• Proceedings of the Korean Operations and Management Science Society Conference
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• 2000.04a
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• pp.251-252
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• 2000

• Journal of Korea Society of Industrial Information Systems
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• v.21 no.6
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• pp.1-12
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• 2016

In this paper, we consider a general discrete-time queueing system with D-BMAP(discrete-time batch Markovian arrival process) and D-policy. An idle single server becomes busy when the total service times of waiting customer group exceeds the predetermined workload threshold D. Once the server starts busy period, the server provides service until there is no customer in the system. The steady-state workload distribution is derived in the form of generating function. Mean workload is derived as a performance measure. Simulation is also performed for the purpose of verification and a simple numerical example is shown.

• Journal of Korea Society of Industrial Information Systems
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• v.29 no.1
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• pp.63-76
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• 2024

In this study, we analyzed queue length and sojourn time of discrete-time BMAP/G/1 queues under the workload control. Group customers (packets) with correlations arrive at the system following a discrete-time Markovian arrival process. The server starts busy period when the total service time of the arrived customers exceeds a predetermined workload threshold D and serves customers until the system is empty. From the analysis of workload and waiting time, distributions of queue length at the departure epoch and arbitrary time epoch and system sojourn time are derived. We also derived the mean value as a performance measure. Through numerical examples, we confirmed that we can obtain results represented by complex forms of equations, and we verified the validity of the theoretical values by comparing them with simulation results. From the results, we can obtain key performance measures of complex systems that operate similarly in various industrial fields and to analyze various optimization problems.

• Management Science and Financial Engineering
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• v.9 no.2
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• pp.1-12
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• 2003

For a stationary queue with BMAP arrivals, Takine and Takahashi [8] present a relationship between the queue length distributions at a random epoch and at a departure epoch by using the rate conservation law of Miyazawa [6]. In this note, we derive the same relationship by using the elementary balance equation, ‘rate-in = rate-out’. Along the same lines, we additionally derive relationships between the queue length distributions at a random epoch and at an arrival epoch. All these relationships hold for a broad class of finite-as well as infinite-capacity queues with BMAP arrivals.

• Journal of Korean Institute of Industrial Engineers
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• v.42 no.1
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• pp.30-37
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• 2016

A multi-server queueing system with an infinite buffer and impatient customers is analyzed. The system operates in the finite state Markovian random environment. The number of available servers, the parameters of the batch Markovian arrival process, the rate of customers' service, and the impatience intensity depend on the current state of the random environment and immediately change their values at the moments of jumps of the random environment. Dynamics of the system is described by the multi-dimensional asymptotically quasi-Toeplitz Markov chain. The ergodicity condition is derived. The main performance measures of the system are calculated. Numerical results are presented.

• Journal of the Korean Mathematical Society
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• v.40 no.1
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• pp.87-107
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• 2003

In this paper, we consider a discrete time queueing system fed by a superposition of an ON and OFF source with heavy tail ON periods and geometric OFF periods and a D-BMAP (Discrete Batch Markovian Arrival Process). We study the tail behavior of the queue length distribution and both infinite and finite buffer systems are considered. In the infinite buffer case, we show that the asymptotic tail behavior of the queue length of the system is equivalent to that of the same queueing system with the D-BMAP being replaced by a batch renewal process. In the finite buffer case (of buffer size K), we derive upper and lower bounds of the asymptotic behavior of the loss probability as $K\;\longrightarrow\;\infty$.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.30 no.1
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• pp.33-40
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• 2007

A multi-server queueing system with finite buffer is considered. The input flow is the BMAP (Batch Markovian Arrival Process). The service time has the PH (Phase) type distribution. Customers from the BMAP enter the system according to the discipline of partial admission. Besides ordinary (positive) customers, the Markovian flow (MAP) of negative customers arrives to the system. A negative customer can delete an ordinary customer in service if the state of its PH-service process belongs to some given set. In opposite case the ordinary customer is considered to be protected of the effect of negative customers. The stationary distribution and the main performance measures of the considered queueing system are calculated.

• The Journal of Engineering Research
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• v.1 no.1
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• pp.31-40
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• 1997

We first describe an approximation method for fitting a k-state MMBP to the departure process of a D-BMAP/Geo/1/K queue. The fitting model is them used in a simple decomposition algorithm to analyze a tandem configuration of finite capacity queue with cell loss.

• Journal of Korea Society of Industrial Information Systems
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• v.10 no.2
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• pp.42-47
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• 2005

A single-server queueing model with the Batch Markovian Arrival Process and disaster ow correlated with the arrival process is analyzed. The numerically stable algorithm for calculating the steady state distribution of the system is presented.

• Journal of Food Hygiene and Safety
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• v.35 no.4
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• pp.391-397
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• 2020

Human infections with livestock-associated methicillin-resistant/-susceptible Staphylococcus aureus (LA-MRSA/LA-MSSA) have recently been increasing significantly. These LA-MRSA and LA-MSSA strains can be transmitted to individuals who have frequent contact with livestock animals and foods of animal origin. In this study, major virulence potentials of S. aureus such as biofilm formation, antimicrobial peptide resistance, and in vitro hydrogen peroxide (H₂O₂) resistance were assessed using 20 MRSA and MSSA strains isolated from raw milk, beef cattle, and workers in the livestock industry. Static biofilm formation assays revealed that there is no difference in levels of biofilm production between MRSA versus MSSA or bovine- versus human-associated strains. In vitro BMAP (bovine myeloid antimicrobial peptide)-28 susceptibility assays also revealed no difference in the resistance to the antimicrobial peptide between MRSA versus MSSA or bovine- versus human-associated S. aureus strains. However, LA-MRSA strains displayed increased resistance to H₂O₂, which may play an important role in survival and dissemination of the pathogen in livestock. These results provide an important basis for understanding pathogenic potentials of LA-MRSA and LA-MSSA strains in human and animal hosts.