Contents & objectives

Transcription

1 S Networ Access 3 cr Medum Access Protocols for Wreless Networs Lecturer: Prof. Ru Jäntt Course assstants: B.Sc. Mrza Alam & M.Sc. Shear Neth Contents & objectves The course ams at provdng the students the fundamentals pacet orented wreless communcaton systems. The focus s on the performance analyss of medum access control protocols MAC. Commonly utlzed MAC protocols wll be brefly revewed and ther performance dscussed. S Networ Access 2

2 Course materal Boo: R. Rom and M. Sd, Multple Access Protocols - Performance and analyss, Sprnger-Verlag, Artcles: G. Banch, "Performance Analyss of the IEEE 802. Dstrbuted Coordnaton Functon," IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, VOL. 8, NO. 3, MARCH pdf + ohters S Networ Access 3 Tentatve schedule Wee Lecture Exercses Computer exercses Homewor 3 L Introducton, stochastc processes 4 L2 Traffc models M/G/ queues E Queung theory 4 L3 Conflc free access 5 L4 Dynamc conflct free access & IEEE E2 Conflct free MAC 5 L5 ALOHA 6 L6 Random access n cellular systems E3 ALOHA protocols 6 L7 CSMA & IEEE802. Analytcal wor 7 E4 CSMA C Computer # 7 L8 IEEE 802. and e 8 E5 Bacoff & Burstng C2 Computer #2 Smulaton wor 8 L9 Collson resoluton 9 E6 Collson resoluton C3 Computer #3 9 L0 IEEE Homewor deadlne 0 S Networ Access 4 2

3 Homewor There are two homewor problems One paper and pencl type of problem One computer smulaton problem Homewor problems are not mandatory, but hghly recommended. They can gve up to 0 extra ponts to the exam S Networ Access 5 Lecture. Introducton to medum access control Recaptulaton of stochastc processes and queung theory S Networ Access 6 3

4 Medum access control Wreless data networs WAN MAN Sensor networ BAN LAN PAN Scatter net S Networ Access 8 4

5 Protocol archtecture L7-L6 Applcaton IEEE 802 Standardt IETF Suostuset L4 L3 Our focus L2 TCP/UDP IP MAC LLC Bluetooth, 802., 5. Master-Slave 802.*, 5.4 CSMA/CA, TDMA OSI HDLC:n varantt L PHY Bluetooth, 802., 5. FH 802., b, 5.4 DSSS 802.a, OFDM S Networ Access Multcarrer UWB 9 Medum access control Wreless transmsson s broadcast n nature. That s more than a sngle recever can potentally receve every transmtted message. Transmssons over a broadcast channel nterfere, n the sense that one transmsson concdng n tme wth another may cause none of them to be receved. The success of a transmsson between a par of nodes s not ndependent of other transmssons. To mae a transmsson successful nterference must be avoded or at least controlled. The channel s a shared resource whose allocaton s crtcal for proper operaton of the networ. The schemes used for channel access are nown n lterature as Multple Access Protocols (MAC). Rado range Recever Transmtter Reuse dstance S Networ Access 0 5

6 Medum access control protocols The tas of the Medum Access Control (MAC) protocol s to dvde the resources between the rado lns such that Interference s avoded or ept at controlled level Utlzaton of the rado resources s maxmzed Qualty of servce QoS dfferentaton among the flow classes s acheved Farness nsde a QoS class s mantaned S Networ Access Medum access control protocols The operaton of the MAC protocol can be Centralzed such that sngle entty controls the resource dvson among the rado lns leadng to conflct free access Decentralzed such that each ln maes transmsson decsons ndependently leadng to contenton based access Contenton schemes dffer n prncple from conflct-free schemes A transmttng user s not guaranteed to be successful. The protocol must prescrbe a way to resolve conflcts once they occur so that all messages are eventually transmtted successfully. S Networ Access 2 6

