Giuseppe Bianchi, Ilenia Tinnirello

Transcription

1 Capacity of WLAN Networs

2 Summary Ł Ł Ł Ł

3 Arbitrary networ capacity [Gupta & Kumar The Capacity of Wireless Networs ] Ł! Ł "!

4 Receiver Model Ł Ł # Ł $%&% Ł $% '( * &%* r (1+ r Ł + 1 / n 1 / n log n

5 Area consumption for each TX Ł Ł,,

6 Area consumption for each TX Ł Ł,,

7 Area consumption for each TX r1 > r1 >(1+ r1 Ł Ł,,

8 Area consumption for each TX > r1 Ł Ł,,

9 Area consumption for each TX > r2 Ł Ł,,

10 Area consumption for each TX > (r1+r2/2 Ł Ł,,-

11 Area consumption for each TX > (r1+r2/2 Ł./

12 Area consumption for each TX r1/2 r2/2 Ł./

13 Area consumption for each TX Ł./0, Ł, 1 2

14 Bound on consumption area Ł 31 Ł 442 Ł 56/-1 2

15 Area Constraint Ł 7 6,4 n / 2 i1 2 1 ( r i 4 4 A

16 Channel Constraints Ł ' 5 / ' (5 / (95 65 Ł - : 1 Ł + & '/9 ;& &.: Ł./5& nt b1 h( b h1 1( H h th hop of bit b is on channel m in slot s nt b1 h( b n WT 2 W m n 2

17 Space Constraints Ł Ł < r( h, b 16 Ł &,0 5&./../ 65& Ł &4& nt h( b b1 h1 2 2 r ( h, b 16 AWT nt h( b b1 h1 r 2 ( h, b H 16AWT 2 H

18 Convexity Convexity nt b b h h nt b b h h H WT A H b h r b h r H 1 2 ( ( 1 16, (, ( 1

19 Space + Channel Constraints + Convexity Ł - $ 4 1 H nt h( b b1 h1 r( h, b 2 nt h( b b1 h1 r 2 ( h, b H 16AWT 2 H nt R nt h( b b1 h1 r( h, b 16AWT 2 H

20 Capacity upper bound Ł = 5&./ 4 nt R 16AWT 2 H WT 8An 8A W 1 R n Ł & W / n Ł > 2 W / n log n

21 Conclusions Ł? n / log n n Ł & Ł + 3 #,5> B

22 Performance Analysis of single-hop DCF

23 Throughput Ł Represents the system efficiency (different definitions. Ł Overheads: bacoff, monitoring times, collisions, headers, ACK/RTS/CTS. Payload bits transmitted in average per each second Fraction of the channel time used for payload transmissions (normalized throughput

24 Delay Ł Time required for a pacet to reach the destination after it leaves the source. Ł Three different components: queue delay, service access delay, transmission delay. queue access tx

25 Saturation Analysis fered load meas. throughput of 0,85 0,80 0,75 0,70 0,65 0,60 0,55 offered load (nominal offered load (measured throughput (measured simulation time (seconds Fixed number of stations, varying arrival rate Arrival rate higher than maximum throughput -> transmission queues build up until saturation (always full Saturation throughput : limit reached by the system throughput as the offered load increases

26 DCF Overheads

27 Frame Transmission Time Ł Let R be the data rate and R* the control rate. Ł Let P be the MSDU size [byte]. 20*8/R* 14*8/R* + 28*8/R P*8/R 14*8/R* T FRAME = T MPDU + SIFS + T ACK +DIFS T FRAME = T RTS + SIFS + T CTS +SIFS + T MPDU + SIFS + T ACK +DIFS

28 different rates (P=1500 bytes RTS/CTS Basic RTS/CTS Basic Tra nsmssion Time (use c DIFS Ave Bacoff RTS+SIFS CTS+SIFS Payload+SIFS ACK

29 Protocol Overhead Ł Suppose to have just a single station, with a never empty queue Ł Each transmission is originated after a bacoff counter expiration Ł Since no collision is possible, and no channel error is considered, each bacoff is extracted in the range [0, CW min ] TX CYCLE A B C D ENTIRE TX PROCESS Ł Different transmission cycles on the channel, composed of: 1 frame transmission time, which depends on the MSDU size; 2 random delay time, which depends on the bacoff extraction.

