Bond Unversty epublctons@bond Informton Technology ppers Bond Busness School Aprl 2004 An Optml Method for Usng Multple Gtewys n ellulr IP Networks Zheng d Wu Bond Unversty, Zheng_D_Wu@bond.edu.u Follow ths nd ddtonl works t: http://epublctons.bond.edu.u/nfotech_pubs Recommended tton Zheng d Wu. (2004) "An Optml Method for Usng Multple Gtewys n ellulr IP Networks".Apr. 2004. http://epublctons.bond.edu.u/nfotech_pubs/23 Ths onference Pper s brought to you by the Bond Busness School t epublctons@bond. It hs been ccepted for ncluson n Informton Technology ppers by n uthorzed dmnstrtor of epublctons@bond. For more nformton, plese contct Bond Unversty's Repostory oordntor.
An Optml Method for Usng Multple Gtewys n ellulr IP Networks Z. D. Wu School of Informton Technology, Bond Unversty Gold ost QLD 4226, Austrl Phone: 61 755 953311; Fx: 61 755 953320; E-ml: wz@bond.edu.u Abstrct ellulr IP requres tht moble host be usng exctly one gtewy to the Internet bckbone wth Moble IP t tme. When multply gtewys re used n cellulr IP network, the optml desgn for the multple domns s needed. In ths pper n nlytcl model s presented for the performnce nlyss of cellulr IPv6 network wth multple gtewys. Bsed on ths model, n optml system desgn cn be theoretclly found n terms of the network sze, trffc lod, user populton, user moblty nd routng lgorthm for IP pckets n domn. onsequently, n lgorthm s proposed for brekng lrge cellulr IP domn nto two smll domns, whch cn be esly used for the system selecton n prctce. Fnlly, some numercl results re demonstrted for number of typcl cses presented n the lgorthm. 1. Introducton Moble IP llows moble node to chnge ts locton wthout need to restrt ts pplctons or termnte ny on gong communcton. It represents smple nd sclble globl moblty soluton but lcks the support for fst hndoff control nd pgng found n cellulr telephone networks. In contrst, 2G nd 3G cellulr systems offer semless moblty mngement but bult on complex nd costly connecton-orented networkng nfrstructure. As soluton to these ssues, the concept of cellulr IP nd lter cellulr IPv6 were proposed to provde semless moblty support n lmted geogrphcl re. The specfcton of ellulr IPv6 hs been drfted by the IETF n [5][6], on whch ths pper s bsed. Sgnfcnt reserch n the feld of cellulr IP hs been publshed over the lst severl yers. The works mnly del wth the desgn, mplementton nd nlyss of cellulr IP protocols, ncludng routng, hndoff, nd pgng performnce wth sngle gtewy [1]-[4]. ellulr IP requres tht moble host be usng exctly one gtewy to the Internet bckbone wth Moble IP t tme [5]. It s recognsed tht f the sze (or the number of nodes) of domn network s lrge, ts gtewy potentlly becomes bottleneck of the system performnce s ll the IP pckets from moble hosts n the domn to the Internet, or vce vers, must go through the gtewy. Thus, cellulr IP network my be equpped wth multple gtewys to reduce the sze of ech domn. However, when the sze of domn network s smll, the frequency of locton updte for the home regstrton wth moble host wll be ncresed, snce the moble host wll hve hgher probblty to move out of the smll domn. As result, t becomes prctcl ssue to fnd out the optml sze of the cellulr IP domn, where the system, ncludng the gtewy, cn cheve the best performnce. In ths pper n nlytcl model s presented for the performnce nlyss of cellulr IPv6 network wth multple gtewys. Bsed on ths model, n optml system desgn cn be theoretclly found n terms of the network sze, trffc lod, user populton, user moblty nd routng lgorthm for IP pckets n domn. onsequently, n lgorthm s proposed for brekng lrge cellulr IP domn nto two smll domns, whch cn be esly used for the system selecton n prctce. Fnlly, some numercl results wll be demonstrted for number of typcl cses presented n the lgorthm. 2. System Descrptons
