Group-Server Queues

Abstract

By analyzing energy-efficient management of data centers, this paper proposes and develops a class of interesting 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.

Optimal energy-efficient policies for data centers through sensitivity-based optimization

“…On the other hand, it is noted that for our queueing model, Group 1 has a large influence on analysis of Group 2 due to introducing new transfer rules. In fact, our queueing model here has been discussed in Li et al [31] with a more general setting.…”

“…Queueing theory and Markov (reward or decision) processes become two useful mathematical tools in analyzing energy-efficient data centers. See Gandhi [9] and Li et al [31] for more details.…”

“…Since then, some multi-server queues have received attention (for example, queues with server vacations, queues with either local setup times or N -policy), and they were successfully applied to energy-efficient management of data centers. Readers may refer to recent publications for more details, among which are Mazzucco et al [34], Schwartz et al [42], Gandhi and Harchol-Balter [12], Gandhi et al [10], Maccio and Down [33], Phung-Duc [38], Chen et al [6], and Li et al [31].…”

A $c/μ$-Rule for Service Resource Allocation in Group-Server Queues

“…First, we prove the sufficient condition. Suppose d * (n) is the solution to the ILP problem (30), ∀n ∈ N. For any other policy d ′ ∈ D e , we know that it must satisfy the constraints in (30) and…”

“…The system controller can dynamically turn on or off servers according to different backlogs (queue lengths) such that the system long-run average cost can be minimized. We call such queueing models group-server queues [30]. Note that any queueing system with heterogeneous servers can be considered as a group-server queue if the servers with the same service cost and rate are grouped as a class.…”