30 Max Throughput Computation TX CYCLE A B C D b B b C b D ENTIRE TX PROCESS Ł From the throughput definition: S P i T FRAME b i i Ł After each transmission, bacoff counters are regenerated. From Renewal Theory: S E[ T E[ P] ] E[ b] FRAME Ł In the case of fixed pacet size, given CW min : S T FRAME P CW min / 2

31 Max Throughput Max Throughput (normalized (normalized! " # $ % & ' ( * +.-, / / , / /

32 Saturation Throughput Analysis

33 DCF Bianchi s model approach Step 1: Discrete-Time model of bacoff for tagged STA bacground STAs summarize into a unique collision probability value p bacground STA Step 2: find transmission prob. t Result: t versus p non-lin function Step 3: assume bacground STAs behave as tagged STA, i.e. transmit with probability t Result: p versus t non-lin function Step 4: solve non linear 2eqs system Tagged STA Finite number n of STA Step 5: find performance figures Throughput, Delay

34 Discrete Not Uniform Time scale Bacoff for station A FRAME ACK SIFS DIFS A Slot time = Time interval between two consecutive bacoff time counter decrements: idle bacoff slot busy time + DIFS + 1 bacoff slot

35 DCF as -persistent CSMA Model Time. Actual Time -In each system slot, each station accesses with probability (and does not access with probability 1-. -Each system slot can assume 3 different sizes: idle slot, successful slot, collision slot. -The ey assumption is that is fixed slot by slot (and then also the collision probability p.

36 Channel Access Probability Given the time scale, 1 transmission every bacoff + 1 slot slots 7 slots 10 slots Note that the access cycle length in discrete time slot is not related to the actual channel time (e.g., the last cycle is the shortest cycle according the channel time, but the longest one according to the model time Whenever W 0 =W 1 =..=W R =W, from renewal theory: =1 / (W/2+1 = 1/ (E[W] + 1 (alternatively, 1/ =E[W]+1 In general, the access time depends on the bacoff stage, i.e. on the number of consecutive collisions.. N.B. Access cycle = transmission cycle for a given station

37 Formal derivation Formal derivation i s TX P TX i s P TX P i s P i s TX P i s P TX i s P TX P / ( / ( ( ( / ( ( / ( ( R o i R i i s TX P TX i s P TX P i s P i s TX P 0 / ( / ( 1 ( 1 ( / (

38 Bacoff stage Probablity Suppose to now the collision probability p: We are in stage i if we were in stage i-1 in the previous attempt and we experienced a collision: Pr(s=i/TX=Pr(s=i-1/TX p; After a success or after R collisions, we come bac to stage 0. Then, this probability has a geometric distribution: i (1 p p P( s i TX i(0,1,... R R1 1 p 1-p p p p R 1-p 1-p 1

39 Channel Access Probability (2 We can finally express the channel access probability as a function of the collision probability p and of the average bacoff values W i /2: 1 p 1 p 1 W R i i p 1 R 1 i0 2 Note: does not depend on the bacoff value distribution, but only on the average value!!!

40 How much is p??? The conditional collision probability p, i.e. the probability to experience a collision in a given slot, given that the tagged station is transmitting, is the probability that at least one of the other N-1 stations is accessing the channel. If we assume that all the stations have the same behavior, and then access the channel with probability, it is easily expressed as: p=1 (1- N-1

41 From &p to Throughput Performance S P E[ T s SUCC Ps E[ P] ] P E[ T c COLL ] P idle Ps E[ P] E[ slot] P N-1 s : Pr success in a contention slot = N (1- =N (1-p P idle = 1- (1- N P c = 1-P S -P idle

42 Delay Computation Ł Very easy, via Little s Result! Clients: Contending pacets which will be ultimately delivered Server: DCF protocol Delay: system permanence time D = E[N] / acc Ł In static scenarios and saturation: A new client is accepted if the pacet is transmitted before the retry limit expiration Arrival rate : e new pacet arrives to the system : When a pacet is successfully transmitted When a pacet is dropped because of a retry limit expiration Accepted traffic acc =throughput! acc ST1 ST4 ST2 ST3 ST5

