On Scheduling Policies with Heavy-Tailed Dynamics in Wireless Queueing Systems

This paper takes a system view and studies a wireless queueing system where heavy-tailness may occur both at the traffic arrival and in the form of the multi-user interference. With the rapid development of AI technologies, this heavy-tailed traffic model has become more prevalent in the current network system, such as the file or data size used in the deep learning algorithm. We first re-visit the standard asymmetric queueing system with a mix of heavy-tailed and light-tailed traffic, but under a new variable-rate service model that not only better models the dynamics of the wireless medium but also includes the previous models as special cases. We then focus on the scheduling problem when heavy-tailed interference disrupts the serving link. The performance of queueing policies is investigated during an ON/OFF renewal channel process with heavy-tailed OFF periods, and the expected queue length and the throughput characteristic is studied under the priority as well as max-weight scheduling policies. The results show that the expected queue length of the heavy queue cannot be maintained as finite even under the most favorable priority policy. On the other hand, a priority policy can guarantee the finiteness of an expected queue length for the light queue, but the system is not throughput optimal any longer. It is further shown that no benefit can be provided by the max-weight scheduling policy to the light queue for the queue length behavior in a steady-state, though the system is always throughput optimal.