Browsing by Author "Ke, Jau-Chuan"

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A batch arrival queue under randomised multi-vacation policy with unreliable server and repair
(2012)
Ke, Jau-Chuan
;
Huang, Kai-Bin
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This article examines an M([x])/G/1 queueing system with an unreliable server and a repair, in which the server operates a randomised vacation policy with multiple available vacations. Upon the system being found to be empty, the server immediately takes a vacation. If there is at least one customer found waiting in the queue upon returning from a vacation, the server will be activated for service. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 - p. When one or more customers arrive when the server is idle, the server immediately starts providing service for the arrivals. It is possible that an unpredictable breakdown may occur in the server, in which case a repair time is requested. For such a system, we derive the distributions of several important system characteristics, such as the system size distribution at a random epoch and at a departure epoch, the system size distribution at the busy period initiation epoch, and the distribution of the idle and busy periods. We perform a numerical analysis for changes in the system characteristics, along with changes in specific values of the system parameters. A cost effectiveness maximisation model is constructed to show the benefits of such a queueing system.
A heuristic algorithm for the optimization of a retrial system with Bernoulli vacation
(2013-03-01)
Ke, Jau-Chuan
;
Wu, Chia-Huang
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
In this study, we consider an M/M/c retrial queue with Bernoulli vacation under a single vacation policy. When an arrived customer finds a free server, the customer receives the service immediately; otherwise the customer would enter into an orbit. After the server completes the service, the server may go on a vacation or become idle (waiting for the next arriving, retrying customer). The retrial system is analysed as a quasi-birth-and-death process. The sufficient and necessary condition of system equilibrium is obtained. The formulae for computing the rate matrix and stationary probabilities are derived. The explicit close forms for system performance measures are developed. A cost model is constructed to determine the optimal values of the number of servers, service rate, and vacation rate for minimizing the total expected cost per unit time. Numerical examples are given to demonstrate this optimization approach. The effects of various parameters in the cost model on system performance are investigated.
A HEURISTIC ALGORITHM FOR THE OPTIMIZATION OF M/M/s QUEUE WITH MULTIPLE WORKING VACATIONS
(2012-02-01)
Wu, Chia-Huang
;
Wang, Kuo-Hsiung
;
Ke, Jau-Chuan
;
Ke, Jyh-Bin
;
工業工程與管理學系
This paper focuses on an M/M/s queue with multiple working vacations such that the server works with different service rates rather than no service during the vacation period. We show that this is a generalization of an M/M/1 queue with working vacations in the literature. Service times during vacation period, or during service period and vacation times are all exponentially distributed. We obtain the useful formula for the rate matrix R through matrix-geometric method. A cost function is formulated to determine the optimal number of servers subject to the stability conditions. We apply the direct search algorithm and Newton-Quasi algorithm to heuristically find an approximate solution to the constrained optimization problem. Numerical results are provided to illustrate the effectiveness of the computational algorithm.
Algorithmic analysis of the multi-server system with a modified Bernoulli vacation schedule
(2011-05-01)
Ke, Jau-Chuan
;
Wu, Chia-Huang
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper considers an infinite-capacity M/M/c queueing system with modified Bernoulli vacation under a single vacation policy. At each service completion of a server, the server may go for a vacation or may continue to serve the next customer, if any in the queue. The system is analyzed as a quasi-birth-and-death (QBD) process and the necessary and sufficient condition of system equilibrium is obtained. The explicit closed-form of the rate matrix is derived and the useful formula for computing stationary probabilities is developed by using matrix analytic approach. System performance measures are explicitly developed in terms of computable forms. A cost model is derived to determine the optimal values of the number of servers, service rate and vacation rate simultaneously at the minimum total expected cost per unit time. Illustrative numerical examples demonstrate the optimization approach as well as the effect of various parameters on system performance measures. (c) 2010 Elsevier Inc. All rights reserved.
An optimum approach of profit analysis on the machine repair system with heterogeneous repairmen
(2015-02-15)
Ke, Jau-Chuan
;
Liu, Tzu-Hsin
;
Wu, Chia-Huang
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
We consider a machine repair problem with queue-dependent heterogeneous repairmen. The stationary probability distribution of the number of failed machines in the system is derived. A profit model is developed to determine the optimal values of threshold to assign/add one more repairman for increasing the total service rate where the service rate is assumed adjustable. The probabilistic global search Lausanne (PGSL) method is employed to find an initial trial solution. Based on this initial solution, a direct search method is applied to obtain the optimal values of the threshold and, then, the Quasi-Newton method is implemented to adjust the corresponding service rates. Some numerical experiments are performed to justify the efficiency of the optimum approach. (C) 2015 Elsevier Inc. All rights reserved.
