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…
Multi-level reflecting Brownian motion on the half line and its stationary distribution
Masakiyo Miyazawa
A semi-martingale reflecting Brownian motion is a popular process for diffusion approximations of queueing models including their networks. In this paper, we are concerned with the…
Tight matrices and heavy traffic steady state convergence in queueing networks
J. G. Dai, Yiquan Ji, Masakiyo Miyazawa
We are interested to prove that the stationary distribution of a multiclass queueing network converges to the stationary distribution of a semimartingale reflecting Brownian motion…
Diffusion approximation of the stationary distribution of a two-level single server queue
Masakiyo Miyazawa
We consider a single server queue which has a threshold to change its arrival process and service speed by its queue length, which is referred to as a two-level single server queue…