Implicit Deregistratio i Cellular Networks Yag Xiao Computer Sciece Divisio, The Uiversity of Memphis, 7 Du Hall, Memphis TN 85 USA Email: yagxiao@ieeeorg Yuguag Fag Departmet of Electrical ad Computer Egieerig, Uiversity of Florida, aiesville, Florida 6 USA Email: fag@eceufledu Yi-Big Li Departmet of Computer Sciece ad Iformatio Egieerig, Natioal Chiao Tug Uiversity, Hsichu, Taiwa, ROC Email: liy@csiectuedutw Abstract I a cellular etwork, the visitor locatio registers (LRs), the gateway locatio registers (LRs), ad the home locatio registers (HLRs) form a three-level mobility database structure Whe users leave a LR/LR service area, deregistratio with a LR/LR is required Deregistratio may create sigificat traffic i the etwork, especially the traffic betwee a LR ad a HLR, which is the remote/iteratioal traffic I this paper, we propose a hierarchical implicit deregistratio scheme with a first/subsequet registratio i cellular etworks to effectively elimiate deregistratio traffic A aalytic model is proposed to carry out the performace of the proposed scheme Our study shows that the proposed scheme ot oly reduces the local deregistratio traffic betwee the LR ad the LR, but also reduces the remote/iteratioal deregistratio traffic betwee the HLR ad the LR This is especially true whe the ratio of the cost of the remote/iteratioal traffic betwee the LR ad the HLR to the cost of local traffic betwee the LR ad the LR is high Keywords- Home locatio register, Registratio I INTRODUCTION The ANSI-4 [] ad SM (lobal System for Mobile commuicatio) MAP (Mobile Applicatio Part) [] have bee stadardized to support mobility maagemet i secod geeratio () wireless cellular etworks Both ANSI-4 ad MAP use a two-tier system of home (HLR) ad visited (LR) locatio databases The HLR database is used to record mobile users iformatio The service area is partitioed ito several locatio areas (LAs) Every LA is associated with a mobility database called the LR, which is used to record mobile users temporary locatio iformatio whe a mobile user eters the visited LA Registratio is the process by which mobile phoes iform the etwork of their curret locatios Deregistratio is the process by which mobile phoes iform the etwork to delete their record i the old LR whe they move out of a LA so that the reclaimed storage ca be used by other mobile phoes I ANSI-4 [] ad SM MAP [], explicit deregistratio schemes are used for registratio ad deregistratio processes I explicit deregistratio schemes, the registratio process esures that a mobile phoe s registratio i a ew LR causes deregistratio i the old LR However, i such schemes, both registratio ad deregistratio may result i sigificat amout of etwork sigalig traffic I [], we proposed a implicit deregistratio scheme that totally elimiates the deregistratio traffic I this scheme, the record of a mobile phoe is ot deleted from the LR whe the mobile phoe leaves that LA If a mobile phoe arrives at a LA ad the LR is full, a radom record is deleted, ad the reclaimed storage is reassiged to the ew arrivig mobile phoe Whe a call arrives ad the call s record is missig i the LR, the call is lost I order to reduce the iteratioal roamig sigalig traffic, the LR withi the UMTS (Uiversal Mobile Telecommuicatio System) Core Network is proposed i specificatio PP 9 [] The LR is a ode betwee a LR ad the HLR It hadles locatio maagemet of roamig subscriber i visited etwork without ivolvig the HLR Deregistratio of the LR may also result i sigificat amout of etwork sigalig traffic The cost of deregistratio of the LR is much more expesive tha that of deregistratio of the LR sice the traffic betwee the LR ad the HLR is remote/iteratioal traffic I this paper, we propose a hierarchical implicit deregistratio scheme with a first/subsequet registratio i cellular etworks to effectively elimiate deregistratio traffic, especially the traffic ivolvig remote/iteratioal calls I the proposed scheme, the record of a mobile phoe is ot deleted from the LR/LR whe the mobile phoe leaves that the LR/LR