!" # !$ # %& '( # ) ' *!+11/06/03 EECS 228A S. Parekh & P. Varaiya,'- $ # $ . / 0 1 - 2- %334'% 2- %33,1 # .1 # 4'% 4 11/06/03 EECS 228A S. Parekh & P. Varaiya,'- $ 2 - - 4% # '/3 3 # 0! %/03 3 # ''4 3- 3 '4%% # '4 34% % ' - 4% !54%4%% % '4% 6!!7!- 28 4 4%!- 9: ; !- 4:59: 3'4 11/06/03 EECS 228A S. Parekh & P. Varaiya ,'- $ 2 +Basic Access Mechanism11/06/03 EECS 228A S. Parekh & P. Varaiya,'- $ 2 <,1 # .1 # $ 11/06/03 EECS 228A S. Parekh & P. VaraiyaInstability and Saturation ThroughputMeasured throughput with increasing offered load (in simulation)Analytically evaluate saturation throughput (i.e., when each station always have a packet to send)11/06/03 EECS 228A S. Parekh & P. VaraiyaMarkov Chain Model for Backoff WindowConsider any one stationLet s(i) {0, 1, …, m} be backoff stageLet b(i) {0, 1, …, w-1} be remaining backoff counterConsider embedded discrete time Markov Chain {s(i), b(i)}, i = 0, 1, 2, …at transition epochsNote that system time during i to i+1 may include idle slot time, packet transmission, or collision11/06/03 EECS 228A S. Parekh & P. VaraiyaMarkov Chain Model for Backoff Window - 2State transition diagramKey assumption is that each packet collides with constant and independent conditional collision probability p (regardless of number of retransmissions)11/06/03 EECS 228A S. Parekh & P. VaraiyaMarkov Chain Model for Backoff Window - 3 Solve for stationary probabilities i,j Let τ = Prob {station transmits in an arbitrary “slot time”} Also,where n = number of stations These non-linear equations can be seen to have a unique solution for τ and p))2(1()1)(21()21(21minmin0,000,mmiippCWCWppp −++−−=−===ππτ1)1(1−−−=npτ11/06/03 EECS 228A S. Parekh & P. VaraiyaThroughputLet Ptr= Prob {at least one transmission in an arbitrary “slot time”}Let Ps= {successful transmission | at least one transmission}S = normalize system throughput =ntrP )1(1τ−−=trnSPnP1)1(−−=ττ]slot time"" a of[length E]slot time"" ain tedn transmitinformatio [payload E11/06/03 EECS 228A S. Parekh & P. VaraiyaThroughput – 2Conditioning on “time slot” type, we getE[P] = Average packet sizeσ = Idle slot time (system slot time)TS= Average time channel is sensed busy due to successful transmissionTC= Average time channel is sensed busy due to collisionCStrSStrtrtrSTPPTPPPPEPPS)1()1(][−++−=σ11/06/03 EECS 228A S. Parekh & P. VaraiyaThroughput - 3Basic access:where H = (PHY + MAC) header,δ = propagation delayE[P*] = average length of longest packet in collisiont)ack timeou(neglect ][][*δδδ+++=++++++=DIFSPEHTDIFSACKSIFSPEHTbasCbasS11/06/03 EECS 228A S. Parekh & P. VaraiyaThroughput - 4RTS/CTS access:Threshold based RTS/CTS scheme can also be analyzed in a similar way neglecting collisions involving more than two packet timeout)CTS(neglect ][δδδδδ++=++++++++++++=DIFSRTSTDIFSACKSIFSPEHSIFSCTSSIFSRTSTrtsCrtsS11/06/03 EECS 228A S. Parekh & P. Varaiya Model ValidationCompare results from a C++ simulator of 802.11 MACConsider 1 Mbps FHSS version11/06/03 EECS 228A S. Parekh & P. VaraiyaMaximum Saturation ThroughputFormula for S can be rearranged asNote TS, TC, E[P], and σ are constantsMaximizing f(τ), we getστττττ/ where)1()1()1()( where)(1][***1CCCnCnCSTTTTnffTTPES=−−−−=+−=−2/1*CTn≈τ11/06/03 EECS 228A S. Parekh & P. VaraiyaMaximum Saturation
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