Modelling Overflow Traffic from Terrestrial Networks into Satellite Networks

Transcription

1 Modellng Overflow Traffc from Terrestral Networks nto Satellte Networks runa Jayasurya, Davd Green, John senstorfer Insttute for Telecommuncaton Research, Cooperatve Research Centre for Satellte Systems, Unversty of South ustrala, Mawson Lakes, S 595, ustrala Teletraffc Research Centre, Unversty of delade, delade S 5, ustrala Tel: Fax: aruna@sprlevelsunsaeduau bstract -- Thrd generaton moble communcaton networks promse to provde a varety of hgh data rate servces wth hgher Qualty of Servce (QoS) than secondgeneraton systems Satellte networks, whch wll be ntegrated wth terrestral networks, are a major feature n thrd generaton networks Satellte networks ntend to provde coverage for rural areas and to act as an overlay network n urban areas These overlay networks can be used to support the users blocked n terrestral handover It s mportant to carefully analyse and dmenson the satellte network to optmse the expensve satellte resources whle provdng the requred QoS for users Channel holdng tme of a cell s one of the major parameters that needs to accurately modelled n theses teletraffc analyses Ths paper focuses on usng Phase-type dstrbutons of Generalsed Erlang form to model channel holdng n satellte networks In ths paper t s assumed that the traffc n satellte network s sorely consst of overflow traffc due to blockng n terrestral networks We also present the Quas-Brth- Death (QBD) process that results from queung models n satellte networks wth Generalsed Erlang servce and exponental nterarrval dstrbutons Further we nvestgate the optmum number of terrestral cells that can be covered by a satellte spot-beam wth a gven number of channels I INTRODUCTION Thrd generaton moble communcaton networks are desgned to take personal communcatons users nto the new nformaton socety [] One of the major problems that need to be addressed n moble networks s the contnuty of a servce durng a handover wthout any data loss, as the user moves from cell to cell Ths s called seamless handover Most of the thrd generaton servces requre a hgher guarantee of beng able to contnue the servce across cell boundares, than that s provded by current moble servces The blockng probablty encountered at handover s an mportant Grade of Servce (GoS) parameter for moble users key aspect of the rd generaton system s the ntegraton of dfferent networks n an optmal and seamless manner Thrd generaton moble networks wll have terrestral and satellte networks connected at system and servce levels [,] Terrestral networks provde the coverage for urban and suburban areas whle a constellaton of Low earth Orbt (LEO) or Medum Earth Orbt (MEO) satelltes provde servces to sparsely populated rural areas In urban areas the satellte network can be used as an overlay network for terrestral networks The satellte network can support some porton of the overflow traffc, due to blockng, from the terrestral networks Ths allows the network to provde hgher Grade of Servce (GoS) for thrd generaton users In ths work we study the mprovements that can be made to the GoS for handover users n thrd generaton networks, usng the overlad satellte networks Once the terrestral users have been blocked at handover, they wll be temporarly supported n the satellte network untl enough resources become avalable n the terrestral network Due to the fact that hgher GoS s requred from thrd generaton networks t s of utmost mportance to carefully dmenson the terrestral and satellte networks to provde the guaranteed GoS levels Durng ths dmensonng phase, number of channels needed to guarantee acceptable blockng probabltes for users wll be estmated for varous network loads Furthermore the number of terrestral cells that can be covered by a satellte spot beam wth a certan number of channels has to be determned In ths paper, we estmate the dfferent blockng probabltes that the moble users wll face at dfferent network loads and demonstrate how the overlad satellte network can be used mprove these blockng probabltes whle optmsng the total capacty of the system The rest of the paper s organsed as follows Secton II brefly descrbes some of the technques that were used to model moble communcaton networks and dscuss some of ther drawbacks Ths s followed by a bref descrpton of Phase-Type (PH) dstrbutons, whch are the dstrbutons that we used to characterse channel occupancy tme n ths study The next secton outlnes the parameters that govern the behavour of overflow traffc nto the satellte network followed by the methods we used to model the channel occupancy for satellte networks Secton IV descrbes how to derve the Quas-Brth-Death (QBD) process for the satellte cell server under nvestgaton, followed by the methods used to solve for the statonary and blockng probabltes of the system The next secton contans the results obtaned n ths study, whch shows that optmum terrestral system capacty of 846% can be acheved, when a satellte spot beam wth channels cover terrestral cells The blockng probabltes at ths operatng pont are 5% for new users and % for handover users We conclude the paper wth closng remarks and some future research drectons