In ths secton cellulr IPv6 wth multple gtewys wll be brefly descrbed nd the detls of the protocol re specfed n [5]. domn 1 Internet w th M oble IP GW GW GW MH domn 2 Node GW: Gtewy MH: Moble Host Home Agent domn n ellulr IP N etw ork Fgure1. ellulr IPv6 network wth multple gtewys As shown n Fg. 1, cellulr IPv6 network conssts of severl domns nd ech domn network ttches to the Internet through one gtewy. The domn network s composed of nterconnected cellulr IP nodes (or bse sttons), whch my represent rel bse sttons n cellulr telephone systems, Access-Ponts used n wreless LANs or wred LAN swtches. A user of moble hosts (MHs) trvellng wthn the network cn dynmclly get wreless connecton to node of the cellulr network so s to send nd receve IP pckets. Dfferent from the Internet cellulr IP uses routecche nd pgng-cche, equpped n the cellulr IP nodes, for routng pckets to/from MHs. In order for ech node to select ts uplnk neghbour, the Uplnk Neghbour Selecton lgorthm s proposed n [5]. Smlr to Moble IPv6, when n MH enters new cellulr IP domn, t must regster wth ts home gent (HA). The regstered cre-of-ddress (oa) s the ddress of the new gtewy. Besdes, the MH must mntn route pths for tself. The MH perodclly sends route-updte or pgng updte pckets to the gtewy. The ntermedte nodes tht receve the pckets updte ther cches nd forwrd the pckets to the gtewy. The gtewy thus uses the reverse pth cches to forwrd IP pckets to the MH from the Internet. ellulr IP llows MHs to enter ether ctve stte or dle stte. If n MH s trnsmttng or recevng IP pckets t s n ctve stte. If the MN does not send or receve ny pcket n pre-defned tme ntervl, t enters n dle stte, n whch t only mntns ts pgng-cches for pssve connecton. By usng dle sttes of MHs ther power consumpton cn be reduced. Idle MHs crossng cell boundres (or cellulr node boundres) wthn Pgng Are (PA), whch conssts of group of cells, do not need to trnsmt control pckets to updte ther locton wth the HA. However, ctve MHs must send loctonupdte pckets whenever they move out of cell rther thn PA. When n IP pcket rrves t gtewy from correspondng node (N), the gtewy serches for ts destned MH n the pgng-cche. If t s found n the cche, the pcket (or pgng pcket) s sent to one of the down-lnk neghbours specfed n the pgngcche. Otherwse, the gtewy brodcsts the pgng pcket to overll down-lnk neghbours. After recevng the pgng pcket, the MH mmedtely sends route-updte pcket to the gtewy for cretng ts down-lnk pth nd enters ctve stte. As result, cellulr IP nodes re ble to route pckets to the correct locton of the MH. Trffc between MHs wth wreless ccess IP network s mportnt consderton for the pplcton t cellulr IP protocol. In order to optmze the network performnce, route optmzton opton s proposed for both cellulr IP nd cellulr IPv6 n [6]. By usng ths mechnsm, two MHs locted n the sme domn network cn exchnge IP pckets drectly wthout contctng the gtewy nd ther home gents. 3. Model nd Optmzton 3.1. Modellng Assume cellulr IPv6 network conssts of N nodes nd G domns, where ech domn hs K modes.
