On the way to a wireless network calculus— The single node case with retransmissions,” Univ

During the last two decades, starting with the seminal work by Cruz, network calculus has evolved as a new theory for the performance analysis of networked systems. In contrast to classical queueing theory, it deals with performance bounds instead of average values and thus has been the theoretical basis of quality of service proposals such as the IETF’s Integrated and Differentiated Services architectures. Besides these it has, however, recently seen many other applications scenarios as, for example, wireless sensor networks, switched Ethernets, avionic networks, Systems-on-Chip, or even to speed-up simulations, to name a few. In this paper, in an attempt to improve the versatility of network calculus, we extend its reach to error-prone wireless links employing ARQ schemes. This is based on a stochastic extension of data scaling as introduced in [17]. Modelling the single node case 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 corrsponding to a certain number of retransmissions. Based on the description of each retransmission flow, probabilistic performance bounds for a wireless system with ARQ can be derived. To illustrate the actual procedures, a numerical example wraps up the paper