2 II NLYSING MOBILE COMMUNICTION NETWORKS Formal analyss technques are mportant n determnng level of servce that can be guaranteed from moble communcaton networks Channel holdng (occupancy) tme s very mportant n ths sense to determne the blockng probabltes experenced by users n moble networks Prevously, analyses used exponental dstrbutons to model channel holdng tme for the sake of tractablty [-7] However expermental data showed that actual channel occupancy dstrbutons are sgnfcantly dfferent of exponental dstrbutons used n these analyses [8] Complex overlayed network archtectures and varable cell szes preferred n rd generaton networks cause these dstrbutons to dffer further from smple exponental dstrbutons In ths research we approxmate the channel holdng tme usng Phase-type (PH) dstrbutons Phase-type dstrbutons represent a set of dstrbutons that are combnatons and convolutons of dfferent exponental dstrbutons [9] Phase type dstrbutons are represented as PH (, T ), where s the ntal probablty vector and T s the rate transton matrx of the dstrbuton Phasetype dstrbutons when used n a renewal process brng about more accurate and detaled nformaton about the behavour of the process Further they can be used to approxmate vrtually any renewal process, wth the dmensonalty of the phase-type dstrbuton ncreasng wth the complexty of the partcular process beng modelled [9] Use of PH dstrbutons also enables explct expressons to be obtaned for performance measurements n stochastc processes, due to ther underlyng Markovan structure [] Channel Holdng Tme For Overflow Traffc n Satellte Networks In ths scheme blocked terrestral users are accepted nto the satellte network and they can resde n the satellte network untl enough resources have been found n the terrestral network to accommodate them Therefore the channel occupancy tme for these users depends on the load on the underlyng terrestral network, whch n effect depends on the moblty patterns of the users and the capacty of the terrestral networks Intra and nter satellte handover patterns are also mportant factors n determnng the behavour of channel holdng tme n satellte networks However due to the predetermned orbtal patterns n LEO and MEO networks the traffc handed over to the next satellte s somewhat balanced by the traffc handed n by the prevous satellte Therefore n ths research t was assumed that the ntra and nter satellte handover traffc does not have any mpact on the behavour of overflow traffc n to the satellte network Thus the channel occupancy tme n satellte network s sought to be dependent only on the behavour of overflow traffc from the terrestral network In ths study t was ntended to expermentally fnd the channel holdng tme for satellte users and approxmate ths pattern wth a phase-type dstrbuton of generalsed-erlang form model network was set up n OPNET to gather the data requred to fnd the channel holdng tme dstrbuton Ths network conssts of terrestral cells and a sngle satellte cell moble users were randomly dstrbuted n the entre coverage area and these users were gven predefned moblty patterns to model the type of behavour shown by moble users n an urban envronment [] Once the users enter the satellte network channel holdng tme for those users were recorded and these data were used to obtan the expermental channel holdng tme dstrbuton for satellte network Expectaton Maxmsaton (EM) was used to fnd the parameters of the Generalsed Erlang dstrbuton that best fts the expermental data [] In ths study we used the Empht teratve algorthm, whch guarantees that the lkelhood functon s ncreased n every teraton We selected a Generalsed Erlang dstrbuton wth three phases to represent the channel holdng tme dstrbuton [] The parameters of the selected dstrbuton are gven below 7 7 T = and = [ ] Fgure shows the dstrbuton obtaned from the smulaton and the ftted phase-type dstrbuton P(x) dstrbuton functons ftted phase type dstrbuton dstrbuton form the smulaton x Fgure Channel holdng tme dstrbuton and the ftted phase-type dstrbuton III QUEING SYSTEM TO REPRESENT THE STELLITE NETWORK ssumng that the arrvals nto the satellte network are exponentally dstrbuted [8] the combned collectve channels n the satellte spot beam can be modelled as a M/PH/n/n queue Where n s the number of channels avalable n a satellte spot beam The rate transton matrx for ths queue has a characterstc block trdagonal form and s gven n ()

