Analysis of finite-buffer state-dependent bulk queues

<p>In this paper, we consider a general state-dependent finite-buffer bulk queue in which the rates and batch sizes of arrivals and services are allowed to depend on the number of customers in queue and service batch sizes. Such queueing systems have rich applications in manufacturing, service operations, computer and telecommunication systems. Interesting examples include batch oven processes in the aircraft and semiconductor industry; serving of passengers by elevators, shuttle buses, and ferries; and congestion control mechanisms to regulate transmission rates in packet-switched communication networks. We develop a unifying method to study the performance of this general class of finite-buffer state-dependent bulk queueing systems. For this purpose, we use semi-regenerative analysis to develop a numerically stable method for calculating the limiting probability distribution of the queue length process. Based on the limiting probabilities, we present various performance measures for evaluating admission control and batch service policies, such as the loss probability for an arriving group of customers and for individual customers within a group. We demonstrate our method by means of numerical examples.</p>

A batch-service queueing model with a discrete batch Markovian arrival process

Queueing systems with batch service have been investigated extensively during the past decades. However, nearly all the studied models share the common feature that an uncorrelated arrival process is considered, which is unrealistic in several real-life situations. In this paper, we study a discrete-time queueing model, with a server that only initiates service when the amount of customers in system (system content) reaches or exceeds a threshold. Correlation is taken into account by assuming a discrete batch Markovian arrival process (D-BMAP), i.e. the distribution of the number of customer arrivals per slot depends on a background state which is determined by a first-order Markov chain. We deduce the probability generating function of the system content at random slot marks and we examine the influence of correlation in the arrival process on the behavior of the system. We show that correlation merely has a small impact on the threshold that minimizes the mean system content. In addition, we demonstrate that correlation might have a significant influence on the system content and therefore has to be included in the model

Delay analysis of a two-class batch-service queue with class-dependent variable server capacity

In this paper, we analyse the delay of a random customer in a two-class batch-service queueing model with variable server capacity, where all customers are accommodated in a common single-server first-come-first-served queue. The server can only process customers that belong to the same class, so that the size of a batch is determined by the length of a sequence of same-class customers. This type of batch server can be found in telecommunications systems and production environments. We first determine the steady state partial probability generating function of the queue occupancy at customer arrival epochs. Using a spectral decomposition technique, we obtain the steady state probability generating function of the delay of a random customer. We also show that the distribution of the delay of a random customer corresponds to a phase-type distribution. Finally, some numerical examples are given that provide further insight in the impact of asymmetry and variance in the arrival process on the number of customers in the system and the delay of a random customer

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