3 papers
math.PR2026
Heavy-traffic limit of stationary distributions of a state-dependent queue
Masahiro Kobayashi, Masakiyo Miyazawa, Yutaka Sakuma
Inspired by the work of Atar and Miyazawa [1] (2026) as well as applications to energy-saving problems, we are interested in the heavy-traffic limit of the stationary queue length…
math.PR2026
Diffusion limit for the stationary distribution of a history-dependent two-level M/M/1 queue
Masahiro Kobayashi, Masakiyo Miyazawa, Yutaka Sakuma
Recently, Atar and Miyazawa [2] introduced a multi-level GI/G/1 queue with a finite number of levels, where both the arrival and service rates depend on the level corresponding to…
math.PR2025
Heavy traffic limit of stationary distribution of the multi-level single server queue
Masahiro Kobayashi, Masakiyo Miyazawa, Yutaka Sakuma
Atar and Miyazawa recently introduced a single server queue with queue length dependent arrival and service processes, and name it a multi-level queue. They prove that the heavy tr…