Jung Woo Baek | Chosun University (original) (raw)

Papers by Jung Woo Baek

The M/M/1 queue with a production-inventory system and lost sales

Applied Mathematics and Computation, 2014

ABSTRACT In this paper, we study an M/M/1 queue with an attached production-inventory system. Cus... more ABSTRACT In this paper, we study an M/M/1 queue with an attached production-inventory system. Customers arrive in the system according to a Poisson process, and a single server serves the customers. The service times are assumed to be i.i.d. exponential random variables. The customers leave the system with exactly one item from the inventory at his service completion epoch. If there is no inventory item, all arriving customers are lost. The stocks are replenished by (1) an external order under (r,Q)-policy, or (2) an internal production. The internal production process is assumed to be a Poisson process. We first derive the stationary joint distribution of the queue length and the on-hand inventory in product form. Using the joint distribution, we introduce long-run performance measures and a cost model. Then, we show numerical examples, which minimize the long-run cost per unit time.

A time-dependent busy period queue length formula for the M/Ek/1 queue

ABSTRACT In this paper, a closed-form time-dependent busy period queue length probability is obta... more ABSTRACT In this paper, a closed-form time-dependent busy period queue length probability is obtained for the M/E_k/1 queue. This probability is frequently needed when we compare the length of the busy period and the maximum amount of service that can be rendered to the existing customers. The transient probability is given in terms of the generalized modified Bessel function of the second type of Griffiths et al. (2006a). The queue length probability for the M/M/1 queue is also presented as a special case.

A workload factorization for BMAP/G/1 vacation queues under variable service speed

Operations Research Letters, 2014

ABSTRACT This paper proposes a simple factorization property for the workload distribution of the... more ABSTRACT This paper proposes a simple factorization property for the workload distribution of the BMAP/G/1/ vacation queues under variable service speed. The server provides service at different service speeds depending on the phases of the underlying Markov chain. Using the factorization principle, the workload distribution at any arbitrary time point can be easily derived only by obtaining the distribution during the idle period. We prove the factorization property and the moments formula. Lastly, we provide some applications of our factorization principle.

A MAP-modulated fluid flow model with multiple vacations

Annals of Operations Research, 2013

ABSTRACT We consider a MAP-modulated fluid flow queueing model with multiple vacations. As soon a... more ABSTRACT We consider a MAP-modulated fluid flow queueing model with multiple vacations. As soon as the fluid level reaches zero, the server leaves for repeated vacations of random length V until the server finds any fluid in the system. During the vacation period, fluid arrives from outside according to the MAP (Markovian Arrival Process) and the fluid level increases vertically at the arrival instance. We first derive the vector Laplace–Stieltjes transform (LST) of the fluid level at an arbitrary point of time in steady-state and show that the vector LST is decomposed into two parts, one of which the vector LST of the fluid level at an arbitrary point of time during the idle period. Then we present a recursive moments formula and numerical examples.

Factorization Properties for a MAP-Modulated Fluid Flow Model Under Server Vacation Policies

Springer Proceedings in Mathematics & Statistics, 2012

Journal of Applied Physics, 2013

Experimental and theoretical investigation of phosphorus in-situ doping of germanium epitaxial layers

Current Applied Physics, 2013

Dopant profile model in a shallow germanium n+/p junction

Journal of the Korean Physical Society, 2013

ABSTRACT A challenging issue is to estimate the n-type dopant profiles and, consequently, their d... more ABSTRACT A challenging issue is to estimate the n-type dopant profiles and, consequently, their diffusivities in shallow Ge n+/p junctions because of their abnormal dopant profiles that do not follow conventional Gaussian-distribution-based diffusion theory. In order to fit the abnormal dopant profiles in shallow junctions, what are due to (1) fast and asymmetric diffusion of n-type dopants and (2) dopant pileup caused by surface back-scattering phenomenon, we propose a new profiling function and verify it by using a fitting algorithm based on the least-squares method. Through this fitting algorithm, we estimate the diffusivity and peak-position values from the raw dopant profile data, and we provide the experimental diffusivity equations as a function of the annealing temperature.

Numerical Linear Algebra with Applications, 2011

We consider a Markov-modulated fluid flow queueing model under D-policy. As soon as the fluid lev... more We consider a Markov-modulated fluid flow queueing model under D-policy. As soon as the fluid level reaches zero, the server becomes idle. During the idle period, fluid arrives from outside according to an underlying continuous time Markov chain (UMC) and the idle server does not process the fluid. We consider two increase patterns of fluid during the idle period: vertical increase (Type-V) and linear increase (Type-L). The idle server is reactivated only when the cumulative fluid level in the system exceeds a predetermined threshold value D. We derive the distributions of fluid level and mean performance measures for both types. We also present cost optimization model to minimize average operating cost per unit time. A MARKOV-MODULATED FLUID FLOW QUEUEING MODEL UNDER D-POLICY Ã . P is used to compute performance measures by using uniformization technique. In the analysis of MMFF-related processes, first passage times play important roles. Let .x/ D i nf ft > 0, U.t/ D xg be the first passage time to level x. Let us define the following Laplace-Stieltjes transforms (LST), ‰ .Â/ ij D EOEe Â .0/ , J. .0// D j jU.0/ D 0, J.0/ D i, .i 2 = 1 , j 2 = 2 /, G 12 .Âjx/ ij D EOEe Â .0/ , J. .0// D j jU.0/ D x, J.0/ D i, .i 2 = 1 , j 2 = 2 /,

A factorization property for BMAP/G/1 vacation queues under variable service speed

Annals of Operations Research, 2008

This paper proposes a simple factorization principle that can be used efficiently and effectively... more This paper proposes a simple factorization principle that can be used efficiently and effectively to derive the vector generating function of the queue length at an arbitrary time of the BMAP/G/1/ queueing systems under variable service speed. We first prove the factorization property. Then we provide moments formula. Lastly we present some applications of the factorization principle.

