• Communications of the Korean Mathematical Society
• /
• v.14 no.3
• /
• pp.611-625
• /
• 1999

We consider ΜΑΡ/G/ 1 finite capacity queue with mul-tiple thresholds on buffer. The arrival of customers follows a Markov-ian arrival process(MAP). The service time of a customer depends on the queue length at service initiation of the customer. By using the embeded Markov chain method and the supplementary variable method, we obtain the queue length distribution ar departure epochs and at arbitrary epochs. This gives the loss probability and the mean waiting time by Little's law. We also give a simple numerical examples to apply the overload control in packetized networks.

• Proceedings of the Korean Operations and Management Science Society Conference
• /
• 2005.05a
• /
• pp.1133-1136
• /
• 2005

Markovian Service Process(MSP)는 기존의 Markovian Arrival Process(MAP)에서 사용하던 위상 개념을 고객의 서비스 과정에 대응시킨 모형이다. 이는 서버의 상태에 따라 달라질 수 있는 서비스 상태를 위상 변화에 대응시키는 모형이다. 본 논문에서는 대기행렬 모형의 중요한 성능 척도인 고객 수 분포에 관하여 임의시점, 고객 도착 직전 시점, 고객 이탈 직후 시점에서의 관계식을 유도한다.

• Journal of the Korean Operations Research and Management Science Society
• /
• v.42 no.1
• /
• pp.19-28
• /
• 2017

Moments of stationary intervals and those of the counting process can be used for moment fittings of the point processes. As for the Markovian arrival processes, the moments of stationary intervals are given as a polynomial function of parameters whereas the moments of the counting process involve exponential terms. Therefore, moment fittings are more complicated with the counting process than with stationary intervals. However, in queueing network analysis, cross-correlation between point processes can be modeled more conveniently with counting processes than with stationary intervals. A Laplace-Stieltjies transform of the stationary intervals of MAP (3)s is recently proposed in minimal number of parameters. We extend the results and present the Laplace transform of the counting process of MAP (3)s. We also show how moments of the counting process such as index of dispersions for counts, IDC, and limiting IDC can be used for moment fittings. Examples of exact MAP (3) moment fittings are also presented on the basis of moments of stationary intervals and those of the counting process.

• 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.

• Proceedings of the Korean Society for Quality Management Conference
• /
• 2004.04a
• /
• pp.499-502
• /
• 2004

Multi-server Markovian retrial model with heterogeneous servers is analyzed. Arriving customers constitute the MMAP(Marked Markovian Arrival Process). Distribution of the primary customers among the servers is performed randomly depending on the type of a customer and the number of the server. Customers from the orbit have the exponential service time distribution with a parameter depending on the server only. The choice of the server for a retrial is made randomly as well. Multidimensional continuous time Markov chain describing operation of the model is investigated by means of reducing to asymptotically quasi-toeplitz Markov chaius.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
• /
• 2003.09a
• /
• pp.13.1-13
• /
• 2003

The Markovian arrival process with marked transitions (MMAP) is useful in modeling input processes of stochastic system with several types. Especially, the MMAP can be used to model the phenomena where the correlation of different types is considered. In this talk we discuss modeling issues for the queue with three types of customers; ordinary customers, negative customers and disasters which are correlated by using MMAP. We also present the recent results and further studies.

• 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.

• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.43 no.2
• /
• pp.277-292
• /
• 2006

We consider a single-server queue with service time distribution of phase type where positive customers, negative customers and disasters arrive according to a Markovian arrival process with marked transitions (MMAP). We derive simple formulae for the stationary queue length distributions. The Laplace-Stieltjes transforms (LST's) of the sojourn time distributions under the combinations of removal policies and service disciplines are also obtained by using the absorption time distribution of a Markov chain.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.4
• /
• pp.985-1004
• /
• 2016

We consider the MAP/PH/c/K queue in which blocked customers retry to get service and servers may take vacations. The time interval between retrials and vacation times are of phase type (PH) distributions. Using the method of mean drift, a sufficient condition of ergodicity is provided. A condition for the system to be unstable is also given by the stochastic comparison method.