Thus, G N / K = lso represents the number of gtewys equpped n the network. Suppose tht moble hosts my trvel between N nodes rndomly. It mens tht ech MH my vst node more thn once nd lso my move bck nd forth between two modes. Snce ctve MHs nd dle MHs hve dfferent rules nd mechnsms for ther locton trckng s dscussed n the lst secton, ther locton trckng re modelled seprtely. Assume movement occurs whenever n ctve MH moves out of node. Therefore, the movements of the MH cn be modelled s dscrete system [8]. At moment 1, the MH my resde n cell 1, 2,, N, where cell represents the coverge of cellulr IP node n whch t cn communctes wth MHs. At moment 2, the MH my move to ny of the other N-1 cells. Assumng tht the MN wll move out to the other N-1 cells wth probblty 1/(N-1). Thus, the probblty of n ctve MH movng out of one domn wth sze k t moment m s m 2 m N k k 1 P =, N 1 N 1 where 2 m < (1) m It notes tht P lso represents the probblty of the MN performng home regstrton t moment m, where m s rndom vrble. Thus, the expectton of M cn be expressed s 1 [ ] = m N E M mp = 1 (2) = N k m 2 The verge locton updte cost conssts of two prts, the route updte cost wthn the domn nd the home regstrton cost when the MH moves out the domn. Assume the verge tme n MH stys n cell of ech domn before mkng movement sτ. Thus, the verge locton updte cost cn be obtned by H LU = E [ M ] τ τ (3) where nd H re the route updte cost nd the home regstrton cost for the ctve MH respectvely. The detls of evlutng nd H wll be gven n the next subsecton. ellulr IP llows dle MHs to rom lrge geogrphc re wthout the need to trnsmt locton updte pckets t cell borders, nsted, t the border of PAs. Assume ech PA hs J nodes. Smlr to dervng Equton (1), the probblty of n dle MH movng out of PA wthn domn wth sze k t moment x s x 2 x k J J 1 P =, k 1 k 1 where 2 x < (4) x Thus, P lso represents the probblty of n dle MH performng pgng-updte t moment x. Further, t cn be shown tht the expectton of rndom vrble X s 1 [ ] = x k E x xp = 1 (5) = k J x 2 As result, the verge locton updte cost for n dle MH s expressed s H = (6) E [ X ] τ E [ M ]τ LU where s the pgng-updte cost for the dle MH n the domn nd H s ts home regstrton cost. The clculton of these two costs wll be lso dscussed n the next subsecton. 3.2 Sgnllng ost Functon
The sgnllng cost n cellulr IP network dels wth the cost of locton updte nd pcket delvery. The performnce metrc of the network s evluted bsed on the totl sgnllng cot n ths pper. 3.2.1 Locton Updte ost For n ctve MH ts locton cost conssts of two prts, ndh, s mentoned before. The cost of route-updte for the ctve MH,, s due to ts locton chnge from one cell to nother wthn domn. ncludes the trnsmsson cost for routeupdte pcket delvery nd the processng cost for route updte t the nodes t trvelled through. Thus, my be evluted s below: = ϕ ϕ ( µ l ω) (7) bs ho where ϕbs s the processng cost t bse stton (or cellulr IP node) through whch the ctve MH s permtted to ccess the cellulr network; ϕ ho s the processng cost of hndoff when the ctve MH moves from one node to nother node. Let l bg be the verge dstnce between the bse stton the ctve MH currently ttched nd the gtewy, through whch the MH delvers IP pckets to the Internet. The dstnce s mesured n terms of the number of hops between them. Assume tht the trnsmsson cost s proportonl to the dstnce between the source nd the destnton nd the proportonlty constnt s u. Snce the trnsmsson cost of the wreless lnk s hgher thn tht of the wred lnk, t s ssumed tht the trnsmsson cost over the wreless lnk s ω tmes hgher thn the unt dstnce wre-lne trnsmsson cost. Therefore, the trnsmsson cost between the MH nd the gtewy s expressed s ( µ lbg ω) u n Equton (7), where µ 1 s used for djustng the cost of wred or wreless lnks on the pth between the bse stton nd the gtewy. When n ctve MH moves out of domn, t performs locton updte v ts home gent nd ths bg u cost s represented by below. = H ϕ ϕ ϕ 2l, whch s clculted s H m g h