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Page 2 Lecture Notes in Computer Science 2865 Edited by G. Goos ...

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Analyz<strong>in</strong>g Split Channel Medium Access Control Schemes 131and the radio propagation delays are negligible and that the traffic generated <strong>by</strong>active nodes (<strong>in</strong>clud<strong>in</strong>g retransmissions) is Poisson with rate λ.We establish the follow<strong>in</strong>g notation:– L c , L d : the length of a control packet and that of a data packet, respectively– k: the ratio of data packet length to the control packet length; i.e., k = L dL c– R, R c , and R d : the data rate of the entire shared channel, the control subchannel,and the data subchannel, respectively; i.e., R = R c + R d– r: the ratio of the data rate of the control subchannel to the data rate of theentire channel <strong>in</strong> the MAC-2 and the MAC-2R schemes; i.e., r = RcR = RcR c+R d– γ 1 , δ 1 : the transmission time of a control packet and the transmission timeof a data packet <strong>in</strong> the MAC-1 scheme, respectively; i.e., γ 1 = LcR and δ 1 =L dR= kγ 1– γ 2 , δ 2 : the transmission time of a control packet and the transmission timeof a data packet, respectively, <strong>in</strong> the MAC-2 or the MAC-2R schemes; i.e.,γ 2 = LcR c= γ1rand δ 2 = L dR d= kγ11−r– δ: normalized data packet transmission time <strong>in</strong> the MAC-2 and the MAC-2Rschemes; i.e., δ = δ2γ 2= kr1−r .3.2 Compar<strong>in</strong>g the Throughput of the MAC-1and the MAC-2 SchemesFig. 1 depicts an example of the operations of the MAC-1, the MAC-2, andthe MAC-2R schemes. We treat the packet transmission on the channel as arenewal process. To send a data packet successfully, two control packets and adata packet need to be transmitted on the shared channel after the contentionresolution period, which is the time between the end of the previous successfuldata transmission and the beg<strong>in</strong>n<strong>in</strong>g of current successful RTS/CTS dialogue.Accord<strong>in</strong>g to [11], the expected value of the normalized contention resolutionperiod <strong>in</strong> ALOHA channels (w) is a constant, when normalized Poisson trafficarrival rate is fixed. In the MAC-1 scheme, the expected time of a data packettransmission cycle is:t 1 = wγ 1 +2γ 1 + δ 1 =(w +2+k) · γ 1 .Thus, accord<strong>in</strong>g to the property of renewal processes, the throughput of theMAC-1 scheme can be expressed asS 1 = δ 1= kγ 1 k=t 1 t 1 w +2+k . (1)In the MAC-2 scheme, the available bandwidth is split <strong>in</strong>to two subchannels.Channel requests can only be transmitted after the current data transmissionends. The throughput of the MAC-2 scheme is a function of r. The expectedtime of a renewal cycle is( w +2t 2 = w · γ 2 +2· γ 2 + δ 2 =r+ k )· γ 1 .1 − r

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