Effective Capacity of Retransmission Schemes: A Recurrence Relation Approach

We consider the effective capacity performance measure of persistent- and truncated-retransmission schemes that can involve any combination of multiple transmissions per packet, multiple communication modes, or multiple packet communication. We present a structured unified analytical approach, based on a random walk model and recurrence relation formulation, and give exact effective capacity expressions for persistent hybrid automatic repeat request (HARQ) and for truncated-retransmission schemes. For the latter, effective capacity expressions are given for systems with finite (infinite) time horizon on an algebraic (spectral radius-based) form of a special block companion matrix. In contrast to prior HARQ models, assuming infinite time horizon, the proposed method does not involve a non-trivial per case modeling step. We give effective capacity expressions for several important cases that have not been addressed before, e.g., persistent-HARQ, truncated-HARQ, network-coded ARQ, two-mode-ARQ, and multilayer-ARQ. We propose an alternative quality-of-service-parameter (instead of the commonly used moment generating function parameter) that represents explicitly the target delay and the delay violation probability. This also enables the closed-form expressions for many of the studied systems. Moreover, we use the recently proposed matrix-exponential distributed modeling of wireless fading channels to provide the basis for numerous new effective capacity results for HARQ.