gh hu (8) where ϕ m s the processng cost t the MH for gettng new cre-of ddress; ϕ g nd ϕ h re the processng cost of locton updte for the home regstrton t the gtewy nd t the home gent respectvely. Smlrly, l gh represents the dstnce between the gtewy nd the home gent nd hu s the proportonlty constnt for the trnsmsson cost between the gtewy nd the home gent. The cost of pgng-updte for n dle MH wthn domn,, s due to ts locton chnge from one pgng re to nother. Usng the smlr method bove, cn be expressed s bs bg u = ϕ ( µ l ω) (9) It notes tht there s no cost for hndoff wth dle MH. Smlr to u, u s the proportonlty constnt for the trnsmsson cost between the dle MH nd the gtewy. When the dle MH moves out of domn, t lso performs locton updte v ts home gent nd ths cost s denoted s H, whch cn be further computed by H = H (10) Suppose n MH enters ctve stte or dle stte t tme wth probbltes p nd p respectvely, where p p = 1. Bse on Equtons (1) (10), the verge locton updte cost for the MH, LU, cn be obtned by LU = p p (11) LU LU
where LU nd LU were ntroduced n the lst subsecton. 3.2.2 Pcket Delvery ost The cost functon for pcket delvery from N to n MH n cellulr IP network cn be derved bsed on two cses, s shown s Fgure 2. MH HA N Node GW Internet GW Node N MH ellulr IP domn In se 1 the processng cost dels wth processng IP pckets t the gtewy nd the HA. The processng cost t the gtewy ncludes decpsulton of the tunnelled IP pckets from the HA, lookng up route nd pgng-cches nd checkng f there s n entry for the destned MH n the cches. The lod of the gtewy for processng nd routng pckets lso depends on the number of nodes, k, n the domn. If k s lrge, the complexty of route nd pgng cches look up n the gtewy s hgh nd thus, the system performnce s degrded. Snce the totl bndwdth of domn s lmted, f the trffc to the gtewy s hevy, the trnsmsson dely nd the number of retrnsmsson cnnot be bounded. Suppose the verge number of MHs n cell s S. The verge number of MHs n domn becomes ks. Further, the complexty of the gtewy cches lookup s proportonl to ks. Snce the route nd pgng cches lookup s smlr to route tble lookup, the complexty of MH entry lookup s proportonl to the logrthm of the length of the cches [9]. Therefore, the processng cost t gtewy s expressed s se 1 se 2 G PD = λξ k αsp βsp ) (13) ( Fgure 2: Two cses for IP pckets delvery from N to MH In se 1 every IP pcket destned for n MH s frst ntercepted by the home gent nd then tunnelled to the gtewy, through whch t s forwrded to the MH. The pcket delvery cost ncludes both trnsmsson nd processng. The trnsmsson cost n se 1 s expressed s T = l l µ l ω) (12) 1 ( ch hg gb where l ch s the dstnce between the N nd the HA; lhg s the dstnce between the HA nd the gtewy; lgb s the dstnce between the gtewy nd the bse-stton currently servng the MN; d d represents the proportonlty constnt for the trnsmsson cost n ths cse. where λ s the pcket rrvl rte for ech MH; α nd β re weghtng fctors of route-updte cche wth ctve MHs nd pgng-updte cche wth dle MH respectvely;ξ s constnt whch chrcterzes the bndwdth llocton cost t the gtewy. The lrger theξ s, the more negtve effects n MH experences due to not enough network bndwdth vlble. The processng cost functon t the HA my be smply defned s H = λϑ (14) PD where ϑ s pcket delvery processng cost constnt t the HA. As result, the pcket delvery cost n se 1 s gven by W = T G H PD out 1 PD PD (15) Suppose the route optmzton opton s employed n se 2, where the N cn send IP pckets to the MN drectly wthout the ssstnce of the HA snce both
