  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 (NC-ARQ),
two-mode-ARQ, and multilayer-ARQ. We propose an alternative QoS parameter
(instead of the commonly used moment generating function parameter) that
represents explicitly the target delay and the delay violation probability.
This also enables closed-form expressions for many of the studied systems.
Moreover, we use the recently proposed matrix-exponential distributed (MED)
modeling of wireless fading channels to provide the basis for numerous new
effective capacity results for HARQ.
