arXiv subjects

Hiroshi Toyoizumi

Publications and source records attributed to Hiroshi Toyoizumi.

2 recordsLinked to original sources

arXiv2020

The Battle of Infinity: Explosive Demand Surge vs Gigantic Service Providers

Infinite server queues have ultimate processing power to accommodate explosive demand surges. We provide a new stability criterion based on the Borel-Cantelli lemma to judge whether the infinite server safely accommodates heavy-tailed demands. We illustrate the battles between heavy-tailed demand and infinite servers in detail. In particular, we show some cases where the explosive demand overwhelms the infinite server queue. The medical demand caused by pandemics such as the COVID- 19 creates huge stress to the healthcare system. This framework indicates that healthcare systems need to account for the tail behavior of the cluster size and hospital stay length distributions to check the stability of their systems during pandemics.

math.PR↗

arXiv2017

Swarm behavior of traders with different subjective predictions in the Market

A combination of a priority queueing model and mean field theory shows the emergence of traders' swarm behavior, even when each has a subjective prediction of the market driven by a limit order book. Using a nonlinear Markov model, we analyze the dynamics of traders who select a favorable order price taking into account the waiting cost incurred by others. We find swarm behavior emerges because of the delay in trader reactions to the market, and the direction of the swarm is decided by the current market position and the intensity of zero-intelligent random behavior, rather than subjective trader predictions.

q-fin.TR↗