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

Autor: A. D. Banik, Souvik Ghosh, Herwig Bruneel, Joris Walraevens
Rok vydání: 2021
Předmět:
PROBABILITIES
Consecutive customer loss (CCL)
Technology and Engineering
STRATEGIES
Performance
Computation
0211 other engineering and technologies
Phase (waves)
Markov process
02 engineering and technology
Management Science and Operations Research
01 natural sciences
Finite-buffer queue
Theoretical Computer Science
Management Information Systems
010104 statistics & probability
symbols.namesake
Markovian
QUEUES
service process (MSP)
INPUT
Batch-size-dependent bulk service
Applied mathematics
Markovian arrival process
Batch Markovian arrival process (BMAP)
0101 mathematics
CONSECUTIVE CUSTOMER LOSSES
Mathematics
Service (business)
Queueing theory
021103 operations research
measures
EFFICIENT COMPUTATIONAL ANALYSIS
Queueing system
Service process
MODEL
Computational Theory and Mathematics
symbols
Zdroj: 4OR-A QUARTERLY JOURNAL OF OPERATIONS RESEARCH
ISSN: 1614-2411
1619-4500
DOI: 10.1007/s10288-021-00478-x
Popis: 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.
Databáze: OpenAIRE
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