Delay Optimal Multichannel Opportunistic Access

The problem of minimizing queueing delay of opportunistic access of multiple continuous time Markov channels is considered. A new access policy based on myopic sensing and adaptive transmission (MS-AT) is proposed. Under the framework of risk sensitive constrained Markov decision process with effective bandwidth as a measure of queueing delay, it is shown that MS-AT achieves simultaneously throughput and delay optimality. It is shown further that both the effective bandwidth and the throughput of MS-AT are two-segment piece-wise linear functions of the collision constraint (maximum allowable conditional collision probability) with the effective bandwidth and throughput coinciding in the regime of tight collision constraints. Analytical and simulations comparisons with the myopic sensing and memoryless transmission (MS-MT) policy which is throughput optimal but delay suboptimal in the regime of tight collision constraints.

💡 Research Summary

The paper addresses the problem of minimizing queueing delay for a secondary user that opportunistically accesses multiple continuous‑time Markov channels in a hierarchical cognitive radio network. Each primary channel is modeled as an independent on/off continuous‑time Markov process (busy/idle) with exponential holding times. In every time slot the secondary user senses exactly one channel, and if the sensed channel is idle it may transmit a fixed‑size packet; a transmission collides with the primary user if the primary is actually busy. A long‑term average collision constraint γ (maximum allowable conditional collision probability) must be satisfied for every primary channel.

Instead of the usual average throughput metric, the authors adopt effective bandwidth as the performance measure. Effective bandwidth a(ε,b) is defined as the largest constant arrival rate a such that, for a buffer of size b≫1 and an overflow probability bound ε, the steady‑state queue length exceeds b with probability at most ε. Using large‑deviation theory, the overflow probability decays as exp(−θ(a)·b), where θ(a) solves aθ + Ψ_R(−θ)=0 and Ψ_R(·) is the Gartner‑Ellis limit of the log‑moment generating function of the service process R_t (successful transmission amount). Effective bandwidth is therefore the exponential‑tilt of the service process and is generally smaller than the mean throughput, reflecting the impact of stochastic service variability on delay.

The optimization problem is to maximize effective bandwidth subject to the collision constraints. The authors formulate this as a risk‑sensitive constrained Markov decision process (CMDP): the objective is the exponential‑type reward E