Tumour Necrosis Factor alpha (TNF) initiates a complex series of biochemical events in the cell upon binding to its type R1 receptor (TNF-R1). Recent experimental work has unravelled the molecular regulation of the signalling complexes that lead either to cell survival or death. Survival signals are activated by direct binding of TNF to TNF-R1 at the cell membrane whereas apoptotic signals by endocytosed TNF/TNF-R1 complexes. Here we describe a reduced, effective model with few free parameters, where we group some intricate mechanisms into effective modules, that successfully describes this complex set of actions. We study the parameter space to show that the model is structurally stable and robust over a broad range of parameter values.