Analysis of a versatile batch-service queueing model with correlation in the arrival process

Abstract

In the past, many researchers have analysed queueing models with batch service. In such models, the server typically postpones service until the number of present customers reaches a service threshold, whereupon service is initiated of a batch consisting of several customers. In addition, correlation in the customer arrival process has been studied for many different queueing models. However, correlated arrivals in batch-service models has attracted only modest attention. In this paper, we analyse a discrete-time D-BMAP/G l,c /1 queue, whereby the service time of a batch is dependent on the number of customers within it. In addition, a timing mechanism is included, to avoid that customers suffer excessive waiting times because their service is postponed until the amount of customers reaches the service threshold. We deduce various useful performance measures related to the buffer content and we investigate the impact of the traffic parameters on the system performance through some numerical examples. We show that correlation merely has a small impact on the service threshold that minimizes the mean system content, and consequently, that the existing results of the corresponding independent system can be applied to determine a near-optimal service threshold policy, which is an important finding for practitioners. On the other hand, we demonstrate that for other purposes, such as performance evaluation and buffer management, correlation in the arrival process cannot be ignored, a conclusion that runs along the same lines as in queueing models without batch service.

System Performance Of A Variable-Capacity Batch-Service Queue With Geometric Service Times And Customer-Based Correlation

“…The maximum number of products that can be processed at the same time, also called the service capacity, is often assumed to be a constant and bounded value, e.g. Banerjee and Gupta 2012;Claeys et al 2012Claeys et al , 2013Goswami et al 2006;Weng and Leachman 1993. The difference with multiserver systems is that a newly arrived customer cannot join an ongoing service, even if the service is not completely full.…”

System Occupancy of a Two-Class Batch-Service Queue with Class-Dependent Variable Server Capacity

“…An important characteristic of such batch-service systems is the maximum size of a batch, that is the maximum number of customers processed simultaneously. In many batch-service systems this number is assumed to be a constant [1][2][3][4][5]. However, in practice, the maximum batch size or capacity of the server can be variable and stochastic, a feature that has been incorporated in only a few papers.…”

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

“…Batch-service systems are common in practice, for example in production environments where a machine can heat or paint multiple components at the same time (Weng and Leachman (1993)) or transportation systems where a number of customers with the same destination are transported simultaneously (Lee and Kim (1994)). Due to the wide area of applications, batchservice queueing models have been studied thoroughly, for instance by Arumuganathan and Jeyakumar (2005), Banerjee and Gupta (2012), Banerjee et al (2015Banerjee et al ( , 2014, Chang and Takine (2005), Chaudhry and Templeton (1983), Claeys et al (2012Claeys et al ( , 2013aClaeys et al ( ,b, 2011, Goswami et al (2006), and Janssen and van Leeuwaarden (2005).…”