service area If a mobile phoe arrives at the LR/LR service area ad the LR/LR is full, a radom record is deleted, ad the reclaimed storage is reassiged to the ew arrivig mobile phoe If a call arrives ad the call s record is missig i the LR/LR, a first or subsequet registratio is executed to restore the LR/LR record before the call setup operatio proceeds II MOBILITY MANAEMENT IN UMTS I etworks with LR, at the first locatio update procedure, the subscriber iformatio is dowloaded from the HLR to the LR The LR hadles Update Locatio messages from the LRs as if it is the HLR of the subscribers at the subsequet locatio updatig procedures The LR eables the procedure ivisible from the home etwork so that this hierarchical locatio maagemet ca reduce the iter-etwork sigalig for locatio maagemet The LR keeps the iformatio util receivig Cacel Locatio (same as deregistratio) message from the HLR The call origiatio procedure sets up a call iitiated by a mobile user usig the LR record The first registratio is hadled by the HLR ad the LR via the LR For all subsequet registratio The work of Yuguag Fag was supported i part by the NSF Faculty Early Career Developmet Award uder grat ANI-94-78-78-4//$7 IEEE 944
operatios, the HLR is o loger ivolved, ad the operatios are performed locally betwee the LRs ad the LR Algorithm I First Registratio Step (First Registratio Request) Step The mobile phoe (a ) seds a registratio request Step The LR creates a temporary LR record for a Step The LR seds a Update Locatio message to the LR Step 4 The LR creates a temporary LR record for a ad stores the LR Number ad servig MSC Number Step 5 The LR seds a Update Locatio message to the HLR with the LR Number as LR Number, ad IM-MSC (Itermediate-MSC) Number as MSC Number Step (First Registratio Respos Step The HLR stores the LR Number ad IM-MSC Number from received message as respectively LR Number ad servig MSC Number Step The HLR iitiates isert subscriber data procedure ad cacel locatio procedure i Algorithm III Step Whe the LR receives Isert Subscriber Data message from the HLR, the LR stores the subscriber s iformatio i the message ad trasport it to the LR Step (First Registratio Ackowledgemet) The HLR ackowledges the Update Locatio message from the LR ad the LR trasports the ackowledgemet to the LR Algorithm II Subsequet Registratio Step Whe the LR receives a Update Locatio message from ewly visited LR ad it holds the subscriber iformatio, the LR stores the ew LR Number ad ew MSC Number Steps -5 The LR iitiates isert subscriber data procedure ad cacel locatio procedure i Algorithm III Step 6 The LR ackowledges to the Update Locatio message Algorithm III Locatio Cacellatio Step The ewly visited LR seds a Update Locatio message the HLR after the MS left the etwork with the LR Step The HLR seds the Cacel Locatio message to the LR Step The LR trasports this Cacel Locatio message to the previously visited LR Step 4 The old LR deletes the user s record, ad seds respose Step 5 After receivig the respose, the LR trasports the respose to the HLR ad delete the roamer s subscriber profile ad locatio iformatio Step 6 The HLR iitiates isert subscriber data procedure to the ewly visited LR Step 7 The ewly visited LR ackowledges the HLR s isert subscriber data procedure Step 8 The HLR ackowledges the ewly visited LR s Update Locatio message Algorithm I Call Origiatio Step The mobile phoe seds the call origiatio request Step The MSC forwards the request to the LR Step The LR checks the profile ad grats the call request Step 4 The MSC sets up the truk accordig to the stadard SS7 call setup procedure as i wireless systems III HIERARCHICAL IMPLICIT DEREISTRATION Whe the implicit registratio is used, the record of a mobile phoe is ot deleted from the LR/LR whe the mobile phoe leaves that the LR/LR service area If a mobile phoe arrives at the LR/LR service area ad the LR/LR is full, a radom record is deleted, ad the reclaimed storage is reassiged to the ew arrivig mobile phoe If a call arrives ad the call s