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Chapter 4Simulation and analytical modelling p4.4.1 Mean access delay formulation for a single node scenarioFor the upstream direction, the Reservation Access mechanism of the DVB/DAVICMAC protocol can be modelled as a queuing system. The upstream timingrepresentation, depicted in Figure 4.13, permits a graphical view of the dynamic of ourqueuing system. This particular figure is shown for a first-come-first-serve orderservice. In this timing diagram the horizontal line just below the upstream channelrepresents the queue (at the NIU) and the horizontal line above the channel representsthe service facility. An arrow approaching the queue from below indicates that anarrival of a data packet has occurred (represented by A pk ). Conversely, arrowsemanating from the server indicate the departure of a data packet from the queue (D pk ).In this queuing system there are mainly two types of delays involved in the transmissionof a data packet, namely waiting delay in queue (W) and service delay (X). Additionally,when a packet departs from the server, there is a constant delay involved, which iscaused by the transmission delay and the propagation delay before the data packetreaches its final destination. Here, only the transmission delay of the last slot of thecurrent data packet is only considered. The transmission delay of the other data slotsform part of the service delay. Hence, the general equation to calculate the total meanaccess end-to-end delay,D ete , is given by:D ete X + W + DSlTx+=_D(4.4)propwhere X and Ware the mean of service and waiting delay, respectively.MCI 0MCI 1 MCI 2MCI 3MCI 4MCI 5MCI 6MCI 7MCI 8MCI 9ServerUpstreamChannelQueueD Pk0D Pk1D Pk2R D D R D DRDDW 1W 2A Pk0A Pk1A Pk2X 1X 2X 0Contention SlotRContention Slot withReservation RequestDData SlotFigure 4.13 – Upstream timing diagram.4-19