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Chapter 4Simulation and analytical modelling pFor certain shared access methods such as the Slotted Aloha, splitting tree or TDMA themaximum normalised throughput is 1/e. 0.478 and 1 respectively [10].At the time of writing this dissertation no accurate analytical model for CATVprotocols, which deal with variable reservation access (queues with contention), hadbeen proposed. When modelling the hybrid DVB/DAVIC protocol, two areas requirespecial consideration:• Analysis of the contention resolution algorithm. We have focused here on thestability of contention resolution algorithms and the time to resolve collisions.• Variable bandwidth of the C-channel. This effect is a direct consequence on theabove feature and the CRA adopted. Depending on the offered load,⎡ MCI⎤CSsc ∈ ⎢ ⋅CC,CC⎥⎢⎣MCImax_slots ⎥⎦(4.2)where c is the bandwidth of the C-channel, MCI CSs is the minimum number ofcontention slots described per MCI frame, and MCI max_slots is the maximum numberof slots described in each MCI frame. The upper bound is realised when the cablenetwork is idle and every MCI frame consists only of contention slots, thus c = CC.The lower bound is realised when the cable network is in congestion and thebandwidth of the C-channel becomes the minimum number of contention slots perMCI frame times the number of MCI frames per second. Thus, the bandwidth of theR and F channels becomes,r + f = MCImax_−(4.3)slotsMCI CSsBy implication, the bandwidth of the R and F channels varies and is correlated to c.This variation is a function of the offered load and the efficiency of the contentionresolution algorithm, which specifies the number of successful transmissions in theC-channel. Therefore, even if the C-Channel was approximated by the SlottedAloha of TDM access algorithm, the throughput calculation proves problematic, asthe channel bandwidth is variable.4-16