A continuous-time queueing model with class clustering and global FCFS service discipline

In this paper the focus is on "class clustering" in a continuous-time queueing model with two classes and dedicated servers. "Class clustering" means that customers of any given type may (or may not) have a tendency to "arrive back-to-back". We believe this is a concept that is often neglected in literature and we want to show that it can have a considerable impact on multiclass queueing systems, especially on the system considered in this paper. This system adopts a "global FCFS" service discipline, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their types. The major aim of our paper is to quantify the intuitively expected (due to the service discipline) negative impact of "class clustering" on the performance measures of our system. The motivation of our work are systems where this kind of inherent blocking is encountered, such as input-queueing network switches, road splits or security checks at airports

Analysis of a batch-service queue with variable service capacity, correlated customer types and generally distributed class-dependent service times

Queueing models with batch service have been studied frequently, for instance in the domain of telecommunications or manufacturing. Although the batch server's capacity may be variable in practice, only a few authors have included variable capacity in their models. We analyse a batch server with multiple customer classes and a variable service capacity that depends on both the number of waiting customers and their classes. The service times are generally distributed and class-dependent. These features complicate the analysis in a non-trivial way. We tackle it by examining the system state at embedded points, and studying the resulting Markov Chain. We first establish the joint probability generating function (pgf) of the service capacity and the number of customers left behind in the queue immediately after service initiation epochs. From this joint pgf, we extract the pgf for the number of customers in the queue and in the system respectively at service initiation epochs and departure epochs, and the pgf of the actual server capacity. Combined with additional techniques, we also obtain the pgf of the queue and system content at customer arrival epochs and random slot boundaries, and the pgf of the delay of a random customer. In the numerical experiments, we focus on the impact of correlation between the classes of consecutive customers, and on the influence of different service time distributions on the system performance. (C) 2019 Elsevier B.V. All rights reserved

Analysis of a two-class single-server discrete-time FCFS queue : the effect of interclass correlation

In this paper, we study a discrete-time queueing system with one server and two classes of customers. Customers enter the system according to a general independent arrival process. The classes of consecutive customers, however, are correlated in a Markovian way. The system uses a global FCFS service discipline, i.e., all arriving customers are accommodated in one single FCFS queue, regardless of their classes. The service-time distribution of the customers is general but class-dependent, and therefore, the exact order in which the customers of both classes succeed each other in the arrival stream is important, which is reflected by the complexity of the system content and waiting time analysis presented in this paper. In particular, a detailed waiting time analysis of this kind of multi-class system has not yet been published, and is considered to be one of the main novelties by the authors. In addition to that, a major aim of the paper is to estimate the impact of interclass correlation in the arrival stream on the total number of customers in the system, and the customer delay. The results reveal that the system can exhibit two different classes of stochastic equilibrium: a strong equilibrium where both customer classes give rise to stable behavior individually, and a compensated equilibrium where one customer type creates overload

A Case Study on Grid Performance Modeling

The purpose of this case study is to develop a performance model for an enterprise grid for performance management and capacity planning1. The target environment includes grid applications such as health-care and financial services where the data is located primarily within the resources of a worldwide corporation. The approach is to build a discrete event simulation model for a representative work-flow grid. Five work-flow classes, found using a customized k-means clustering algorithm characterize the workload of the grid. Analyzing the gap between the simulation and measurement data validates the model. The case study demonstrates that the simulation model can be used to predict the grid system performance given a workload forecast. The model is also used to evaluate alternative scheduling strategies. The simulation model is flexible and easily incorporates several system details

Variable and class-dependent service capacity with a multi-class arrival process

In manufacturing, a single batch server can often group a number of customers that require the same type of service. In this paper, a shared queue without customer reordering is used in order to reduce the variability of throughput time of material throughout the manufacturing process which guarantees a global First-Come-First-Served (FCFS) service discipline. This is a significant difference with the more common polling systems where each type of customer has a dedicated queue. The batch server in this paper has a variable service capacity that depends on the classes of the customers in the queue. This paper extends previous work by considering a general number of N customer classes. During the analysis, we focus on the system occupancy of this system at random slot boundaries