record is missig i the LR/LR, a first or subsequet registratio is executed to restore the LR/LR record before the call setup operatio proceeds To implemet the implicit deregistratio, we propose the followig LR/LR algorithms I, II, ad I Notice that the Locatio Cacellatio Algorithm is elimiated Algorithm I : First Registratio Step (First Registratio Request) Step Step i Algorithm I is executed Step If the LR is ot full, Step i Algorithm I is executed Otherwise, a radomly chose record is deleted, ad the reclaimed storage is reassiged for a Step Step i Algorithm I is executed Step 4 If the LR is ot full, Step 4 i Algorithm I is executed Otherwise, a radomly chose record i the LR (with equal probability) is deleted, ad the reclaimed storage is reassiged for a ad stores the LR ID ad servig MSC ID Step 5 Step 5 i Algorithm I is executed Step (First Registratio Respos Step Step i Algorithm I is executed Step The HLR iitiates isert subscriber data procedure, however, the locatio cacellatio procedure will ot be iitiated Step Step i Algorithm I is executed Step (First Registratio Ackowledgemet) Step i Algorithm I is executed Algorithm II : Subsequet Registratio Step Step The mobile phoe (a ) seds a registratio request to the LR If the LR is full, it creates a temporary LR record for a Otherwise, a radomly chose record (with equal probability) is deleted, ad the reclaimed storage is reassiged to a The LR seds a Locatio Update message to the LR Step Whe the LR receives a Locatio Update message from the ewly visited LR ad if it holds the subscriber iformatio for the user, the LR stores the ew LR ID ad the ew servig MSC ID Otherwise, a radomly chose record (with equal probability) is deleted, the reclaimed storage is reassiged to a ad stores the LR ID ad the servig MSC ID, ad Step 5 ad Step i Algorithm I are executed Steps -5 The LR iitiates the isert subscriber data procedure, however locatio cacellatio procedure will ot be iitiated Step 6 Step 6 i Algorithm II is executed Algorithm I : Call Origiatio Steps - Steps - i Algorithm I are executed Step If both the LR ad the LR fid the user s record, Step i Algorithm I is executed ad the algorithm proceeds to Step 4 Otherwise, the mobile phoe iitiates the Subsequet Registratio Algorithm II ad Algorithm I is executed I this case, the algorithm exits without executig Step 4 Step 4 Step 4 i Algorithm I is executed I AN ANALYTICAL MODEL We observe that i wireless etworks, the sigalig traffic betwee the HLR ad the LR is usually remote/iteratioal with high cost, whereas the sigalig traffic betwee the LR ad the LR is usually local with low cost We will study the performace issues of the record- 945
missig probability for both the LR ad the LR, ad the gais from the traffic reductio betwee the HLR ad LR (the iteratioal/remote traffic) ad betwee the LR ad the LR (local traffic) To do so, we ivoke the followig assumptios: (a) the residece time of a user i a LA follows a geeral probability distributio with probability desity fuctio f ), the mea /η, the Laplace trasform m ( s = f * ( s) = f ( ) e d, ad the probability distributio fuctio F( ); (b) the call arrivals to a user form a Poisso process with the call arrival rate λ Let be the call iterarrival time Let N be the umber of users i a LA, K be the umber of LRs coected to a LR, M be the size of a LR, ad L be the size of a LR From assumptio (a), if N is sufficietly large, we ca approximate the arrivals of mobile phoes ito a LR by a Poisso process with rate N η [4, 6] Moreover, the et call arrivals to the mobile phoes i the LR form a Poisso process with rate N λ [4, 6] Similarly, we ca approximate the arrivals of mobile phoes ito the LR by a Poisso process with rate KN η, ad the et call arrivals to the mobile phoes i the LR by a Poisso process with rate KN λ If the LR record replacemet is doe radomly with equal probability, the probability that a LR record is ot selected for replacemet is ( ) q = M M () Similarly, if the LR record replacemet is doe radomly with equal probability, the