• Journal of applied mathematics & informatics
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• v.15 no.1_2
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• pp.405-414
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• 2004

This paper considers overload control in telecommunication networks. Markov-modulated Bernoulli process ( MMBP ) has been extensively used to model bursty traffics with time-correlation. Thus, we investigate the transient behavior of the queueing system MMBP/D/l/K queue with two thresholds. The model is analyzed recursively by using the generating function method. We obtain the transient queue length distribution and waiting time distribution at an arbitrary time. The transient behavior of the queueing system helps observing the temporary system behavior.

• Journal of Korean Society for Quality Management
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• v.19 no.2
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• pp.145-157
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• 1991

Thid study intends to pursue behavioral-structure of production behavior through statistical models which are using in PERT and Queueing theory. We can corprehand the orders of human production behavior's characteristics by several related attributes of probablity/statistics. These attributes are poisson, Beta, exponential distributions and P.S Laplace's natural probability. Human production behavior is related and regressed to these attributes in many divisions intermediately. Progressive numerical understanding in many essential human behavior acts on the application of practical behavior standard in production word and operation.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.11 no.3
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• pp.179-196
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• 1986

In this paper, the peformance of a statistical packet voice/data multiplexer is studied. In ths study we assume that in the packet voice/data multiplexer two separate finite queues are used for voice and data traffics, and that voice traffic gets priority over data. For the performance analysis we divide the output link of the multiplexer into a sequence of time slots. The voice signal is modeled as an (M+1) - state Markov process, M being the packet generation period in slots. As for the data traffic, it is modeled by a simple Poisson process. In our discrete time domain analysis, the queueing behavior of voice traffic is little affected by the data traffic since voice signal has priority over data. Therefore, we first analyze the queueing behavior of voice traffic, and then using the result, we study the queueing behavior of data traffic. For the packet voice multiplexer, both inpur state and voice buffer occupancy are formulated by a two-dimensional Markov chain. For the integrated voice/data multiplexer we use a three-dimensional Markov chain that represents the input voice state and the buffer occupancies of voice and data. With these models, the numerical results for the performance have been obtained by the Gauss-Seidel iteration method. The analytical results have been verified by computer simylation. From the results we have found that there exist tradeoffs among the number of voice users, output link capacity, voic queue size and overflow probability for the voice traffic, and also exist tradeoffs among traffic load, data queue size and oveflow probability for the data traffic. Also, there exists a tradeoff between the performance of voice and data traffics for given inpur traffics and link capacity. In addition, it has been found that the average queueing delay of data traffic is longer than the maximum buffer size, when the gain of time assignment speech interpolation(TASI) is more than two and the number of voice users is small.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.10B
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• pp.1971-1978
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• 1999

In this paper, we study the effects of long-range dependence (LRD) in VBR video traffic on queueing system. This paper consists of Part I and II. In Part I, we present a (LRD) video traffic model based on the shifting-level (SL) process. We observe that the ACF of an empirical video trace is accurately captured by the shifting-level process with compound correlation (SLCC): an exponential function in short range and a hyperbolic function in long range. We present an accurate parameter matching algorithm for video traffic. In the Part II, we offer the queueing analysis of SL/D/1/K called ‘quantization reduction method’. Comparing the queueing performances of the DAR(1) model and the SLCC with that of a real video trace, we identify the effects of SRD and LRD in VBR video traffic on queueing performance. Simulation results show that Markoivian models can estimate network performances fairly accurately under a moderate traffic load and buffer condition, whereas LRD may have a significant effect on queueing behavior under a heavy traffic load and large buffer condition.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.20 no.43
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• pp.153-162
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• 1997

M/G/1 queueing system is one of the most widely used one to model the real system. When operating a real systems, since it often takes cost, some control policies that change the operation scheme are adopted. In particular, the N-policy is the most popular among many control policies. Almost all researches on queueing system are based on the assumption that the arrival rates of customers into the queueing system is constant, In this paper, we consider the M/G/1 queueing system whose arrival rate varies according to the servers status : idle, set-up and busy states. For this study, we construct the steady state equations of queue lengths by means of the supplementary variable method, and derive the PGF(probability generating function) of them. The L-S-T(Laplace Stieltjes transform) of waiting time and average waiting time are also presented. We also develop an algorithm to find the optimal N-value from which the server starts his set-up. An analysis on the performance measures to minimize total operation cost of queueing system is included. We finally investigate the behavior of system operation cost as the optimal N and arrival rate change by a numerical study.

• Proceedings of the Korea Multimedia Society Conference
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• 2000.11a
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• pp.561-566
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• 2000

Computer-Communication System may be classified into two kinds of systems considering connection capability among terminal and computing facility : time sharing and distributed computer systems According to the different input characteristic, the buffer behavior of two systems is quite different. Here we restrict our study to the analysis of queueing behavior of a demultiplexing buffer of time sharing systems. The analysis shows that M/G/1 queueing model can be used model such behavior.

• 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 Institute of Industrial Engineers
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• v.28 no.3
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• pp.319-330
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• 2002

We consider BMAP/G/1 queueing system with N-policy and multiple vacations. We derive the vector generating functions of the queue length in a factorized form and interpret the factorization. We also derive the mean queue length.

• Journal of the Korean Statistical Society
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• v.23 no.2
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• pp.483-498
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• 1994

Suppose that a stationary process ${X_t}$ has a marginal distribution whose support consists of sufficiently large integers. We are concerned with some analogous law of large numbers for such distribution function F. In particular, we determine a weak law of large numbers for maximum queueing length in $M/M\infty$ system. We also present a limiting behavior for the maxima based on AR(1) process with binomial thining and poisson marginals (INAR(1)) introduced by E. Mckenzie. It turns out that the result of AR(1) process is the same as that of $M/M/\infty$ queueing process in limit when we observe the queues at regularly spaced intervals of time.

• Industrial Engineering and Management Systems
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• v.15 no.2
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• pp.131-142
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• 2016

We consider a multi-server queueing system without buffer and with two types of customers as a model of operation of a mobile network cell. Customers arrive at the system in the marked Markovian arrival flow. The service times of customers are exponentially distributed with parameters depending on the type of customer. A part of the available servers is reserved exclusively for service of first type customers. Customers who do not receive service upon arrival, can make repeated attempts. The system operation is influenced by random factors, leading to a change of the system parameters, including the total number of servers and the number of reserved servers. The behavior of the system is described by the multi-dimensional Markov chain. The generator of this Markov chain is constructed and the ergodicity condition is derived. Formulas for computation of the main performance measures of the system based on the stationary distribution of the Markov chain are derived. Numerical examples are presented.