A detailed note on the finite-buffer queueing system with correlated batch-arrivals and batch-size-/phase-dependent bulk-service

Abstract

This paper analyzes a finite-buffer queueing system, where customers arrive in batches and the accepted customers are served in batches by a single server. The service is assumed to be dependent on the batch-size and follows a general bulk service rule. The inter-arrival times of batches are assumed to be correlated and they are represented through the batch Markovian arrival process (B M AP). Computation procedure of the queue-length distributions at the post-batch-service completion, an arbitrary, and the pre-batch-arrival epochs are discussed. Various performance measures along with the consecutive customer loss probabilities are studied considering batch-size-dependent renewal service time distributions. Further, the above finite-buffer bulk-service queueing model is also investigated considering correlated batch-service times which are presented through the Markovian service process (M S P). The phase-dependent consecutive loss probabilities for the correlated batch-service times are determined. In the

Mathematical Modelling of MX/G(a, b)/1 Bulk Service Queue Model with Two Vacations and Setup Time in Ceramic Technology

“…In addition, the same researchers looked at a state-dependent arrival, which means that while the server is busy, the rate of arrival would progressively grow, but when it is on vacation, the arrival rate will gradually fall. Ghosh et al [9] have analysed a finitebuffer bulk service queue system where arrival service is correlated. e GI x /M/C/N queue system was analysed by Laxmi and Gupta [10].…”

Analysis of Tandem Queue with Multi-Server Stages and Group Service at the Second Stage

“…It is worth mentioning that a significant contribution to the study of isolated queues with group customer service was made by S. Chakravarthy; see, e.g., [8][9][10][11][12][13]. Mention also the papers [14][15][16][17]. In [14][15][16], the MAP process or its generalizations is supposed.…”

“…Mention also the papers [14][15][16][17]. In [14][15][16], the MAP process or its generalizations is supposed. In [17], dependence of a group service time on its size is examined and applications to fog and cloud computing systems are discussed.…”