probability that a LR record is ot selected for replacemet is ( ) q = L L () Mobile phoe eters LA Mobile phoe leaves LA t t t t Previous call Curret call Fig The timig diagram of mobile phoe P ad its calls Fig shows the timig diagram for a mobile phoe P that eters a LA at time t, ad leaves the LA at time t is P s residece time i the LA Assume that a call to P arrives at time t where max (t, t ) < t < t, ad the previous call to P arrives at time t We do ot assume that t > t Let = t t, = t t, = t t ad = mi(, ) We otice that is the call iterarrival time, both ad had already defied i assumptios (a) ad (b) Sice the Poiso call arrivals are radom observers to P s residece time, followig the residual life theorem [7], s desity fuctio is [ F ( )] rm ( ) = η fm( t) = η m t= Let R m ( ) be the distributio fuctio of r m ( ) ad the Laplace trasform for be f*(s) We have, () λ λ λ ( ) = ( ) λ m + λ m( ) = m( ) + λ m( ) t= = { [ ]} f e r d e r d e r R * s * () = () = λ + λ + η ( m ( λ+ )) ( = f s e f d s s f s s Let e deote the evet that that whe a call to a mobile phoe P arrives, the LR record r of P does ot exist Let P(e ) deote the probability that the evet e v occurs P(e ) is called the record-missig probability for the LR Let e deote evet that whe a call to a mobile phoe P arrives (P is i oe of the LRs i the LR), the LR record r of P does ot exist Let P(e ) be the probability that the evet e occurs P(e ) is called the record-missig probability for the LR Note that P has records i both the LR ad the LR at times t, t, ad t, sice the records are potetially restored either by a forced first-registratio (at t ) or by a forced subsequet registratio (at t, t, ad t ) Before t, t, ad t, P s records i both the LR ad the LR may ot exist if the records are replaced due to the hierarchical implicit deregistratio O the other had, P s records i either the LR or the LR may be replaced durig the period [ max(t, t ), t], if either a forced first/subsequet registratio or a call setup for aother mobile phoes selects P s record i either the LR or i the LR for replacemet durig this period This period is Notice that eve though P s record i the LR is ot replaced, P s record i the LR may still be replaced O the other had, if P s record i the LR is replaced, P s record i the LR may ot be replaced Whe a call to a mobile phoe P arrives at t, P s record i the LR is replaced i the period either by a forced first/subsequet registratio or by a call request to aother mobile phoe whose LR record does ot exist The replacemet rate due to the forced registratio is N η ad the replacemet rate due to call requests is with rate P(e )Nλ The latter statemet is obtaied as follows: sice Nλ is the rate for call arrivals to mobile phoes i the LR, P(e )Nλ is the rate of call requests for which the correspodig LR records do ot exist We also otice that P s record i a LR is selected for replacemet with probability q Let X be the umber of such operatios i period that may cause the replacemet of a LR record The, the rate of operatios that may cause the replacemet of a LR record is give as follows: λ * = M η + P( e ) λ N ( η + P( e ) λ) N = q Similarly, whe a call to a mobile phoe P arrives at t, P s record i the LR is replaced i the period either by a forced first/subsequet registratio (with rate KN η ) or by a call request to aother mobile phoe whose LR record does ot exist (with rate P( e ) KNλ ) Agai, the latter statemet is obtaied as follows: KNλ is the rate for call arrivals to mobile phoes i the LR, is the rate of call requests for )KNλ P(e which the correspodig LR records do ot exist Moreover, the P s record i the LR is selected for replacemet with (4) (5) (6) 946