7 Conflct free access In conflct free protocols, the resource allocaton can be Statc - not dependent on the traffc or channel condtons (TDMA, FDMA, F/TDMA, OFDMA, CDMA, OFCDMA, ) Dynamc based on demand and/or channel condtons Toen passng Channel reservaton (satellte systems, IEEE , ) Dynamc schedulng (UMTS R99, WMAX, ) Channel dependent opportunstc schedulng (e.g. CDMA2000 xev-do/dv, HSDPA, LTE) S Networ Access 3 Contenton based access In contenton based protocols, the conflcts caused by colldng pacets (nterference) must be resolved. Conflct resoluton methods can be dvded nto Statc - the actual behavor s not nfluenced by the dynamcs of the system. The transmsson schedule for the nterferng users can be Fxed: based on node IDs or prortes Probablstc: schedule s chosen from a fxed dstrbuton (p-persstent CSMA) Dynamc the actual behavor of the system depends system dynamcs. Transmsson schedule could be determned by the tme of the arrval Probablstc: Transmsson schedule depends on the number of colldng pacets (BEB n IEEE802.3 and IEEE802.) S Networ Access 4 7

8 Classfcaton of MAC protocols Medum Access Protocols Contenton Conflct free Dynamc Resoluton Statc Resoluton Dynamc Resoluton Statc Resoluton Tme of Arrval Node ID/ prortes Toen passng Probablstc Probablstc Reser- Vaton & Schedulng Opportunstc Fxed resource allocaton S Networ Access 5 Medum access control protocols The ssues affectng the performance of the channel access Connectvty Can all the nodes hear each other or are there hdden termnals? What s the networ topology? Sngle hop, mult-hop (mesh/ad hoc) Channel type What s the requred Sgnal-to-Interference rato for correct recepton? Is there possblty for capture n case of collsons? Do protocol messages get lost due to fadng? Synchronsm Is the networ synchronzed,.e. slotted or can transmssons start and end at arbtrary tme nstances. Feedbac nformaton Can collsons be detected? Can the colldng nodes be dentfed? How much nformaton can be shared among the nodes? Is correct recepton acnowledged by the recever? Traffc Is the message sze fxed or does t vary? Is pacets generated randomly or wth steady rate? Can transmsson buffers assumed to be saturated (TCP tends to saturate buffers) or are they lely to be empty at tmes? User populaton Is the number of users fxed or random? Can t be nown by the system? Bufferng capablty How many pacets can the nodes buffer? Wll pacets be lost due to buffer overflow? S Networ Access 6 8

9 Other relevant courses Smulaton tools S Networ smulaton 5 cr Mathematcal tools S Queue Theory 5 cr Traffc modelng and performance analyss S Teletraffc theory 5 cr Conflct free access S Rado Resource Management Methods 3 cr S Networ Access 7 Stochastc processes and queung theory 9

10 Stochastc processes A stochastc process s a set of ndexed random varables { Xt (, ω), t T, ω Ω} The ndex set t T s called parameter space of the process Each ndvdual random varable s a mappng from the sample space to set of real (or complex) numbers. A parameterzed set X(t) correspondng to a sample ω s called realzaton/trajectory/path of the process. ω X(t,ω) S Networ Access 9 t realzaton Stochastc processes State-space of the process s a set of values that X() tmay obtan. State space s dscrete, f the number of states s fnte or numerable. The correspondng stochastc process s called dscrete tme process/sequence/chan { X( t )}, t { t0, t, t2,... } State space s contnuous, f the number of states s nnumerable. The correspondng stochastc process s called contnuous tme process/sequence/chan X(), t t (0, ] S Networ Access 20 0

11 Marov-processes Marov property: The state of the process at tme n depends only on ts state at the prevous tme nstance { X ( tn+ ) = xn+ X ( tn) = xn X ( tn ) = xn X ( t) = x} ( ) ( ) Pr,,..., { } = Pr X tn+ = xn+ X tn = xn Marov-Process: The process stays n a state x n random tme nterval after whch t changes t state randomly accordng to certan state transton probabltes. Marov-Process has the Marov property, f the state tme dstrbuton of the process s memoryless. That s, transton s allowed to tae place every tme nstant. Contnuous tme Marov-Process: State tme dstrbuton s exponental Dscrete tme Marov-Process: State tme dstrbuton s geometrc t + t n S Networ Access 2 Other related processes Sem-Marov process: State tme dstrbuton can be arbtrary. At the nstance of state transtons, the process behaves as Marov chan. Imbedded Marov-chan, Sem-Marov process observed at state transton tmes. Random wal/process wth ndependent ncrements: Locaton of a partcle movng n space: Next poston=prevous poston + random varable Sn = S, 0 n + Xn S0 = where X,X 2, s a sequence of ndependent dentcally dstrbuted random varables, n s the number of state transtons S Networ Access 22

