Group-Server Queues

TL;DR

This paper introduces and analyzes Group-Server Queues, a new class of queueing models inspired by energy-efficient data center management, with applications across various practical systems and potential for dynamic control improvements.

Contribution

It develops two types of Group-Server Queues using loss networks and impatient customers, providing model descriptions, mathematical analysis, and simulation results.

Findings

Expected queue lengths and sojourn times are characterized.

Group-server queues are applicable in multiple practical domains.

Dynamic control mechanisms can be designed using these models.

Abstract

By analyzing energy-efficient management of data centers, this paper proposes and develops a class of interesting {\it Group-Server Queues}, and establishes two representative group-server queues through loss networks and impatient customers, respectively. Furthermore, such two group-server queues are given model descriptions and necessary interpretation. Also, simple mathematical discussion is provided, and simulations are made to study the expected queue lengths, the expected sojourn times and the expected virtual service times. In addition, this paper also shows that this class of group-server queues are often encountered in many other practical areas including communication networks, manufacturing systems, transportation networks, financial networks and healthcare systems. Note that the group-server queues are always used to design effectively dynamic control mechanisms through regrouping and recombining such many servers in a large-scale service system by means of, for example, bilateral threshold control, and customers transfer to the buffer or server groups. This leads to the large-scale service system that is divided into several adaptive and self-organizing subsystems through scheduling of batch customers and regrouping of service resources, which make the middle layer of this service system more effectively managed and strengthened under a dynamic, real-time and even reward optimal framework. Based on this, performance of such a large-scale service system may be improved greatly in terms of introducing and analyzing such group-server queues. Therefore, not only analysis of group-server queues is regarded as a new interesting research direction, but there also exists many theoretical challenges, basic difficulties and open problems in the area of queueing networks.