• Journal of Korea Society of Industrial Information Systems
• /
• v.10 no.2
• /
• pp.42-47
• /
• 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 Korean Society of Industrial and Systems Engineering
• /
• v.30 no.1
• /
• pp.33-40
• /
• 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.

• Journal of Korean Institute of Industrial Engineers
• /
• v.42 no.1
• /
• pp.30-37
• /
• 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 Korea Society of Industrial Information Systems
• /
• v.23 no.1
• /
• pp.53-63
• /
• 2018

In this paper, we analyze the waiting time of a queueing system with D-BMAP (discrete-time batch Markovian arrival process) and D-policy. Customer group or packets arrives at the system according to discrete-time Markovian arrival process, and an idle single server becomes busy when the total service time 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 waiting time distribution is derived in the form of a generating function. Mean waiting time is derived as a performance measure. Simulation is also performed for the purpose of verification and validation. Two simple numerical examples are shown.

• Proceedings of the Korea Society of Information Technology Applications Conference
• /
• 2005.11a
• /
• pp.271-275
• /
• 2005

Queueing models are good models for fragments of communication systems and networks, so their investigation is interesting for theory and applications. Theses queues may play an important role for the validation of different decomposition algorithms designed for investigating more general queueing networks. So, in this paper we illustrate that the batch size distribution affects the loss probability, which is the main performance measure of a finite buffer queues.

• Journal of Korea Society of Industrial Information Systems
• /
• v.11 no.1
• /
• pp.1-6
• /
• 2006

Queueing models are good models for fragments of communication systems and networks, so their investigation is interesting for theory and applications. Theses queues may play an important role for the validation of different decomposition algorithms designed for investigating more general queueing networks. So, in this paper we illustrate that the batch size distribution affects the loss probability, which is the main performance measure of a finite buffer queues.

• Journal of Korea Society of Industrial Information Systems
• /
• v.21 no.6
• /
• pp.1-12
• /
• 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
• /
• v.9 no.3
• /
• pp.32-37
• /
• 2004

This paper investigates the mathematical model of multi-server retrial queueing system with the Batch Markovian Arrival Process (BMAP), the Phase type (PH) service distribution and the finite buffer. The sufficient condition for the steady state distribution existence and the algorithm for calculating this distribution are presented. Finally, a formula to solve loss probability in the case of complete admission discipline is derived.

• Journal of the Korean Mathematical Society
• /
• v.40 no.1
• /
• pp.87-107
• /
• 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 Korea Society of Industrial Information Systems
• /
• v.29 no.1
• /
• pp.63-76
• /
• 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.