12 Other related processes Renewall/recurrent process: Related to the random wal, but nstead of poston, we nterested n countng the number of transtons X(t) that tae place as a functon of tme t. I.e. X(t) s a random varable that states the number of transtons that have taen place n tme nterval t. X(t) t Transton ξ(t) S Networ Access 23 Classfcaton of stochastc processes f τ (t) probablty densty functon of tme spent n a state p j transton probablty q state transton rate Sem Marov Process f τ (t) arbtrary p j arbtrary Marov Process f τ (t) memoryless p j arbtrary Brth-death process f τ (t) memoryless p j =0 for -j > Random wal f τ (t) arbtrary p j = q j- Posson process Renewal process f τ (t) arbtrary q = S Networ Access 24 2

13 Dscrete-tme Marov chans Defnton: The sequence of random varables X,X 2, forms a dscrete-tme Marov chan f for all n (n=,2, ) and all possble values of the random varables we have that { Xn+ = xn+ Xn = xn Xn = xn X = x} = { Xn+ = xn+ Xn = xn} Pr,,..., Pr The state varable x n = mples that the state of the system was E at tme slot n. S Networ Access 25 Dscrete-tme Marov chans Marov chan s sad to be homogenc (statonary), f state transton probabltes are ndependent of tme ndex. Pr{ Xn+ = j Xn = } = Pr { Xm+ = j Xm = } = pj m, n For homogenc Marov chan, the state transton probablty from state E : X n =j to state E j : X n+ = can be defned as: p Pr X = j X = { } j n n S Networ Access 26 3

14 Dscrete-tme Marov chans Assume that the state space s ndependent of the tme ndex n. Probablty that the system s n state E j at tme nstant n+m (X m+n =j) condtoned that t was n state E at tme m (X n =) s n n m j Pr{ m+ n = m = } = j = 0 p X j X p p Chapman-Kolmogorov equaton If there exsts an nteger m 0 such that p j m0>0, the Marov chan s sad to be rreducble. Let A denote the set of all states n a Marov chan. A subset A A s sad to be closed f no one-step transton s possble from any sngle state n A to ts complement A C =A\A. If A consst of a sngle state E j, the state s called absorbng state. If A s closed and does not contan any proper closed subsets, then A forms rreducble sub- Marov chan. S Networ Access 27 Dscrete-tme Marov chans The chan s rreducble f p > 0, j j E_3 s absorbng state f pj > 0, 3 p33 = p = 0 32 E_2 and E_3 form an rreducble sub-marov chan f p > 0, (, j) (2,) j p 2 = 0 p 0 p E 0 E E 2 E 3 p0 p2 p 22 p 23 p 32 p 33 S Networ Access 28 4

15 Dscrete-tme Marov chans Probablty that the chan returns to state E : ( n ) Pr ( n f = X = X = = p ) wth n steps { + } n m m ( n) = f n= f at all If f = Marov chan s called recurrent; otherwse t s called transent. If the ntal state s revsted n regular tme ntervals, the chan s sad to be perodc; otherwse t s called aperodc (non-perodc). Mean recurrence tme of state E ( n) =Recurrent null M = nf <Recurrent nonnull n= S Networ Access 29 Dscrete-tme Marov chans Marov chan s Ergodc stochastc process f t s aperodc, recurrent f = and recurrent nonnull M < Probablty that the system s n state E at tme nstant n ( n) π = Pr X = State probablty { } n Theorem. In rreducble, aperodc, homogeneous Marov chan, the lmt value π = lm π ( n) n fulflls ether a) f < ta M = π = 0 b) f =, M < π = = π jp j π = M for all (for all states E ) j S Networ Access 30 5

