33 citations · 46 across the 10 of their papers we have counts for
10 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 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…
Exact asymptotic formulae of the stationary distribution of a discrete-time 2d-QBD process: an example and additional proofs
Toshihisa Ozawa, Masahiro Kobayashi
A discrete-time two-dimensional quasi-birth-and-death process (2d-QBD process), , is a two-dimensional skip-free random walk $\{(X_{…
Exact asymptotic formulae of the stationary distribution of a discrete-time two-dimensional QBD process
Toshihisa Ozawa, Masahiro Kobayashi
We consider a discrete-time two-dimensional process on with a supplemental process on a finite set, where individual processes $\…
Simple error bounds for the QBD approximation of a special class of two dimensional reflecting random walks
Hiroyuki Masuyama, Yutaka Sakuma, Masahiro Kobayashi
This paper considers the QBD approximation of a special class of two-dimensional reflecting random walks (2D-RRWs). A typical example of the 2D-RRWs is a two-node Jackson network w…
Structure-reversibility of a two dimensional reflecting random walk and its application to queueing network
Masahiro Kobayashi, Masakiyo Miyazawa, Hiroshi Shimizu
We consider a two dimensional reflecting random walk on the nonnegative integer quadrant. It is assumed that this reflecting random walk has skip free transitions. We are concerned…
Tail asymptotics of the stationary distribution of a two dimensional reflecting random walk with unbounded upward jumps
Masahiro Kobayashi, Masakiyo Miyazawa
We consider a two dimensional reflecting random walk on the nonnegative integer quadrant. This random walk is assumed to be skip free in the direction to the boundary of the quadra…
Join the shortest queue among parallel queues: tail asymptotics of its stationary distribution
Masahiro Kobayashi, Yutaka Sakuma, Masakiyo Miyazawa
We are concerned with an -type join the shortest queue (-JSQ for short) with parallel queues for an arbitrary positive integer , where the servers may be heterogen…
Revisit to the tail asymptotics of the double QBD process: Refinement and complete solutions for the coordinate and diagonal directions
Masahiro Kobayashi, Masakiyo Miyazawa
We consider a two dimensional skip-free reflecting random walk on a nonnegative integer quadrant. We are interested in the tail asymptotics of its stationary distribution, provided…