3 B B Q = B,n,n,n rrval Rate for the Satellte Network,n Once the users have been blocked n the terrestral network, they wll seek resources from the satellte network to contnue ther servces There-fore the nterarrval rates for traffc offered to satellte, sat, can be calculated as follows,,n sat = ter P block ( ter ) () ter Where s the nterarrval rate n the terrestral network and p block ( ter ) s the blockng probablty at that nterarrval rate ssumng there are k terrestral cells covered by one satellte cell the combned nterarrval rate nto satellte system s k sat B Rate Transton Matrx for The Satellte Server We assume an exponental arrval dstrbuton wth parameter and a -phase generalsed Erlang servce dstrbuton wth parameters PH (, T ), where T and are gven as follows T = and = [ ] () B () Matrces B, B and B are gven n equaton (4) [9] = B = τ (4) B = Te Where symbol represents the Kronecker product between the two matrces and e s a unt vector However, the constructon of and for general, phase-type dstrbutons s very complex and s beyond the scope of ths artcle [,] However rate transton matrx for the above system can be created by applyng the detaled reasonng and smplfcatons for a -phase system presented n [] State of the system can be represented by ( n, n, n ) where n, n, n s the number of users n phases, and respectvely at a gven nstant The lnear orderng of the states gven n table was used to obtan the characterstc tr-dagonal form of the rate transton matrx The elements of the matrces are calculated by observng the possble transtons allowed between dfferent states Transtons allowed between dfferent states are gven n fgures and Transtons rates for these transtons can be calculated from data gven n table Due to space consderatons of the artcle, detals about creatng these matrces are not presented n ths paper state Number of users n phase Number of users n phase Number of users n phase m m m + m m + m m + m m + m p m p k ( m ) k k p, m m p m, m p m, m p m m Table Lnear orderng of all possble states of the system Where state number p k are gven by pk = S m+ S( m ) k (5) for =,, m and k =, m n where S n = j = n( n + ) / (6) j= nd the number of allowable states when there are m users n the system s S m+ Frst few states of the system are gven n fgure,,,,,,,,,,,,,,,,,, Fgure Frst few states and transtons of the system,,,,,,,,,,,,,,,,,,,,

4 n k+,n-,m-k-n k-,n+,m-k-n k,n,m-k-n+ We defne vector e(l) and () as follows e ( l) = [,,,] a row vector of ones wth length l and ( ) = [ e( ),e( ),, je( + j),, ( ) e(), e()] Then a, a,, a,, a ] = ( ) [ +, + j, j r, c k-,n,m-k-n k k,n,m-k-n (k+) (m-k-n+) k+,n,m-k-n s a matrx of sze [( + )( + ) / ] [( + )( + ) / ] and we defne vector z(l) and $ (k) as follows z(l) s a row vector of zeros wth length l and ( k ) = [,,, k] $ k,n,m-k-n- (m-k-n) (n+) k+,n-,m-k-n k,n+,m-k-n- m- users n the system m users n the system m+ users n the system Fgure ll possble transtons nto other states when there are m users n the system ll possble transtons when there are m users n the system are gven n fgure In fgures and the selftranstons, transtons nto the same state, have been gnored n order to mprove the clarty of the dagrams From To Rate Event,, rrval,, Departure n,n,n n +,n,n rrval n,n,n n,n,n - n Departure n,n,n n -,n +,n n phase change n,n,n n,n -,n + n phase change n,n,n n,n,n -(+ n + n + n ) self transton Table : Transton rates between dfferent states Matrces,, for a phase generalse erlang servce dstrbuton are gven below s a matrx of sze [( + )( + ) / ] [ ( + ) / ], gven n (6) a = a +, Where c = ( + ) / and r = ( + )( + ) / a + j, j a r, c (6) We defne the p th dagonal of the matrx as the upper dagonal of the matrx offset by p places from the man dagonal Then the p th dagonal of, d p s gven by d p = [ z( S+ S p p), $ ( p), z( S p )] (7) for p =,, Where S j was defned earler st dagonal d s gven by, d = ( ), ( ), (),, ] (8) [ where ( k) = [ k, k,,,] (9) Man dagonal of s found by observng that raw sums are zero for Q n any QBD process [9] ll other elements are zero s a matrx of sze [( + )( + ) / ] [( + )( + ) / ] and s gven n () = () where l = I(l) and I(l) s an dentty matrx of sze l C Statonary Probabltes of the QBD Process Statonary probabltes, x, of ths QBD process can be found by solvng equaton (), whch states that effectve probablty flow out of a state s balanced by the probablty flow nto the state xq = () In ths work we used stochastc complmentaton methods to solve the above system Stochastc complmentaton allows to decouple an large rreducble Markov chan nto smaller rreducble Markov chans [4] Then the statonary probabltes