43 Retry Limit = Ł = Throughput [p/s] D N S / N E[ P] N P S E[ slot] ST2 ST4 ST1 ST5 ST3

44 Ł E[N] = N(1-p lost Retry Limit = R D E[ N] acc N(1 plost S / E[ P] acc ST2 ST4 ST3 R ST1 ST5

45 Pacet loss probability Pacet loss probability Ł In a generic contention slot, with access probability, the pacet loss probability depends on the number of already suffered collisions: R i lost i s P i s lost P p 0 ( / ( i 0 i R p i s lost P 1 / ( 2 / (1 1 (1 / ( / ( ( ( 1 i R i W p p p i s TX P TX i s P TX P i s P

46 How to tae into account the 2-way or 4-way access mode? Ł By simply defining opportunely frame transmission times and collision times. Assuming fixed MPDU size: BASIC ACCESS: T FRAME = T MPDU + SIFS + T ACK + DIFS T COLL RTS/CTS: = T MPDU + DIFS T FRAME = T RTS + SIFS + T CTS +SIFS T MPDU + SIFS + T ACK + DIFS T COLL = T RTS + DIFS Note: The channel access probability and the collision probability do not depend on the employed access mode!

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49 EDCA model

50 CW differentiation < 5 (1 2 p (1 2(1 2 p p R 1 (1 W p (1 R p 1 (1 (2 p R 1,13 p C (1 r 1 1 (1 n r

51 Per Per-class Throughput class Throughput < & (1 1 1 ( 1, 1 C r r n r n success p n n P r & c C r success C r n r C r s success C r n r success T P T P E P P S r r ( (1 1 ( (1 ] [ (

52 Throughput Ratio Throughput Ratio ( ( P j P S S success success j +4 2 W 1 2 j j j j j j j n W W n W n W n n n S S (1 (1

53 Performance Optimizations

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56 Throughput vs CWmin P=1000 bytes

57 And in actual networs? Ł CW opt =f(load, AIFSN, but.. Load estimation Function f evaluation f depends on the traffic sources, which need to be estimated and modeled! complex f expressions for notsaturated traffic sources no close expression for every traffic conditions..

58 How to compute CWopt? Ł Our solution: not fixed CWmin, but adaptive corrections on the basis of the channel monitoring status, to force idle slots and collision equalization [Gallagher]? CWmin = CWopt CWmin(t = CWmin(t-1 + CW CW has an opposite effects on the two different events of channel wastes of the access protocol: BACKOFF, COLLISIONS Large CW -> too long bacoff expirations Small CW -> too high collision probability Optimal CW as a tradeoff between these channel wastes different tuning algorithms are possible based on: If (COLLISIONS > BACKOFF -> increase the CWmin If (BACKOFF > COLLISIONS -> decrease the CWmin No estimation of the system status, but simple channel monitoring of BACKOFF and COLLISIONS Intrinsically suitable for dynamic networ conditions

59 An example Ł Ł Assume that every 10 seconds a new data station joins the networ.. At each beacon: double the contention window at each beacon in which the collisions overcome the bacoff times; half the contention window at each beacon in which the bacoff overcomes the collision times time

60 An example Ł Ł Assume that every 10 seconds a new data station joins the networ.. At each beacon: double the contention window at each beacon in which the collisions overcome the bacoff times; half the contention window at each beacon in which the bacoff overcomes the collision times time

61 An example Ł Ł Assume that every 10 seconds a new data station joins the networ.. At each beacon: double the contention window at each beacon in which the collisions overcome the bacoff times; half the contention window at each beacon in which the bacoff overcomes the collision times time

62 References: Ł G. Bianchi, Performance Analysis of the IEEE Distributed Coordination Function, IEEE Journal on Selected Areas in Communications, vol. 18, no. 3, March 2000 Ł G. Bianchi, and I. Tinnirello, Remars on IEEE DCF Performance Analysis, to appear in IEEE Communication Letters Ł F. Cali, M. Conti, and E. Gregori, "Dynamic Tuning of the IEEE Protocol to Achieve a Theoretical Throughput Limit," IEEE/ACM Trans. Networing (TON, vol. 8, No. 6, Dec Ł Giuseppe Bianchi and Sunghyun Choi, "IEEE Ad-Hoc Networs," a chapter in Wireless Ad hoc and Sensor Networs, Ed. Kluwer, to be published in 2004.