affected by the incement of paging costs than Combinatoial Mobile IP.. Conclusion Figue 9. Total signaling costs accoding to the weight of the efesh ate. Figue 0. Total signaling costs accoding to the ate of active MNs. Figue. Total signaling costs accoding to the ate of C p /C. In ode to calculate the total signaling costs, we have used a andom walk model on a connected gaph. Since the total signaling costs contain the lage potions of egistation costs, it is impotant to calculate egistation costs coectly fo optimizing the total egistation costs. Registation costs lagely depend on the cell cossing ate, and the cell cossing ate depends on the tansition pobabilities. The tansition pobabilities depend on cell neighbohoods. Most netwok models use a fixed shape such as a squae o a hexagon. A fixed shape model does not coectly simulate the eal wold netwok. A andom walk model does not define the numbe of cell neighbos but has an abitay numbe of cell neighbos. Theefoe, it expesses the eal wold netwok moe coectly than the othe netwok models. We have poposed a new efficient mobility management scheme fo Mobile IP using local egistation and minimized paging. In implementing mobility management, it is impotant to conside the chaacteistics of the netwok. The Intenet is diffeent fom telephone netwoks fom the stat. Theefoe, Mobile IP and cellula netwoks ae based on diffeent systems such as the Intenet and telephone netwok, espectively. Paging and location updates ae two impotant components fo mobility management fo cellula netwoks. In applying paging to Mobile IP, it is impotant to keep in mind that paging and location updates have a complementay natue. If location update costs ae inceased, paging costs ae educed. On the othe hand, if location update costs ae deceased, paging costs incease. In ode to optimize signaling costs, the tadeoff between paging and location updates should be studied caefully. Theefoe, we have studied how egistation costs and paging costs have influenced the total signaling costs. We have shown that the total signaling costs in Combinatoial Mobile IP ae less than those in Mobile IP and Mobile IP Regional Registation. Mobile IP is suitable fo macomobility, but it teats mico-mobility and maco-mobility in the same way. Theefoe, the total signaling costs in Mobile IP ae enomous if the distance between the HA and FA is lage. Mobile IP Regional Registation sepaates micomobility fom maco-mobility but it teats active and idle

11 COMBINATORIAL MOBILE IP 32 modes in the same way. Combinatoial Mobile IP sepaates not only mico-mobility fom maco-mobility, but also active mode fom idle mode. Theefoe, it educes the total signaling costs efficiently. Refeences [] A. Campbell, J. Gomez, C.-Y. Wan, S. Kim, Z. Tuanyi and A. Valko, Cellula IP, Intenet Daft (2000), wok in pogess, daft-ietfmobileip-cellulaip-00.txt [2] A.T. Campbell and J. Gomez-Castellanos, IP mico-mobility potocols, ACM SIGMOBILE Mobile Computing and Communications Review (MC2R) () (2000) 3. [3] S.K. Das and S.K. Sen, A new location update stategy fo cellula netwoks and its implementation using a genetic algoithm, in: Poceedings of the 3d Annual ACM/IEEE Intenational Confeence on Mobile Computing and Netwoking (MOBICOM), Budapest, Hungay (997) pp [] A. Gamst, Application of gaph theoetical methods to GSM adio netwok planning, in: Poceedings of IEEE Intenational Symposium on Cicuits and Systems (June 99) pp [] E. Gustafsson, A. Jonsson and C. Pekins, Mobile IPv egional egistation, Intenet Daft (200), wok in pogess, daft-ietfmobileip-eg-tunnel-0.txt [] H. Haveinet and J. Malinen, Mobile IP egional paging, Intenet Daft (2000), wok in pogess, daft-haveinen-mobileip-egpaging-00.txt [7] G. Kiby, Locating the use, Communication Intenational (Octobe 99). [8] L. Kleinock, Queueing Systems: Theoy, Vol. (Wiley, 97). [9] R. Motwani and P. Raghavan, Randomized Algoithms (Cambidge Univesity Pess, 99). [0] C. Pekins, IP mobility suppot, Intenet RFC 2002 (99). [] R. Ramjee, T.L. Pota, S. Thuel, K. Vaadhan and S.Y. Wang, HAWAII: A domain-based appoach fo suppoting mobility in wide-aea wieless netwoks, in: Poceedings of IEEE Intenational Confeence on Netwok Potocols (ICNP 99), Toonto, Canada (999) pp [2] S. Ross, Stochastic Pocess (Wiley, 983). [3] S.K. Sen, A. Bhattachaya and S.K. Das, A selective location update stategy fo PCS uses, ACM/Baltze Wieless Netwoks () (999) [] S. Subamanian and S. Madhavapeddy, System patitioning in a cellula netwok, in: Poceedings of th IEEE Vehicula Technology Confeence, Atlanta, CA (99) pp [] X. Zhang, J. Castellanos, A. Campbell, K. Sawada and M. Bay, P-MIP: Minimal paging extensions fo mobile IP, Intenet Daft (2000), wok in pogess, daft-zhang-pmip-00.txt Taehwan Choi eceived the B.S. degee in mathematics fom Sogang Univesity, Seoul, Koea, in 998. He had been woking fo POSDATA fom 998 to He eceived the M.S degee in compute science fom Yonsei Univesity, Seoul, Koea, in He is cuently the eseach enginee of CDMA Handsets Laboatoy of Telecommunication Equipment Handset Company at LG Electonics in Seoul, Koea. His cuent eseach inteests focused on Mobility Management of Wieless Communications such as Mobile IP, Wieless LAN, SIP, CDMA, and IMT ctlight@emeald.yonsei.ac.k Laeyoung Kim eceived the B.S. degee in compute science fom Ewha Womans Univesity, Seoul, Koea, in 99 and the M.S. degee in compute science fom Yonsei Univesity, Seoul, Koea, in Since 2002 she has been a Ph.D. candidate in compute science at Yonsei Univesity. Fom 99 to 2000 she woked at Samsung Electonics. He eseach inteests cove Mobile IP, optical netwoks, and wieless netwoks. leon@emeald.yonsei.ac.k Jeongeun Nah eceived the B.S. degee in compute science fom Yonsei Univesity, Seoul, Koea, in 988, and the M.S. degee in compute science fom Yonsei Univesity, in 990. She had woked fo Accentue and IBM Consulting Goup as a consultant of Business Pocess Reengineeing fom 990 to 999. Since 999 she has been a Ph.D. student in compute science at Yonsei Univesity. He eseach inteests include Mobile IP, infomation secuity, and system and softwae equiements engineeing. jenah@yonsei.ac.k Jooseok Song eceived the B.S degee in electical engineeing fom Seoul National Univesity, Seoul, Koea, in 97, and the M.S. degee in electical engineeing fom KAIST, Koea, in 979. In 988, he eceived the Ph.D. degee in compute science fom Univesity of Califonia at Bekeley. He had been an Assistant Pofesso of Naval Postgaduate School fom 988 to 989. He is cuently a Pofesso of Compute Science at Yonsei Univesity, Seoul, Koea. His eseach inteests include mobile IP, cyptogaphy, infomation secuity, wieless communication, and optical netwok. jssong@emeald.yonsei.ac.k