1 citations · 2 across the 9 of their papers we have counts for
9 papers
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…
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…
Heavy-tail asymptotics for the length of a busy period in a Generalised Jackson Network
Sergey Foss, Masakiyo Miyazawa, Linglong Yuan
We consider a Generalised Jackson Network with finitely many servers, a renewal input and service times at each queue. We assume the network to be stable and, in addition,…
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…
Heavy traffic limit with discontinuous coefficients via a non-standard semimartingale decomposition
Rami Atar, Masakiyo Miyazawa
This paper studies a single server queue in heavy traffic, with general inter-arrival and service time distributions, where arrival and service rates vary discontinuously as a func…
The stationary distributions of state-dependent diffusions reflected at one and two sides
Masakiyo Miyazawa
Consider a one-dimensional diffusion process which has state-dependent drift and deviation and is reflected at the origin, which is called a one-side reflected diffusion or simply…