k-Nearest Neighbor Queues with Delayed Information

被引：0

作者：

Pender, Jamol ^{[1
]}

机构：

[1] Cornell Univ, Sch Operat Res & Informat Engn, 228 Rhodes Hall, Ithaca, NY 14853 USA

来源：

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS | 2022年 / 32卷 / 12期

关键词：

Queueing theory; k-nearest neighbor; delayed information; delay differential equation; stochastic process; fluid limit; Hopf bifurcation; JOIN; APPROXIMATIONS;

D O I：

10.1142/S0218127422501747

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we analyze a model called the k-nearest neighbor queue with the possibility of having delayed queue length feedback. We prove fluid limits for the stochastic queueing model and show that the fluid limit converges to a system of delay differential equations. Using the properties of circulant matrices, we derive a closed form expression for the value of the critical delay, which governs whether the delayed information will induce oscillations or a Hopf bifurcation in our queueing system.

引用

页数：14

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