probability q Let X be the umber of such operatios i the period, leadig to the replacemet of a LR record The, the rate of operatios that may cause the replacemet of a LR record is λ * = + P e q KN L η ( ) λ ( η + P( e ) λ) KN = X ad X are two Poiso radom variables with the probability mass fuctios [7] P P [ ] ( λ * ) λ * X = = e (8)! [ ] ( λ * ) λ * X = = e (9)! Sice f * ( s) is aalytic i the right complex plae by observatio, from (4) ad power series expasios, the recordmissig probabilities P e ) ad P e ) ca be expressed as ( Pe ( ) = q P X = f( ) d ( (7) [ ] () = = A A A fm A ( A + λ η [ *( ] = where A = λ *( q ) [ ] () Pe ( ) = q P X = f( ) d = = A + λa ηa [ f * ( A ] =, where A = λ *( q ) m ( A Both P ( e )(with (6) ad ()) ad P ( e ) (with (7) ad ()) ca be computed by the followig iterative algorithms Let the pair ( P (, λ *) stad for either the pair ( P ( e ), λ * ) or the pair ( P e ), λ *) ( Step Select the iitial value for P ( Step Compute λ * based o (6) or (7) Step Let P ( old P ( Step 4 Compute P ( based o () or () Step 5 Let δ be a predefied small value If P( P( old < δ P(, the exit Otherwise, P ( P ( old ad go to step The above iterative algorithm has bee extesively used ad validated by may experimets [6] We ca easily show that the above algorithm coverges to the uique solutio P e ) or P e ), ad the covergece is expoetially fast ( ( For a LR, let µ be the saved deregistratio traffic betwee the LR ad the LR i the hierarchical implicit deregistratio scheme ad µ be the extra traffic created betwee the LR ad the LR due to the forced first/subsequet registratios The, we have µ = Nη ad µ = P( e ) Nλ Similarly, for a LR, let µ be the saved deregistratio traffic betwee the HLR ad the LR i the hierarchical implicit deregistratio scheme ad µ be the extra traffic created betwee the HLR ad the LR due to the forced registratio Similarly, we have µ = KNη ad µ = P( e ) KNλ Let α be the ratio of a deregistratio cost to a registratio cost for the LR, ad α be the ratio of a deregistratio cost to a registratio cost for the LR I a typical mobile phoe etwork, we have <α < ad <α < [4] Let σ be the traffic cost ratio of the remote/iteratioal traffic cost betwee the LR ad HLR versus the local traffic betwee the LR ad the LR Normally, we expect that σ >> The saved remote traffic remote, the saved local traffic local, ad the saved total traffic i the hierarchical implicit deregistratio scheme for a LR with K associated LRs are give as follows remote = σ [ µ α µ ] = KN [ ση P( e ) αλ] () local = K[ µ α µ ] = KN[ η P( e ) α λ] () ( ) ( ( ) ( ) ) = remote + local = KN σ + η Pe α + Pe α λ (4) NUMERICAL RESULTS I this sectio, we carry out the performace aalysis for the hierarchical implicit deregistratio scheme with forced first/subsequet registratio We further assume that the LA residece times have a amma desity fuctio with mea /η ad variace ν [4] The Laplace trasform for the amma LA residece time distributio is ( ηυ ) fm *( s) = + s /( η υ ) Therefore, ()-() ca be rewritte as A + λ A η A [ ( + ηυ A + ηυλ) ] Pe ( ), where A *( q) /( ηυ) = = λ ( A A + λ A η A [ ( + ηυ A + ηυλ) ] Pe ( ), where A *( q ) /( ηυ) = = λ ( A (5) (6) (7) Based o (6) ad (6), we ca calculate P ( e ) usig the iterative algorithm itroduced i the previous sectio Similarly, we ca calculate P ( e ) based o (7) ad (7) The, we ca calculate remote, local, ad usig the values of P ( e ) ad P ( e ) based o ()-(4) Based o remote, local, ad, we ivestigate the performace of the hierarchical implicit deregistratio with forced first/subsequet registratio as follows Fig plots the saved total traffic agaist λ/η (the expected umber of calls to a mobile phoe whe a mobile phoe is i a LA) Here, we assume that M=, N=, L=6, α =, α =, σ=5,, 5, ad ν=/η, /η, /η i the hierarchical implicit deregistratio scheme for a LR with associated LRs The figure idicates that by exercisig the hierarchical implicit deregistratio, the portio of deregistratio traffic ca be sigificatly reduced, especially whe σ is high We expect σ higher whe the traffic betwee the LR ad HLR is the iteratioal traffic The figure also shows that the saved total traffic decrease as λ/η icreases That is, if the mobile phoe s mobility is high or the call arrival rate is low, it is more likely that whe a call arrives, the correspodig LR record ad LR record have bee replaced Furthermore, the figure demostrates how the variace ν of the amma cell residece time distributio affects the system performace with a fixed mea /η: the 947
