On the convergence to fairness in overloaded FIFO systems
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Many of computing and communication systems are based on FIFO queues whose performance, e.g., in terms of throughput and fairness, is highly influenced by load fluctuations, especially in the case of short-term overload. This paper analytically proves that, for both Markovian and heavy-tailed/self-similar arrivals, overloaded FIFO queues are asymptotically fair in the sense that each flow or aggregate of flows receives a weighted fair share over large time scales. In addition, the paper provides the corresponding transient results and convergence rates, i.e., the amount of time it takes for a flow to probabilistically attain the fair share. Interestingly, for Markovian arrivals, the paper indicates smaller convergence rates at higher utilizations, which is exactly the opposite behavior characteristic to underloaded queueing systems.