3 citations · 3 across the 5 of their papers we have counts for
6 papers · 1 filter
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 $\…
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…