Performance modelling and analysis of unreliable links with retransmissions using network calculus

During the last two decades, starting with the seminal work by Cruz, network calculus has evolved as an elegant system theory for the performance analysis of networked systems. It has found numerous usages as, for example, in QoS-enabled networks, wireless sensor networks, switched Ethernets, avionic networks, Systems-on-Chip, or, even to speed-up simulations. One of the basic assumptions in network calculus is that links are reliable and operate loss-free. This, of course, is a major abstraction from the reality of many application scenarios, where links are unreliable and often use retransmission schemes to recover from packet losses. As of today, standard network calculus cannot analyze such links. In this paper, we take the challenge to extend the reach of network calculus to unreliable links which employ retransmission-based loss recovery schemes. Key to this is a stochastic extension of the known data scaling element in network calculus [21], which can capture the loss process of an unreliable link. Based on this, modelling links with retransmissions results in a set of equations which are amenable to a fixed-point solution. This allows to find the arrival constraints of each flow that corresponds to a certain number of retransmissions. Based on the description of each retransmission flow, probabilistic performance bounds can be derived. After providing the necessary theory, we illustrate this novel and important extension of network calculus with the aid of a numerical example.