5 of these smaller Markov chans can be combned to fnd the statonary probabltes of the orgnal system Dvdeand-conquer technques were used to fnd the couplng factors and stochastc complments of the Markov chan [4] Reference [4] gves the solutons for the equaton () xp = x () By comparng equatons () and () we can deduce that, Q = P I () Once the statonary probabltes, x, of the system have been obtaned where xe =, where e s a column vector of s, we can fnd the probablty of havng users n the system, p (), as follows, p ( ) = x() SS + S + j= SS + p( ) = x ( j) for (4) where n SS = m n= m= and S = j j= (5) Blockng probablty of the satellte network, P block _ sat, s gven by, Pblock _ sat = p( n), (6) where n s the number of channels avalable n the satellte network In ths system the satellte network supports handover users blocked by the terrestral network untl enough resources have been found n terrestral network to support them Therefore the blockng probablty experenced by the handover users, P _ s gven by, P block ho P P block _ ho = block _ ter block _ sat (7) IV RESULTS In ths secton, results obtaned through the abovedescrbed queung models are presented In partcular analyss has been performed to determne the blockng probabltes that handover and new users experence wth a varous number of channels avalable form satellte network Further nvestgatons were carred out to fnd the optmum number of terrestral cells that can be covered by a satellte spot-beam wth a gven number of channels In these analyses t was assumed that a typcal terrestral cell has 5 channels [] It was also assumed that the GoS blockng probabltes for new and handover users must be less than 5% and % respectvely The operatng pont of the system s taken to be the maxmum capacty that leads to blockng probabltes less than or equal to the above stated values Further t was observed that wth an average call length of mnutes users make 8 handovers per call Therefore we selected, = 8 (8) h n Fgure 4, created from the data presented n [] shows that the operatng pont of the system s 785% of the capacty to meet the GoS for both types of users t ths stage the system does not dstngush between the handover and new users, thus promptng us to operate at a capacty where we can provde the GoS requred for handover users But f the satellte network can support the blocked handover users we can mprove the operatng capacty to 846% where both types of users suffer blockng probablty of 5% t ths operatng pont the overflow traffc nto the satellte network should be subject to blockng probablty of less than 4% (%/5%) Ths gves the overall blockng probablty of less than % for handover users Blockng probablty of 4% s only applcable to the overflow handover traffc nto the satellte network Intra and nter satellte handover users and users who start calls n satellte networks should suffer blockng probabltes n the range of -5% Selectng 846% as the operatng capacty of the terrestral system, and usng () gves that the arrval rate of the overflow traffc nto the satellte network from a sngle terrestral cell s 7 Fgure 5 shows the blockng probabltes experenced by the overflow traffc n the satellte network, under dfferent network confguratons In ths scenaro we have consdered networks wth varable number of channels avalable from the satellte networks Further the number of terrestral cells covered by a sngle satellte spot beam was vared Blockng Probablty rrval rate = 4 Operatng capacty = 788 % rrval rate = 78 Operatng capacty = 799 % rrval Rate Fgure 4 Operatng ponts for terrestral system s expected the blockng probablty exponentally ncreases wth number of terrestral cells covered by satellte spot beam and exponentally decreases wth the number of channels avalable per spot beam The lne where the blockng probablty of the satellte system s 4 s gven n fgure 6 It shows almost a lnear relatonshp between the number of channels avalable per spot-beam and number of terrestral cells covered by a spot-beam Wth channels avalable perspot beam one spot-beam can handle overflow traffc from up to terrestral cells, whle provdng blockng probablty of less than or equal to 4

