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This article focuses on the problem of quality of service mapping between layers in a cascade. Protocol stacks in telecommunications networks are composed of functional layers. QoS provision depends on the performance achieved at each layer and is based on functions performed at layer interfaces. In practice, QoS derives from reliable physical and link layers that can offer specific transport services to upper network layers. The data flows (or bundles of flows) generated by the upper layers (e.g., the network layers) are forwarded down to a physical interface that transports the information along a channel that provides, if possible, the expected QoS to the upper layers. The action is called vertical QoS mapping and poses many challenges for a communication scientist, in particular if it is applied to wireless interfaces. This article states the definition of vertical QoS mapping, proposes a formal separation between technology-dependent and technology-independent layers, models each functional layer as a battery of buffers, generalizes the relation between layers through a chain of buffers in a cascade, formalizes the theoretical problems of vertical QoS mapping, and suggests possible solutions that use dynamic bandwidth allocation schemes.