the N nd MH re locted n the sme domn. onsder the topology of cellulr IP domn network s tree pproxmtely, where the gtewy plys role of the root. The lrgest pth from n MH to the gtewy s log b k, where b s the verge number of the network nterfces equpped n ech bse stton, through whch t communctes wth ts neghbours. Thus, the processng cost n se 2 my be obtned by W PD n = 2 log k ϕ (16) d b where ϕ c denotes the processng cost t crossover node; 2 log b k represents the dstnce between the N nd the MH v crossover node nd d s the proportonlty constnt for trnsmsson cost between them. The totl pcket delvery cost per unt tme for n MH,, s summed up s below. PD c ( k, λ, τ ) = ( k, λ, τ ) ( k 1, λ, τ ) (19) where λ nd τ re the verge pcket rrvl rte nd the verge resdence tme n cell for ll MH respectvely. Snce k s n nteger nd the cost functon s not contnuous functon of k, t s not pproprte to tke dervtve wth respect to k of the cost functon to get the mnmum. However, gven, the solutons to solvng the locl mnmum cn be obtned bsed on n tertve lgorthm s below: 1, f ( k = 2, λ, τ ) > 0 k opt ( λ, τ ) = mx { k : ( k, λ, τ )}, otherwse Once k opt s found out, the optml number of gtewys cn be determned by G opt N / kopt, where N s the totl number of nodes n the cellulr IP network. PD = p W ( 1 p ) W (17) n PD n n PD out 4. Algorthm where p n represents the probblty of both the N nd MH resde n the sme domn when they communcte wth ech other. Bsed on the bove nlyss, the verge sgnllng cost per tme unt for n MH,, cn be fnlly evluted by where = LU PD (18) LU ws gven n Secton 3.1. 3.3 Optmzton In order to cheve the optml system desgn for cellulr IPv6 network wth multple gtewys, n optmzton method s ntroduced n ths secton. The optml number of cellulr IP nodes n domn s defned s the vlue of k tht mnmzes the cost functon s gven n Equton (18). Smlr to the lgorthms ntroduced n [10] the cost dfference functon between the system wth k nd the system wth k-1 ( k 2) s derved s To fnd k opt n vrous stutons depends on the specfcton of mny prmeters s defned n the lst secton. Snce the computton for k opt s tedous work, n lterntve lgorthm for the optml system desgn s proposed n ths secton, whch cn be esly used n prctce. In order to fnd the optml number of gtewys for cellulr IPv6 network, one prctcl problem s tht when the sze (or trffc lod) of domn becomes lrge, the system desgner must decde f the lrge domn s broken nto two smll domns. In other words, t s necessry to fnd wy to mke decson between the two schemes, usng one lrge domn or two smll domns, so s to cheve the best system performnce. Ths s cn be cheved by decson lgorthm whch s proposed s the followngs. Suppose tht vector V r contns the vlue of ll of the system prmeters, such s N, k, J, λ, τ, l bg, ϕ bs nd the others, whch re defned for clcultng the cost functons n Equtons (1)-(18). Smlr to the nlyss n PS networks, the cll-to-moblty rto
(MR) s defned s the rto of the pcket rrvl rte to the moblty rte,.e., MR = λτ. The cost functon (18) my be rewrtten s r = f ( MR, V ). Thus, the verge sgnllng cost per tme unt for ech MH,, s functon of vrble MR gven the vlue of V r. Further, denote l rg e ( MR) nd smll (MR) s the cost functons of the lrge domn nd the two smll domns respectvely. Decson Algorthm: Specfy the vlues of V r For ech MR = r, = 1,2,..., I, nd r r < 1, clculte r L ( r ) = { l rg e ( r ) = 1,2,..., I.} nd r S ( r ) = { smll ( r ) = 1,2,... I.} ompre r L ( r ) wth r S ( r ) se 1: If r L ( r ) > r S ( r ) for ll r hoose the desgn wth two smll domns. se 2: If r L ( r ) r S ( r ) hoose the desgn wth lrge domn. se 3: If r L ( r ) > r S ( r ) for r, = 1,2,..., R nd r L ( r ) r S ( r ) for r, = R 1, R 2,..., I The decson s subject to the requrement of the MR. If the MR requrement s lower, or MR rr, choose the desgn wth two smll domns, otherwse, choose sngle lrge domn desgn, where r R s crtcl vlue of MR. se 4: It s n opposte stuton of se 3. The sme prncple of the decson s n se 3 cn be ppled. omprng wth clcultng the optml sze of domn, k opt, s shown n the lst secton, ths lgorthm s consderbly smple n use wthout losng the orgnl gol. Thus, t s more prctcl. 5. Numercl Results As dscussed n the lst secton, the desgn lgorthm s bsed on the computton of the cost functon for cellulr IPv6 network domn. In ths secton, number of typcl cses ddressed n the lgorthm re demonstrted numerclly. Suppose tht the system specfcton vector,v r, s ntlzed bsed on the vlues gven n tble 1, for exmples, J=4,. ϕ =25 nd α =0.3. h Tble 1: A set of ntlzed vlues for the system specfcton vector,v r. J ϕbs ϕ µ ho 4 10 10 0. 