# Application of Network Calculus to General Topologies

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Network calculus is a general paradigm for the provision of quality of service (QoS) in communication networks.

The main principle of network calculus is to show that if all the input flows to a network satisfy a certain set of constraints, then so do all the flows within the network. The formulation of the constraints is simple enough to allow the computation of bounds on various performance measures, such as delay and queue length, at each element of the network.

Network calculus is known to apply in general only to feed-forward routing networks, i.e., networks where routes do not create cycles of interdependent packet flows. In this project, we address the problem of using network calculus in networks of arbitrary topology. For this purpose, we introduce a novel algorithm, called turn-prohibition (TP), that breaks all the cycles in a network and, thus, prevents any interdependence between flows. We prove that the TP-algorithm prohibits the use of at most 1/3 of the total number turns in a network, for any network topology. Using analysis and simulation, we show that the TP-algorithm significantly outperforms other approaches for breaking cycles, such as the spanning tree and up/down routing algorithms, in terms of network utilization and delay bounds. Our simulation results also show that the network utilization achieved with the TP-algorithm is within a factor of two of the maximum theoretical network utilization, for networks of up to 50 nodes of degree four. Thus, in many practical cases, the restriction of network calculus to feed-forward routing networks may not represent a significant limitation.

Breaking all the cycles in a network using turn-prohibition.