Detailed Analytical and Computational Studies of D-BMAP/D-BMSP/1 Queueing System

• Published in: Methodology and computing in applied probability Vol. 25; no. 1; p. 12
• Main Authors: Samanta, Sujit Kumar, Das, Kousik
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.03.2023; Springer Nature B.V
• Subjects: Automation; Big Data; Business and Management; Economics; Electrical Engineering; Investigations; Life Sciences; Manufacturing; Markov analysis; Markov chains; Mathematical analysis; Mathematics and Statistics; Matrices (mathematics); Methods; Probability; Queuing theory; Statistics; Transition probabilities; Wireless networks; Discrete-time batch Markovian arrival process; Queueing; 90B22; Sojourn time; ); 68M20; Matrix analytic method; 60K25; factorization; Discrete-time batch Markovian service process
• ISSN: 1387-5841; 1573-7713
• DOI: 10.1007/s11009-023-10012-7

This paper studies a discrete-time single server batch arrival and batch service queueing model with unlimited waiting space. The discrete-time batch Markovian arrival process and discrete-time batch Markovian service process, respectively, manage the arrival and service processes. We adopt the UL -type RG -factorization approach based on censoring methodology for variable size batch service queue to calculate the stationary probability vectors of the transition probability matrix with general structure Markov chain at outside observer’s epoch. We reblock the transition probability matrix to its desired M/G/1 structure to find the stationary probability vectors at outside observer’s epoch for fixed size batch service queue using the matrix analytic method. We also develop relationships to determine probability vector expressions for other important time epochs such as pre-arrival, intermediate, post-departure, and random epochs. The most challenging aspect of our study is to obtain the probability mass functions of sojourn time in the system for both the variable and fixed size batch service queues. We use our suggested queueing model to derive the results of several specific well-known queueing models. We also discuss about possible managerial implication of our model to produce fruit juices in manufacturing industry. We present computational experience based on the execution of parametrized experiments with various categories in order to validate the analytical results reported in this study.