Analysis of an infinite multi-server queue with an optional service
(2013-06-01)
Ke, Jau-Chuan
;
Wu, Chia-Huang
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper deals with an infinite-capacity multi-server queueing system with a second optional service (SOS) channel. The inter-arrival times of arriving customers, the service times of the first essential service (FES) and the SOS channel are all exponentially distributed. A customer may leave the system after the FES channel with a probability (1 - theta), or the completion of the FES may immediately require a SOS with a probability theta (0 <= theta <= 1). The formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix analytical approach. A cost model is developed to simultaneously determine the optimal values of the number of servers and the two service rates at the minimal total expected cost per unit time. Quasi-Newton method and Particle Swarm Optimization (PSO) method are employed to deal with the optimization problem. Under optimal operating conditions, numerical results are provided from which several system performance measures are calculated based on the assumed numerical values of the system parameters. (c) 2013 Elsevier Ltd. All rights reserved.
ANALYSIS OF AN UNRELIABLE SERVER M([x])/G/1 SYSTEM WITH A RANDOMIZED VACATION POLICY AND DELAYED REPAIR
(2010-01-01)
Ke, Jau-Chuan
;
Huang, Kai-Bin
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This article examines an M([x])/G/1 queueing system with a randomized vacation policy and at most J consecutive vacations. Whenever the system is empty, the server immediately takes a vacation. Upon returning from a vacation, the server will be immediately activated for service if there is at least one customer waiting in the queue. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 - p. This pattern continues until the number of vacations taken reaches J. If the system is empty at the end of the J th vacation, the server becomes idle in the system until at least one customer arrives at the queue. Assume that the server may suffer an unpredictable breakdown and the repair may be delayed. For such a system, we derive the distributions of some important system characteristics, such as the system size distribution at a random epoch and at a departure epoch, the system size distribution at the initiation epoch of a busy period, the distributions of idle and busy periods, and reliability indices. Finally, a cost model is developed to determine the joint parameters (p, J) that correspond to minimum cost, and some numerical examples are presented for illustrative purpose.
ANALYSIS OF AN UNRELIABLE SERVER M-[x]/G/1 SYSTEM WITH A RANDOMIZED VACATION POLICY AND DELAYED REPAIR
(2010-01-01)
Ke, Jau-Chuan
;
Huang, Kai-Bin
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This article examines an M-[x]/G/1 queueing system with a randomized vacation policy and at most J consecutive vacations. Whenever the system is empty, the server immediately takes a vacation. Upon returning from a vacation, the server will be immediately activated for service if there is at least one customer waiting in the queue. Otherwise, if no customers are waiting for service at the end of a vacation, the server either remains idle with probability p or leaves for another vacation with probability 1 - p. This pattern continues until the number of vacations taken reaches J. If the system is empty at the end of the J th vacation, the server becomes idle in the system until at least one customer arrives at the queue. Assume that the server may suffer an unpredictable breakdown and the repair may be delayed. For such a system, we derive the distributions of some important system characteristics, such as the system size distribution at a random epoch and at a departure epoch, the system size distribution at the initiation epoch of a busy period, the distributions of idle and busy periods, and reliability indices. Finally, a cost model is developed to determine the joint parameters (p, J) that correspond to minimum cost, and some numerical examples are presented for illustrative purpose.
Analysis of the Machine Repair Models With Multi-Threshold Synchronous Vacations
(2013-05-01)
Wu, Chia-Huang
;
Ke, Jau-Chuan
;
Choudhury, Gautam
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工業工程與管理學系
;
Department of Industrial Engineering and Management
In this paper, we present an analysis of a machine repair problem with M operating machines and S standbys, in which c repairmen are responsible for supervising these machines and follow a multi-threshold, synchronous vacation policy. With such a policy, at a repair completion instant, if the number of the failed machines in the system is less than a preset threshold value, partial idle servers together take a single vacation (or leave for a random amount of time doing other secondary job). At the end of a vacation, they return to repair the failed machines (or waits for the arrival). The steady-state probabilities are solved by using the matrix-analytic method, and formulae of system performance measures are thereby obtained. A cost model is then developed to formulate an optimization problem to find the minimum cost. The direct search and quasi-Newton methods are implemented to determine the optimal number of servers, the optimal threshold policy and the optimal repair rate.
Bootstrapping comparison on availability of parallel systems with non-identical components
(2008)
Ke, Jau-Chuan
;
Chu, Yunn-Kuang
;
Lee, Jia-Huei
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工業工程與管理學系
;
Department of Industrial Engineering and Management
Purpose - In order to develop a feasible and efficient method to acquire the long-run availability of a parallel system with distribution-free up and down times, the purpose of this paper is to perform the simulation comparisons on the interval estimations of system availability using four bootstrapping methods. Desigri/methodology/approach - By using four bootstrap methods; standard bootstrap (SB) confidence interval, percentile bootstrap (PB) confidence interval, bias-corrected percentile bootstrap (BCPB) confidence interval, and bias-corrected and accelerated (BCa) confidence interval. A numerical simulation study is carried out in order to demonstrate performance of these proposed bootstrap confidence intervals. Especially, we investigate the accuracy of the four bootstrap confidence intervals by calculating the coverage percentage, the average length, and the relative coverage of confidence intervals. Findings - Among the four bootstrap confidence intervals, the PB method has the largest relative coverage in most situations. That is, the PB method is the best one made by practitioners who want to obtain an efficient interval estimation of availability. Originality/value - It is the first time that the relative coverage is introduced to evaluate the performance of estimation method, which is more efficient than the existing measures.