16 Dscrete-tme Marov chans If the number of states s fnte, the state probabltes can be solved from the followng set of lnear equatons π = = π jp j M j π = Defne ) π = ( π... π m Row vector contanng state probabltes P = ( p j ) state transton probablty Non-negatve π= πp Equaton for left egenvalues of P State probabltes are defned by the (left) Perronegenvector of the state transton matrx P that fulflls π = S Networ Access 3 Dscrete-tme Marov chans The state transton matrx P has the followng propertes P s a nonnegatve matrx P 0 The largest egenvalue n modulus ρ(p) s equal to : λx = xp ρ( P) = max{ λ } =, λ = The row and column sums of P are equal to pj =, pj = j If the chan s rreducble, then also P s an rreducble matrx, and the Perron egenvector can be taen to be strctly postve π= πp π >0 S Networ Access 32 6

17 Dscrete-tme Marov chans The state probablty can be solved smply by usng the power method for solvng the Perron egenvector π( n) P 0.5 π( n + ) = T π( n) P π(0) > = (... ) 0.3 Example 0.25 P=[...8;.3.3.4;.7.2.]; 0.2 P=rand(,3); 0.5 I=ones(sze(P)); Iteraton for =:0 P(+,:)=P(,:)*P/(P(,:)*P*I'); end; plot(0:0,p) π π 2 π 3 S Networ Access 33 Some useful tools Characterstc functon and moment generatng functon Probablty generatng functon 7

18 Characterstc / moment generatng functon Moment generatng functon = Fourer-transformaton of the probablty densty functon ω ( ) { } X ωx ψ ω = E e = e p( x) dx, = Inverse Fourer-transform ω x p( x) = ψ ( ω) e dω 2π th dervatve of the characterstc functon d ω x ψ ( ω) = ( x) e p( x) dx dω th moment d X = E{ X } = lmω 0 ( ) ψ ( ω ) dω S Networ Access 35 Laplace transform Consder random varable X wth support [0,]. That s, X 0 The pdf of the varable s p(x) Laplace-transform of the pdf * ( ) E { sx sx P s = e } = e p( x) dx Characterstc functon * ψ () s = P ω th moment ( ) d X = E X = P s ds * { } lm 0 ( ) s ( ) S Networ Access 36 8

19 Probablty generatng functon Dscrete random varable Pr{ X = } = p =0,,2,3, Probablty generatng functon = Z-transform of the probablty X ( ) { } G z = E z = z p, z = 0 Propertes of G(z) () G = p = ( ) = 0 = 0 = 0 G z < z p < p =, z S Networ Access 37 Probablty generatng functon Frst dervatve yelds expected value: d E{ X} = p = G( z) z= dz = 0 2nd dervatve yelds 2nd moment 2 d G z z ( ) z = = p z= = p p = E X dz E X 2 { } ( ) { } { } E X = G''() G'() = = = [ ] var X = G''() G'() G'() 2 S Networ Access 38 9

20 Probablty generatng functon Let {X } be a set of ndependent dentcally dstrbuted dscrete random varables. Pr{X =}=p for all. X G z = E z = z p G ( z) ( ) { } X X = 0 Let N be a dscrete random varable ndependent of {X }. Pr{N=}=q ( ) = { } = G E N N z z z q = 0 S Networ Access 39 Probablty generatng functon Consder a random sum N SN = X = Probablty generatng functon of S N : N X N S N = X E z N = E z N = E z = GX ( z) = { } { } [ ] SN { } [ ] Wald's Lemma E{S N }=E{N}E{X } G '( z) = G ' G ( z) G '( z) N { } [ ] ( ) G ( z) = E z = E G ( z) = G ( z) q = G G ( z) SN X X N X = 0 S ( ) N N X X { S } = G = G ( G ) G = G ( ) G = { N} { X } E '() ' () '() ' '() E E N SN N X X N X S Networ Access 40 N 20