saved total traffic i the hierarchical implicit deregistratio decreases asν icreases 5 x 4 5 5 σ=5, υ=/η σ=5, υ=/η σ=5, υ=/η σ=, υ=/η σ=, υ=/η σ=, υ=/η σ=5, υ=/η σ=5, υ=/η σ=5, υ=/η 4 5 6 λ/η(m=, N=, K=, L=6) 5 5 5 5 4 x 4 Fig Effects of σ, ν ad λ/η o M=, N=*M M=, N=*M M=, N=5*M M=5, N=*M M=5, N=*M M=5, N=5*M M=, N=*M M=, N=*M M=, N=5*M 4 5 6 λ/η(σ=, K=, L=*M, υ=/η ) 5 5 5 x 4 Fig Effects of M, N, ad λ/η o Remote, N=*M Remote, N=*M Remote, N=5*M Local, N=*M Local, N=*M Local, N=5*M 4 5 6 λ/η(σ=, K=, L=*M,M=,υ=/η ) Fig 4 The saved remote traffic vs saved local traffic Fig plots the saved total traffic agaist λ/η with σ=, L=*M,ν=/η, α =, α =, M=, 5,, ad N=M, M, 5M i the hierarchical implicit deregistratio for a LR with associated LRs The figure shows that by exercisig the hierarchical implicit deregistratio, the portio of deregistratio traffic ca be sigificatly reduced, especially whe M (the size of the LR) is large The saved traffic icreases whe M icreases The figure also shows that the saved total traffic icreases sigificatly whe N/M icreases Furthermore, the figure demostrate that whe M is large (M ) ad N/M is large (N/M ), the saved total traffic decreases as λ/η icreases That is, whe both M ad N/M are large, if the mobile phoe s mobility is high or the call arrival rate is low, i which case, it is more likely that whe a call arrives, the correspodig LR record ad the correspodig LR record will be replaced O the other had, whe M is small (M<) ad N/M is small (N/M<), the saved total traffic is isesitive as λ/η icreases Fig 4 plots the saved remote traffic remote ad the saved local traffic local agaist λ/η with σ=, L=*M,ν=/η, α =, α =, M=, ad N=M, M, 5M i the hierarchical implicit deregistratio for a LR with associated LRs The figure idicates that by exercisig the hierarchical implicit deregistratio, the portio of the saved remote traffic ca be sigificatly larger tha the saved local traffic, especially whe N/M is large Both the saved remote traffic ad the saved local traffic icrease whe N/M icreases I CONCLUSIONS This paper proposes a hierarchical implicit deregistratio scheme to reduce the sigalig traffic due to deregistratio i wireless cellular systems A aalytical model is developed to evaluate the performace of the proposed scheme The saved remote traffic, the saved local traffic, ad the total saved traffic are used as the output performace measures The study idicates that by exercisig the hierarchical implicit deregistratio, the portio of deregistratio traffic ca be sigificatly reduced, especially whe the traffic cost ratio of the remote/iteratioal traffic cost betwee the LR ad HLR versus local traffic betwee the LR ad the LR is high Moreover, by exercisig the hierarchical implicit deregistratio, the portio of the saved remote traffic ca be sigificatly larger tha the saved local traffic The portio of deregistratio traffic ca be sigificatly reduced, especially whe the size of the LR is large The saved traffic icreases whe the size of the LR icreases The total saved traffic icreases dramatically whe the ratio of the umber of mobile phoes to the size of the LR databases icreases The results ca be useful i mobility database dimesioig ad QoS provisioig i wireless etwork desig REFERENCES [] Cellular itersystem operatios (Rev C), EIA/TIA, Tech Rep IS-4, 995 [] Mobile applicatio part (MAP) specificatio, versio 48, ETSI/TC, Tech Rep, Recommedatio SM 9, 994 [] Y-B Li ad A Noerpel, Implicit deregistratio i a PCS etwork, IEEE Trasactios o ehicular Techology 4 (4) (994) 6- [4] Ai-Chu Pag, Yi-Big Li ad Yuguag Fag, Implicit Deregistratio with Forced Registratio fo PCS Mobility Maagemet, Wireless Networks, 7,, pp 99-4 [5] ateway Locatio Register (LR) - Stage, TS 9, March [6] Y-B Li, Modelig techiques for large-scale PCS etworks, IEEE Commuicatio Magazie (February 997) [7] L Kleirock, Queueig Systems: olume I- Theory, Joh Wiley ad Sos, New York, 976 948