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Chapter 4Simulation and analytical modelling pperiod, T bp , plus an adjacent idle period, T ip , this gives:T +bc = T bp T ip(4.36)In Equation 4.36, the busy period ( Tbp) is defined to begin with the arrival of a datapacket to an idle channel and ends when the channel next becomes idle. Accordance toGross [23], this busy period can be found by using the ratio:TTbpipPr obability _ that _ the _ system _ is _ busy==Pr obability _ that _ the _ system _ is _ idle 1−λµλµSince the arrivals are assumed to follow a Poisson distribution, the idle period isexponential with mean1T ip= . Thus, the busy period is given by:λλµ11 1T bp =λ⋅ = =(4.37)λλ1−⋅ (1 − ) µ − λµµµBy substituting Equation 4.37 in Equation 4.36, the busy cycle results in:1 1 µ 1T bc = T bp + T ip = + ==(4.38)λµ − λ λ λ ⋅ ( µ − λ ) λ ⋅ (1 − )The number of packets served in a busy cycle is now considered. This value can beobtained by making the following analysis. If a data packet is served in X units, thenthe number of packets served in the busy cycle is given by dividing the average time ofthe busy period between the average time that it takes a packet to be served, so:1Tbpµ − λ 1 1Lbc = = ==X X X ⋅ ( µ − λ)1−(4.39)Finally, the number of packets served per second is then calculated as:1λL bc(1 −µ)Lx= =T bc1= λ(4.40)λ(1 − )λµTherefore our formulation now is complete and the throughput can be obtained by:λµµ4-29