Computational algorithm and parameter optimization for a multi-server system with unreliable servers and impatient customers
(2010-12-01)
Wu, Chia-Huang
;
Ke, Jau-Chuan
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
We consider an infinite capacity M/M/c queueing system with c unreliable servers, in which the customers may balk (do not enter) and renege (leave the queue after entering). The system is analyzed as a quasi-birth-and-death (QBD) process and the necessary and sufficient condition of system equilibrium is obtained. System performance measures are explicitly derived in terms of computable forms. The useful formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix analytical approach. A cost model is derived to determine the optimal values of the number of servers, service rate and repair rate simultaneously at the minimal total expected cost per unit time. The parameter optimization is illustrated numerically by the Quasi-Newton method. (C) 2010 Elsevier B.V. All rights reserved.
Cost Analysis of a vacation machine repair model
(2011-01-01)
Ke, Jau-Chuan
;
Wu, Chia-Huang
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Liou, Cheng-Hwai
;
Wang, Tsung-Yin
;
工業工程與管理學系
This paper investigates a machine repair problem with homogeneous machines and standbys available, in which multiple technicians are responsible for supervising these machines and operate a (R, V, K) synchronous vacation policy. With such a policy, if any V idle technicians exist in the system, these V (V < R) technicians would take a synchronous vacation. Upon returning from vacation, they would take another vacation if there is no broken machine waiting in the queue. This pattern continues until at least one failed machine arrives. It is assumed that the number of teams/groups on vacation is less than or equal to K (0 <= KV < R). The matrix analytical method is employed to obtain a steady-state probability and the closed-form expression of the system performance measures. Efficient approaches are performed to deal with the optimization problem of the discrete / continuous variables while maintaining the system availability at a specified acceptable level. (C) 2011 Published by Elsevier Ltd. Selection and/or peer-review under responsibility of the Asia Pacific Business Innovation and Technology Management Society
Multi-server machine repair model with standbys and synchronous multiple vacation
(2012-02-01)
Ke, Jau-Chuan
;
Wu, Chia-Huang
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper investigates a machine repair problem with homogeneous machines and standbys available, in which multiple technicians are responsible for supervising these machines and operate a (R, V, K) synchronous vacation policy. With such a policy, if any V idle technicians exist in the system, these V (V < R) technicians would take a synchronous vacation. Upon returning from vacation, they would take another vacation if there is no broken machine waiting in the queue. This pattern continues until at least one failed machine arrives. It is assumed that the number of teams/groups on vacation is less than or equal to K (0 <= KV < R). The matrix analytical method is employed to obtain a steady-state probability and the closed-form expression of the system performance measures. Efficient approaches are performed to deal with the optimization problem of the discrete/continuous variables while maintaining the system availability at a specified acceptable level. (C) 2011 Elsevier Ltd. All rights reserved.
Multi-server machine repair model with standbys and synchronous multiple vacation (vol 62, pg 296, 2012)
(2012-05-01)
Ke, Jau-Chuan
;
Wu, Chia-Huang
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
Multi-server machine repair problems under a (V,R) synchronous single vacation policy
(2014-04-01)
Wu, Chia-Huang
;
Ke, Jau-Chuan
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper considers a machine repair problem with M operating machines and S standbys, in which R repairmen are responsible for supervising these machines and operate a (V,R) vacation policy. With such policy, if the number of the failed machines is reduced to R - V (R > V) (there exists V idle repairmen) at a service completion, these V idle servers will together take a synchronous vacation (or leave for other secondary job). Upon returning from the vacation, they do not take a vacation again and remain idle until the first arriving failed machine arrives. The steady-state probabilities are solved in terms of matrix forms and the system performance measures are obtained. Algorithmic procedures are provided to deal with the optimization problem of discrete/continuous decision variables while maintaining a minimum specified level of system availability. (C) 2013 Elsevier Inc. All rights reserved.
