Spatial queues with nearest neighbour shifts

被引：1

作者：

Kumar, B. R. Vinay ^{[1
]}

Leskela, Lasse ^{[2
]}

机构：

[1] Eindhoven Univ Technol, POB 513, NL-5600 MB Eindhoven, Netherlands

[2] Aalto Univ, Dept Math & Syst Anal, Otakaari 1, Espoo 02150, Finland

来源：

PERFORMANCE EVALUATION | 2024年 / 166卷

关键词：

Queues; Electric vehicles; Nearest neighbour; Spatial queues; k-NN graphs; Spatial point process; STABILITY;

D O I：

10.1016/j.peva.2024.102448

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

This work studies queues in a Euclidean space. Consider N servers that are distributed uniformly in [0, 1]d. Customers arrive at the servers according to independent stationary processes. Upon arrival, they probabilistically decide whether to join the queue they arrived at, or shift to one of the nearest neighbours. Such shifting strategies affect the load on the servers, and may cause some of the servers to become overloaded. We derive a law of large numbers and a central limit theorem for the fraction of overloaded servers in the system as the total number of servers N -> infinity . Additionally, in the one-dimensional case (d = 1 ), we evaluate the expected fraction of overloaded servers for any finite N . Numerical experiments are provided to support our theoretical results. Typical applications of the results include electric vehicles queueing at charging stations, and queues in airports or supermarkets.

引用

页数：11

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