Threshold Workload Control in the BMAP/G/1 Queue

ABSTRACT We analyze the distribution of the workload in the queueing system with batch Markovian ... more ABSTRACT We analyze the distribution of the workload in the queueing system with batch Markovian arrival process (BMAP) controlled according to the D-policy. The server begins to serve the customers only when the total workload exceeds some predetermined threshold value D. We first explore the stochastic nature of the idle period. Then we derive the Laplace-Stieltjes transform of the workload and the mean values at an arbitrary time. Finally we provide computational experiences and discuss the effects of the BMAP arrivals. Our study shows that the naive Poisson assumption heavily underestimates the workload in a queueing system. We also discuss the effect of the workload threshold control

The integrated core network architecture and various mobile subscriber behaviors can result in a ... more The integrated core network architecture and various mobile subscriber behaviors can result in a significant increase of signaling loads inside the evolved packet core network proposed by 3GPP in Release 8. Consequently, an authentication signaling analysis can provide insights into reducing the authentication signaling loads and latency, satisfying the quality-of-experience. In this paper, we evaluate the signaling loads in the EPS architecture via analytical modeling based on the renewal process theory. The renewal process theory works well, irrespective of a specific random process (i.e. Poisson). This paper considers various subscribers patterns in terms of call arrival rate, mobility, subscribers' preference and operational policy. Numerical results are illustrated to show the interactions between the parameters and the performance metrics. The sensitivity of vertical handover performance and the effects of heavy-tail process are also discussed.

Analysis of discrete-time Geo/G/1 queue under the D -policy

ABSTRACT In this paper, we present a theoretical and analytical framework to analyze the discrete... more ABSTRACT In this paper, we present a theoretical and analytical framework to analyze the discrete-time queue in which the on-off of the server is controlled by workload threshold. For this purpose, we consider the discrete-time Geo/G/1 queue under the D-policy. We derive the queue length, waiting time, sojourn time distributions and the mean performance measures. We then perform numerical computations to see the effect of the threshold and the variability of the service time distributions on the system performance. We will also see if our discrete-time results can approximate the continuous-time M/G/1/D-policy queueing system. The approach of this paper can be used as a basis for the analysis of more complex queueing systems in which the server is controlled by workload.

Discrete Event Dynamic Systems, 2008

This paper studies the steady-state queue length process of the MAP/G/1 queue under the dyadic co... more This paper studies the steady-state queue length process of the MAP/G/1 queue under the dyadic control of the D-policy and multiple server vacations. We derive the probability generating function of the queue length and the mean queue length. We then present computational experiences and compare the MAP queue with the Poisson queue.

MAP/G/1 Queue Under Workload Control and Postprocessing

Stochastic Analysis and Applications, 2009

ABSTRACT This article studies the performance of the MAP/G/1 queue under workload control and pos... more ABSTRACT This article studies the performance of the MAP/G/1 queue under workload control and post processing. We first obtain the probability generating function of the queue length distribution. Then we derive the mean queue length. We present computational experiences and compare the MAP queue with the Poisson queue.

Two-class M/G/1 queue under workload control

International Journal of Modelling, Identification and Control, 2009

ABSTRACT In this paper, we consider a queueing system under the D-policy in which there are two c... more ABSTRACT In this paper, we consider a queueing system under the D-policy in which there are two classes of customers. Class-1 customers have a non-preemptive priority over class-2 customers. The idle server begins to serve the customers only when the total workload of the waiting customers (regardless of their classes) exceeds D. We derive the Laplace-Stieltjes transform of the waiting time of each class of customers. We then derive the mean waiting times. Lastly, we compare our analytical results with the simulation estimates for verification purposes.

In this chapter, we model and solve a very general single-machine production system with early se... more In this chapter, we model and solve a very general single-machine production system with early setup, bilevel threshold control, and extra job operations. The first threshold is used to control the setup starting time and the second threshold is used to control the production starting time. The system is modeled by the BMAP/G/1 queue and the manufacturing lead time is analyzed. The factorization principle is used to derive the distribution of the manufacturing lead time and the mean value. A numerical example is provided.

Factorization properties for a MAP-modulated fluid flow model under server vacation policies (abstract only

Sigmetrics Performance Evaluation Review, 2012

In this paper, we study a MAP-modulated fluid flow model under generalized server vacation polici... more In this paper, we study a MAP-modulated fluid flow model under generalized server vacation policies and propose factorization properties that can be efficiently used to derive the fluid level distributions at an arbitrary time point. Our model is an extension of the conventional Markov modulated fluid flow (MMFF) model to control the servers idle state. We consider two types of

Analysis of the M X / G /1 Queue Under D -Policy

Stochastic Analysis and Applications, 2005

We study the queue length of the M /G/1 queue under D-policy. We derive the queue length PGF at a... more We study the queue length of the M /G/1 queue under D-policy. We derive the queue length PGF at an arbitrary point of time. Then, we derive the mean queue length. As special cases, M/G/1, M /M/1, and M/M/1 queue under D-policy are investigated. Finally, the effects of employing D-policy are discussed.

BMAP/G/1 Queue Under D-Policy: Queue Length Analysis

Stochastic Models, 2005

ABSTRACT We study the queue length distribution of a queueing system with BMAP arrivals under D-p... more ABSTRACT We study the queue length distribution of a queueing system with BMAP arrivals under D-policy. The idle server begins to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We derive the vector generating functions of the queue lengths both at a departure and at an arbitrary point of time. Mean queue lengths are derived and a numerical example is presented.