Multi-server retrial queue with second optional service: algorithmic computation and optimisation
(2011)
Ke, Jau-Chuan
;
Wu, Chia-Huang
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
We consider an infinite-capacity M/M/c retrial queue with second optional service (SOS) channel. An arriving customer finds a free server would enter the service (namely, the first essential service, denoted by FES) immediately; otherwise, the customer enters into an orbit and starts generating requests for service in an exponentially distributed time interval until he finds a free server and begins receiving service. After the completion of FES, only some of them receive SOS. The retrial system is modelled by a quasi-birth-and-death process and some system performance measures are derived. The useful formulae for computing the rate matrix and stationary probabilities are derived by means of a matrix-analytic approach. A cost model is derived to determine the optimal values of the number of servers and the two different service rates simultaneously at the minimal total expected cost per unit time. Illustrative numerical examples demonstrate the optimisation approach as well as the effect of various parameters on system performance measures.
Multi-threshold policy for a multi-server queue with synchronous single vacation
(2013-03-01)
Wu, Chia-Huang
;
Ke, Jau-Chuan
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper considers an infinite buffer M/M/c queueing system in which servers follow a multi-threshold vacation policy. With such a policy, at a service completion instant, if the number of customers in the system is less than a prefixed threshold value, part of servers together take a single vacation (or leave for a random amount of time doing other secondary job). At the vacation completion instant, they return to the system for serving the customers. Some practical production and inventory systems or call centers could be modeled as this Markovian queue with a multi-threshold vacation policy. Using the Markovian process model, we obtain the exact closed-form expression of rate matrix and the stationary distribution of the number of customers in the system. A cost model is developed to search the joint optimal values of the thresholds of vacation policy and service rate of each server, which minimizes the long-term average cost. Some numerical results are presented to illustrate the optimization procedures. (C) 2012 Elsevier Ltd. All rights reserved.
Optimal randomized control policy of an unreliable server system with second optional service and startup
(2008)
Yang, Dong-Yuh
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Wang, Kuo-Hsiung
;
Ke, Jau-Chuan
;
Pearn, Wen Lea
;
工業工程與管理學系
Purpose - To study the optimization of a randomized control problem in an M/G/1 queue in which a removable and unreliable server may provide two phases of heterogeneous service to arriving customers. Design/methodology/approach - Arriving customers follow a Poisson process and require the first essential service (FES). As soon as FES of a customer is completed, the customer may leave the system or opt for the second optional service (SOS). The service times of FES channel and SOS channel are assumed to be general distribution functions. The server requires a startup time with random length before starting service. When the server is working, he may meet unpredictable breakdowns but is immediately repaired. The inter-breakdown time and repair time of the removable server are exponentially random variable and generally random variable, respectively. By the convex combination property and the renewal reward theorem, several system performances are obtained. A cost model is developed to search the optimal two-threshold policy at a minimum cost. Sensitivity analysis is performed. Findings - Expressions for various system performances are derived. Sensitivity analysis of optimal randomized control policy (based on the developed expected cost function) with respect to system parameters is investigated. Originality/value - It is the first time that analytic results of sensitivity analysis of optimal randomized control policy for the complex system have been obtained which is quite useful and significant for engineers.
RANDOMIZED POLICY OF A POISSON INPUT QUEUE WITH J VACATIONS
(2010-03-01)
Ke, Jau-Chuan
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Huang, Kai-Bin
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper studies the operating characteristics of an M/G/1 queuing system with a randomized control policy and at most J vacations. After all the customers are served in the queue exhaustively, the server immediately takes at most J vacations repeatedly until at least N customers are waiting for service in the queue upon returning from a vacation. If the number of arrivals does not reach N by the end of the J(th) vacation, the server remains idle in the system until the number of arrivals in the queue reaches N. If the number of customers in the queue is exactly accumulated N since the server remains idle or returns from vacation, the server is activated for services with probability p and deactivated with probability (1-p). For such variant vacation model, other important system characteristics are derived, such as the expected number of customers, the expected length of the busy and idle period, and etc. Following the construction of the expected cost function per unit time, an efficient and fast procedure is developed for searching the joint optimum thresholds (N*, J*) that minimize the cost function. Some numerical examples are also presented.
The multi-server retrial system with Bernoulli feedback and starting failures
(2015-05-04)
Yang, Dong-Yuh
;
Ke, Jau-Chuan
;
Wu, Chia-Huang
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
In this paper, we present a detailed analysis of a multi-server retrial queue with Bernoulli feedback, where the servers are subject to starting failures. Upon completion of a service, a customer would decide either to leave the system with probability p or to join the retrial orbit again for another service with complementary probability 1-p. We analyse this queueing system as a quasi-birth-death process. Specifically, the equilibrium condition of the system is given for the existence of the steady-state analysis. Applying the matrix-geometric method, the formulae for computing the rate matrix and stationary probabilities are obtained. We further develop the matrix-form expressions for various system performance measures. A cost model is constructed to determine the optimal number of servers, the optimal mean service rate and the optimal mean repair rate subject to the stability condition. Finally, we give a practical example to illustrate the potential applicability of this model.