5 ϕ h lgh hu u lbg ω u ϕ m ϕ g 4 10 0.8 15 20 p p l ch d 25 10 0.1 0. 0.2 0.8 10 0.3 0.1 6 α β S ϑ b N ϕ c pn pout 0.3 0.7 100 5 4 10 0.8 0.2 30 The performnce comprson of the verge costs between lrge domn nd the two smll domns s gven n Fgure 1, where the lrge domn hs N = 30 nodes nd ech of the smll domns hs 15 nodes. The specfctons of ll the other prmeters re the sme for the both schemes s shown n Tble 1. The result shows the cost of the lrge domn s lower under ll the condtons of BR. Ths corresponds to se 2 n the lgorthm. Thus, the lrge domn wll be selected. ξ
450 400 Fgure 1: Result for se 2 n the decson lgorthm the scheme wth the two smll domn should be dopted. Totl ost 350 300 250 200 150 100 Wth two smll domns Wth one lrge domn 50 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 BR r() Totl ost 500 450 400 350 300 250 200 Fgure 3: Result for se 3 n the decson lgorthm Wth two smll domns Wth one lrge domn 150 800 750 700 650 Fgure 2: Result for se 1 n the decson lgorthm Wth one lrge domn 100 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 BR r() onclusons Totl ost 600 550 500 450 400 Wth two smll domns 350 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 BR r() If we chnge the sze of the lrge domn to N = 500 (or ech of smll domns hs 250 nodes) nd retn the rest of specfctons, the result of the performnce comprson between the two schemes s shown n Fgure 2, whch s opposte to Fgure 1. In ths stuton, the two smll domns should be employed. It llustrtes se 1 nlysed n the lgorthm. If the sze of the lrge domn chnges to N = 100, the result of se 3 dscussed n the lgorthm tkes plce, whch s demonstrted n Fgure 3. In such stuton, the lrge domn s selected f the BM requrement s lower thn R = 0. 45, where R = 0.45 s the crtcl pont for mkng decson. Otherwse, It s prctcl ssue to fnd the optml desgn for ellulr IP network wth multple gtewys, s t depends on mny fctors, such s the network sze, trffc lod, user populton, user moblty nd routng lgorthm. Ths pper presented n nlytcl model for ellulr IP networks wth multple gtewys. Bsed on ths model, theoretcl optmzton cn be obtned. In order to use ths model esly n prctce, decson lgorthm ws developed nd ts numercl exmples were demonstrted. References [1] A. T. mpbell, Gomez, J., Km, S., Turny, Z., Wn, -Y, nd A, Vlko, Desgn, Implementton nd Evluton of ellulr IP, IEEE Personl ommunctons, June/July 2000. [2] Andrew T. mpbell, Jvew Gomez, Snghyo Km, nd heh-yh Wn, omprson of IP Mcromoblty Protocols, IEEE Wreless ommunctons, Februry 2002. [3] A. Vlko, ellulr IP new pproch of Internet host moblty, AM omputer ommuncton Revews, Jnury, 1999.
[4] A. T. mpbell, J., Km, S., Turny, Z., Wn, -Y, nd A, Vlko, Internet Mcromoblty, Journl of Hgh Speed Networks, Specl Issue on Multmed n Wred nd Wreless Envronment, Vol. 11, No. 3-4, pp.177-198, September 2002. [5] Zch D. Shelby, Donsos Gtzouns, Andrew mpbell, nd heh-yh Wn, ellulr IPv6, <drft-sheby-cellulrpv6-01.txt>, Internet Drft, July 2001. [6] Zch D. Shelby, Petr Mhonen, Donsos Gtzouns, Alessndro Inzerll, nd Vlle Typpo, ellulr IP route Optmzton, <drft-shelby-cprouteoptmztonn-00.txt. [7] D. Johnson nd. Perkns, Moblty Support n IPv6, <drft-etf-moblep-pv6-24.txt>, June 2003. [8] J. Xe nd I.F Akyldz, A Novel Dstrbuted Dynmc Locton Mngement Scheme for Mnmzng Sgnllng ost n Moble IP, IEEE Trnsctons on Moble omputng, July-September 2002. [9] H.-Y. Tzeng nd T. Przygend, On Fst Address- Look Algorthms, IEEE J. Selected Are n omm. (JSA), vol. no. 6, pp.1067-1082, June 1999. [10] H. Xe, S. Tbbne, D. J. Goodmn, Dynmc Locton Are Mngement nd Performnce Anlyss, Proc. 43 rd IEEE Vehculr Technology onf., pp. 536-539, 1993. [11] Z.D. Wu, An Approch for Optmzng Bndng Lfetme wth Moble IPv6, Proc. of 28 th IEEE onference on Locl omputer Networks, pp.82-88, 2003.