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

Souvik Ghosh (), A. D. Banik (), Joris Walraevens () and Herwig Bruneel ()
Additional contact information
Souvik Ghosh: Tel Aviv University
A. D. Banik: Indian Institute of Technology Bhubaneswar, Argul Campus
Joris Walraevens: Ghent University
Herwig Bruneel: Ghent University

4OR, 2022, vol. 20, issue 2, No 4, 272 pages

Abstract: 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 (BMAP). 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 (MSP). The phase-dependent consecutive loss probabilities for the correlated batch-service times are determined. In the form of tables and graphs, a variety of numerical results for different batch-service time distributions are presented in this paper.

Keywords: Finite-buffer queue; Batch Markovian arrival process (BMAP); Markovian service process (MSP); Batch-size-dependent bulk service; Performance measures; Consecutive customer loss (CCL); Primary 60K25; 68M20; Secondary 90B22 (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10288-021-00478-x

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