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Chapter 4Simulation and analytical modelling pS = λ ⋅ Pk , ∀ρ< 1(4.41)size4.4.3 Bounds on maximum system throughputSo far, we have formulated the mean access delay and the throughput for a single nodeconfiguration. However, for a larger number of nodes we have derived some boundsthat can be used to estimate the maximum system throughput sustainable by theDVB/DAVIC’s upstream channel. These bounds depend mainly on the traffic typesbeing delivered and on the maximum bandwidth assigned for contention and reservationaccess, as well as the contention resolution algorithm used. In this section we presentbounds for three different configurations. These bounds will play a vital role to validatemore complex traffic configurations in the following chapters.A simple bound on the maximum upstream throughput would be when only data slotsare being transmitted, so that 48 bytes out of 64 bytes are transmitting payload for anefficiency of (48/64=) 75%. This would be approached in theory if very large packetswere transmitted, so that the capacity of the contention-based access region wasnegligible. But in practice, part of the bandwidth is reserved for contention access, andthe efficiency heavily depends on the bandwidth assigned to this access mode.Therefore, the maximum system efficiency can be estimated by Equation 4.42.Smax_ l arg e _ packets48⋅RS= (4.42)64 ⋅ ( RSs + CSc)where RSs and CSs are the number of reservation and contention access slots describedper signalling frame, respectively.The simple bound of the maximum upstream throughput presented in Equation 4.42cannot be used to calculate the maximum throughput of variable packet sizes. This isbecause such estimation was based only on large packets being transmitted when mostof the bandwidth was allocated to the reservation-based access region and did not takeinto account the additional bandwidth that should be allocated to the contention-basedaccess region so as to resolve collision. In [96] and [98] a more efficient calculation toestimate the maximum throughput of a CATV network (based on the IEEE 802.144-30