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Queue length violation probability, i.e., the tail distribution of the queuelength, is a widely used statistical quality-of-service (QoS) metric inwireless communications. Characterizing and optimizing the queue lengthviolation probability have great significance in time sensitive networking(TSN) and ultra reliable and low-latency communications (URLLC). However, itstill remains an open problem. In this paper, we put our focus on the analysisof the tail distribution of the queue length from the perspective ofcross-layer design in wireless link transmission. We find that, under thefinite average power consumption constraint, the queue length violationprobability can achieve zero with diversity gains, while it can have alinear-decay-rate exponent according to large deviation theory (LDT) withlimited receiver sensitivity. Besides, we find that the arbitrary-decay-ratequeue length tail distribution with the finite average power consumption existsin the Rayleigh fading channel. Then, we generalize the sufficient conditionsfor the communication system belonging to these three scenarios, respectively.Moreover, we apply the above results to analyze the wireless link transmissionin the Nakagami-m fading channel. Numerical results with approximation validateour analysis.

Bounding Queue Length Violation Probability of Joint Channel and Buffer Aware Transmission