6 Blockng probablty n satellte network Number of channels avalable n a satellte spot beam 4 Blockng probablty = Number of terrestral cells covered by a satellte spot beam Fgure 5 Blockng probabltes of the satellte system under dfferent operatng condtons V CONCLUSIONS ND FUTURE DIRECTIONS In ths study we modelled the channel holdng tme of the overflow traffc nto a satellte network from a terrestral network as a generalsed Erlang dstrbuton We also generated the block tr-dagonal rate transton matrx for the M/PH/n/n queue, whch we used to model the collectve channels of a sngle spot beam We nvestgated the performance of the system under dfferent confguratons Number of channels avalable n a satellte spot beam Number of terrestral cells covered by a satellte spot beam Fgure 6 Operatng ponts for satellte system We have shown that the operatng capacty of the system can be mproved from 785% to 846% by usng a spotbeam wth channels avalable For these condtons a sngle spot-beam can support overflow traffc from terrestral cells lthough the use of satellte networks mproves the operatng capacty of the system t has some drawbacks The man beng the ncrease n cost Further the QoS provded by satellte networks are less than what s provded by terrestral networks Therefore graceful degradaton and updradaton of QoS has to be provded durng handover from terrestral to satellte and satellte to terrestral respectvely Because of the ncreased cost assocated wth usng satellte channels, the tme the users spent n satellte network has to be mnmsed The handover process must contnuously montor the load condtons n terrestral networks and once enough 7 resources have been found to accommodate a user, the user must be mmedately handed back to the terrestral network The effects on ntra and nter satellte handover traffc on the channel occupancy tme has to be nvestgated to frmly support the assumptons made about the model The performance of the network can be further mproved by utlsng a more ntellgent handover processng mechansm, whch dentfes the probable target cells, both satellte and terrestral, and use early reservaton to reduce the blockng probablty for handover users[5-6] CKNOWLEDGEMENT Ths work was supported by ustralan government Cooperatve Research Centre program REFERENCES [] UMTS Task Force Report, tech rep, Mar 996 [] J P Castro and El-Hoyd, Space Segment Integraton n Future Moble Systems, Proc Internatonal Moble Satellte Conference, pp , 997 [] E Del Re, R Fantacc and G Gambene, Handover and Dynamc Channel llocaton Technques n Moble Cellular Networks, IEEE Trans Veh Technol, vol 44, no, pp 9-7, 995 [4] D Hong and S S Rappaport, Traffc Model and Performance analyss for Cellular Moble Rado Telephone systems wth Prortzed and Non Prortzed Handoff Producers, IEEE Trans Veh Technol, pp 77--9, ug 986 [5] S Rappaport, Modellng the Hand-off Problem n Personal Communcaton Networks, Proc IEEE Veh Technol Conf, pp 57--5, 99 [6] P Orlk and S Rappaport, Model for Teletraffc Performance and Channel Holdng Tme Characterzaton n Wreless Cellular Communcaton wth General Sesson and Dwell Tme Dstrbutons, n IEEE J Selected reas of Commun, vol 6, pp 788-8, June 998 [7] Y Fang and I Chlamtac, Teletraffc nalyss and Moblty Modellng of PCS Networks,'' n IEEE Trans Commun, vol 47, pp 6--7, July 999 [8] C Jedrzyck and V Leung, Probablty Dstrbuton of Channel Holdng Tme n Cellular Telephony Systems, Proc IEEE Veh Technol Conf, pp 47--5, May 996 [9] M Neuts, Matrx-Geometrc Solutons n Stochastc Models, John Hopkns Publshers, pp [] Jayasurya, D Green and J senstorfer, Modellng Servce Tme Dstrbuton n Cellular Networks Usng Phase-Type Servce Dstrbutons, Proc ICC (accepted for publcaton) [] S smussen, O Nerman, and M Olsson, Fttng Phase-type Dstrbutons va the EM algorthm, Scandnavan Journal of Statstcs, vol, pp 49-44, 996 [] V Ramaswam and D Lucanton, lgorthms for mult-server queue wth phase-type servce, Comm Statstc Stochastc Models, vol,no, pp 9-47, 985 [] V Naoumov, U Kreger and D Wagner, nalyss of a Multserever Delay-Loss system wth a General Markovan rrval Process, Proc st nternatonal Conf On Matrx- nalytc Methods (MM) n Stochastc Models, Mchgan, US [4] C Meyer, Stochastc Complmentaton, Uncouplng Markov Chans and the Theory of Nearly Reducble Systems, SIM revew, vol, no, pp 4-7, June 989 [5] Jayasurya et al, Protocol for Internetwork Handover between Terrestral UMTS and Satellte UMTS networks, usng ntellgent systems, Proc IEEE Int workshop on Intellgent sgnal Process and Commun systems, pp 47-4, Nov 998 [6] Jayasurya and J senstorfer, Handover Management n Thrd Generaton Moble Communcaton Systems, n Proc SoftCom, pp , vol, Oct