通信网理论基础-第4章-网内业务分析-多址接入系统

4.1.4.2.−=≡∆•N4.2.1.4.3.4.4.4.4.1.−==≡−==≡≡≡∆=MA−=≡≡∆≡∆∆=MAC≡≡≡MAC∆∆≡MAC∆∆−=≡∆∆≡∆≡∆∆=≡≡∆≡=≡≡M≡∆∆≡∆∆=≡≡≡∆≡∆≡MAC∆∆=≡≡∆≡≡∆∆4.4.2.ALOHA−U1U2U3===λ=≡≡=≡≡≡=ALOHA−=P≡τ≡P1=λλ==Pa=trratrreratp−⋅=!)(=tatep−=0=≡tt∆vvvt-T0Pn-1PnPn+1tt+T0T0—nPnt—n1Pn1tT0—n1Pn1tT0≡p0=e-2a≡1-e-2a=r≡≡P1∆≡∆ara(1-e-2a)∆rae-2a(4-153)≡rmaxa0.5∆rmax0.5e-2×0.50.184≡ra00.511.522.533.544.5500.020.040.060.080.10.120.140.160.180.2a*exp(-2a)raar=18.4%≡≡≡∆∆∆≡aa0.5ar≈∆∆≡a0.5∆∆4.4.3.Slotted-ALOHA−=≡=≡=≡U1U2U3−=≡≡≡∆=e-a≡1-e-a=raa(1-e-a)r≡rae-a4156≡≡()∆a1r0.368∆∆≡ALOHAALOHA00.511.522.533.544.5500.050.10.150.20.250.30.350.4a*exp(-a)raar00.511.522.533.544.5500.050.10.150.20.250.30.350.4a*exp(-a)a*exp(-2a)raar4.4.4.CSMA−=CSMA==≡∆≡∆=−=CSMA-P≡≡∆=CSMA-NP≡∆∆∆=CSMA-p≡∆p∆(1-p)≡∆∆=CSMA-CD≡≡≡−CSMA-NP≡CSMA-NPε=ε=0≡∆∆∆1=BT≡a∆a∆aTI/1=≡IBTT+∆≡raaar+=+=1/1114-159∆∆a1∆1∆••=ε0≡≡εn∆t1t2……tn∆n+1∆t1012n-1nn+1t2tnYtn+1tttttt∆y=t1+t2+……+tnε∆y+tn+1ε≡)1(1)(0εεεaeadyyypy−−−==∫4-161≡ε++=1yTB≡εεεaIBeaayTTT−++=+++=+=11211∆y=0∆e-aεεae−≡εεεεaaaeaaeTer−−−++==)21(4-162≡ra0246810121416182000.10.20.30.40.50.60.70.80.91=0=0.01=0.05=0.1=0.5=1raar∆ε−≡≡≡=ε=0≡a1≡aTI/1=≡nPn=(1-e-a)n-1e-a∆n-1(1-e-a)n-1∆ne-a∆1nn•nnannaaBeenenT=−==∑∞=−−−11)1(≡aeTTTaIB1+=+=≡∆∆∆•••∆aaeae−−−1•aae−•ae−−1∆aPeaennnnaa+=−−+=∑∞=−−11)1(11≡aaaeaaaeaTar++=++=+=1)1(/1114-163∆a=1.03rmax0.54≡ra012345600.10.20.30.40.50.60.7CSMA-Praar=ε0≡aTI/1=≡)1(11)1(21εεε+−−+−−+=aaBeaeT≡IBTTT+=≡)1()1()1()1()1()1()1()1()1()1()1()1(1)1(11)1(1111)1(1εεεεεεεεεεεεεεεεεεεε+−+−−+−+−−+−+−−+−+−+−+−−+−+−−+++⋅⋅=++++=+−⋅−+++=aaaaaaaaaaaaaaaaaeaeeeeaeeeeeeeeaeeeen≡12)1()1()21(−+++++==+−−+−εεεεεaaeeeaaaTnraaa4-164≡ra00.20.40.60.811.21.41.61.8200.10.20.30.40.50.60.7=0=0.01=0.05=0.1=0.5=1=10CSMA-Praar≡rε-2-1.8-1.6-1.4-1.2-1-0.8-0.6-0.4-0.2000.10.20.30.40.50.60.7a=0.06a=0.1a=0.5a=1a=1.5a=2CSMA-Prepsilonlog(epsilon)r−(CSMA-CD)≡∆∆••∆≡(CSMA-NP-CD)≡aTI/1=≡[]))1(112)(1()1(εεεεεεaaaBeaaeeT−−−+−+−++=≡[]εεεεεaaIBeaeaaaaTTT2)1()22()1(21−−++−+−+=+=≡εεεεεεaaaeaeaaaaer2)1()22()1(2−−−++−+−+=4-165≡ε=0∆4-163≡ra0510152025303540455000.10.20.30.40.50.60.70.80.91=0=0.01=0.05=0.1=0.5=1CSMA-CDraar≡rε00.020.040.060.080.10.120.140.160.180.200.10.20.30.40.50.60.70.80.91a=3a=10a=20a=30a=40a=50CSMA-CDrepsilonepsilonr4.4.5.Polling−≡=#1#2#N=N≡P≡P−=≡≡∆∆≡∆=≡≡∆P∆∆≡∆−=≡P≡E≡T1P11E1P2E2P3PNENP1ε2ε2ε22NT≡∆11b∆b=P+2ε+E(4-167)∆ε∆2ε∆ε≡∆b=Tp≡TnnNnnNnppCp−−=)1(≡Tn1bNnbNbn=λ0≡NbNnNnnNNnnbNnNnTppeeppCepep]1[1)1(]1[]1[00000)(0−+−=−⋅−=⋅−=−⋅⋅−−=+⋅−=−∑∑λλλλ∆•0000!)(=−−=kTTekTeλλλT0•T•Te01λ−−T≡NNbepep)]1(1[100λλ−−−−=−4168≡λ0bNp=pbppNNbpNnNbnTnr+=+=+==4169≡λ0→∞p→1rmaxbr+=11max1170EPbr+++=+=ε21111max1170≡rmaxε∆P+E=0.05-10-8-6-4-202400.10.20.30.40.50.60.70.80.91repsilonlog(epsilon)r4.4.6.−a=≡r≈a(1-2a)≡r≈a(1-a)≡CSMAr≈a[1-(1+2ε)a]≡CSMAr≈a(1-εa)4172≡r≈a(1-εa)≡r≈a(1-ba/2)∆ε∆bpE•b=P+2ε+E(EPb++=ε2)=r≈a≡≡a2∆≡∆≡∆≡∆pE=a2≡ε∆CSMACSMA∆CSMA≡∆∆ε≡a∆∆−aa→∞=≡r≡∆∆∆=≡≡−ε=ε-3-2.5-2-1.5-1-0.500.5100.10.20.30.40.50.60.70.80.91CSMA-CDCSMA-NPCSMA-PSlotted-ALOHAPure-ALOHAPollingrepsilonlog(epsilon)r=≡ε∆≡ε∆−==≡∆∆T≡)(22pbNT+==ω4173≡ωr)1(2rbN−⋅=ω4174≡Nλ0Nλ0=a∆ω∆ωNb/2∆N∆∆=≡rrmax∆∆a∆r∆∆≡rrmax∆∆pR=(a-r)/a∆(a-r)∆a∆c∆kkckRp∆∑∞=−⋅⋅=−⋅=−=12)1()1(1)(kkraracararcarakcω4175∆NNaN=0λ∆∆=≡≡≡()