We investigate the performance of multiple relays cooperative go back n automatic repeat request(MRC-GBn-ARQ) protocol with limited retransmission. An N +2-state Markov transition model is constructed for analyzing arbitrary packet transmission process with limited retransmission. Then the system's steadystate distribution is derived by using the Kolmogorov equations.Further, the mean packet transmission delay and startup delay are obtained respectively; the channel utilization is derived based on discrete-time Geom/G/1 queue model with startup. Also, we get the energy efficiency of the MRC-GBn-ARQ based on energy analytical model. Especially, the presented models are contrary to the classical ARQ protocols of always allowing infinite retransmission, and our analysis of the MRC-GBn-ARQ protocol with limited retransmission provides theoretical results for reducing the system's delay and energy consumption. Finally, analysis is validated through some numerical simulations.
Applicability of the angular properties of scatter elements as a tool to achieve improved slow light performance with small group velocity dispersion and large bandwidth in photonic crystal waveguides is investigated. A polyatomic photonic crystal waveguide, including two scatter elements with different geometrical shapes in each primitive cell, is proposed to investigate the feasibility of our method. Numerical results show that a versatile control of the dispersion relation of slow light modes, with large normalized delay-bandwidth products ranging from 0.2085 to 0.3394, can be obtained using a unique geometrical parameter.
