Multiclass Multiserver Threshold-Based Systems: A Study of Noninstantaneous Server Activation

Abstract

In this paper, we consider performance evaluation of a system which shares K servers (or resources) among N heterogeneous classes of workloads, where server allocation and de-allocation for class i is dictated by a class specific threshold-based policy with hysteresis control. In particular, the server activation time for class i is non-instantaneous. There are many systems and applications where a multi-class threshold-based queueing system can be of great use. One important utility of using threshold-based approaches is in situations where applications may incur server usage costs. In these cases, one needs to consider not only the performance aspects but also the resulting cost/performance ratio. The motivation for using hysteresis control is to reduce the unnecessary cost of server setup (or activation) and server removal (or deactivation) whenever there are momentary fluctuations in workload. Moreover, servers in such systems and applications are often needed by multiple classes of workloads, and hence, it is desirable to find good approaches to sharing server resources among the different classes of workloads, preferably without statically partitioning the server pool among these classes. An important and distinguishing characteristic of our work is that we consider the modeling and analysis of a multi-class system with non-instantaneous server activation, which is of use in studying many important applications. The main contributions of this work are (a) in developing an efficient approximation method for solving such models, (b) in verifying the convergence of our iterative method, and (c) in evaluating the resulting accuracy of the technique for computing performance measures of interest, which can subsequently be used in making system design choices.

Queueing System with Potential for Recruiting Secondary Servers

“…The stated result follows from Equations ( 6), (9), and (11) along with the expression for λ given in Equation ( 2).…”

“…One group, seemingly a larger one, assumes a switching-on and a switching-off mechanism for the backup servers based on the current queue length using thresholdtype and hysteresis-type strategies. It is worth mentioning a few works from this group, namely, papers [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22].…”

Artificial Intelligent Multi-Access Edge Computing Servers Management

“…The problem of managing the computing capabilities of the servers has attracted the researchers' interest early enough in the literature. In 2007, the problem of noninstantaneous server activation (i.e., the non-zero time to replicate and activate a server) is studied in [8]. The authors introduce a dynamic approach in order to share the servers' resources among multiple users, while considering the hysteresis control to reduce the servers' activation and deactivation cost when momentary fluctuations of the workload occur.…”

The PH/PH/1 Multi-threshold Queue

“…After each service completion, the server chooses a queue to serve according to a threshold policy. A generalisation of this model is analysed in [5] where customers from multiple classes arrive according to a Poisson process and require an exponential amount of service. The queueing system contains a fixed number of servers which are allocated to a customer class according to a threshold policy.…”