Browsing by Author "Wang, Kuo-Hsiung"

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A HEURISTIC ALGORITHM FOR THE OPTIMIZATION OF M/M/s QUEUE WITH MULTIPLE WORKING VACATIONS
(2012-02-01)
Wu, Chia-Huang
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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.
A recursive method for the F-policy G/M/1/K queueing system with an exponential startup time
(2008-06-01)
Wang, Kuo-Hsiung
;
Kuo, Ching-Chang
;
Pearn, W. L.
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper deals with the optimal control of a finite capacity G/M/1 queueing system combined the F-policy and an exponential startup time before start allowing customers in the system. The F-policy queueing problem investigates the most common issue of controlling arrival to a queueing system. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining interarrival time, to develop the steady-state probability distribution of the number of customers in the system. We illustrate a recursive method by presenting three simple examples for exponential, 3-stage Erlang, and deterministic interarrival time distributions, respectively. A cost model is developed to determine the optimal management F-policy at minimum cost. We use an efficient Maple computer program to determine the optimal operating F-policy and some system performance measures. Sensitivity analysis is also studied. (c) 2007 Elsevier Inc. All rights reserved.
ANALYTICAL METHOD FOR ACCURACY ANALYSIS OF THE RANDOMIZED T-POLICY QUEUE
(2012-03-01)
Wang, Kuo-Hsiung
;
Yang, Dong-Yuh
;
Pearn, W. L.
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
We consider a randomized policy to control the M/G/1 queueing system with an unreliable server, second optional service and general startup times. The server is subject to breaking down according to a Poisson process, and the repair time obeys a general distribution. All arrived customers demand the first required service, and only some of the arrived customers demand the second optional service. After all the customers are served in the system, the server immediately takes a vacation and operates the (T, p)-policy. For this queueing system, we employ maximum entropy approach with several constraints to develop the probability distributions of the system size and the expected waiting time in the queue. Based on the accuracy comparison between the exact and approximate methods, we show that the maximum entropy approach is quite accurate for practical purpose, which is a useful method for solving complex queueing systems.
Comparative analysis of a randomized N-policy queue: An improved maximum entropy method
(2011-08-01)
Wang, Kuo-Hsiung
;
Yang, Dong-Yuh
;
Pearn, W. L.
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
We analyze a single removable and unreliable server in an M/G/1 queueing system operating under the < p,N >-policy. As soon as the system size is greater than N, turn the server on with probability p and leave the server off with probability (1 p). All arriving customers demand the first essential service, where only some of them demand the second optional service. He needs a startup time before providing first essential service until there are no customers in the system. The server is subject to break down according to a Poisson process and his repair time obeys a general distribution. In this queueing system, the steady-state probabilities cannot be derived explicitly. Thus, we employ an improved maximum entropy method with several well-known constraints to estimate the probability distributions of system size and the expected waiting time in the system. By a comparative analysis between the exact and approximate results, we may demonstrate that the improved maximum entropy method is accurate enough for practical purpose, and it is a useful method for solving complex queueing systems. (C) 2011 Elsevier Ltd. All rights reserved.
Comparison of two randomized policy M/G/1 queues with second optional service, server breakdown and startup
(2010-06-01)
Wang, Kuo-Hsiung
;
Yang, Dong-Yuh
;
Pearn, W. L.
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
The problem addressed in this paper is to compare the minimum cost of the two randomized control policies in the M/G/1 queueing system with an unreliable server, a second optional service, and general startup times. All arrived customers demand the first required service, and only some of the arrived customers demand a second optional service. The server needs a startup time before providing the first required service until the system becomes empty. After all customers are served in the queue, the server immediately takes a vacation and the system operates the (T, p)-policy or (p, N)-policy. For those two policies, the expected cost functions are established to determine the joint optimal threshold values of (T, p) and (p, N), respectively. In addition, we obtain the explicit closed form of the joint optimal solutions for those two policies. Based on the minimal cost, we show that the optimal (p, N)-policy indeed outperforms the optimal (T, p)-policy. Numerical examples are also presented for illustrative purposes. (C) 2010 Elsevier B.V. All rights reserved.
Controlling arrivals for a queueing system with an unreliable server: Newton-Quasi method
(2009-07-01)
Wang, Kuo-Hsiung
;
Yang, Dong-Yuh
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper deals with the control policy of a removable and unreliable server for an M/M/1/K queueing system, where the removable server operates an F-policy. The so-called F-policy means that when the number of customers in the system reaches its capacity K (i.e. the system becomes full), the system will not accept any incoming customers until the queue length decreases to a certain threshold value F. At that time, the server initiates an exponential startup time with parameter c and starts allowing customers entering the system. It is assumed that the server breaks down according to a Poisson process and the repair time has an exponential distribution. A matrix analytical method is applied to derive the steady-state probabilities through which various system performance measures can be obtained. A cost model is constructed to determine the optimal values, say (F*, mu*, gamma*), that yield the minimum cost. Finally, we use the two methods, namely, the direct search method and the Newton-Quasi method to find the global minimum (F*, mu*, gamma*). Numerical results are also provided under optimal operating conditions. (C) 2009 Elsevier Inc. All rights reserved.
Optimal control of the N policy M/G/1 queueing system with server breakdowns and general startup times
(2007-10-01)
Wang, Kuo-Hsiung
;
Wang, Tsung-Yin
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper deals with an N policy M/G/1 queueing system with a single removable and unreliable server whose arrivals form a Poisson process. Service times, repair times, and startup times are assumed to be generally distributed. When the queue length reaches N(N >= 1), the server is immediately turned on but is temporarily unavailable to serve the waiting customers. The server needs a startup time before providing service until there are no customers in the system. We analyze various system performance measures and investigate some designated known expected cost function per unit time to determine the optimal threshold N at a minimum cost. Sensitivity analysis is also studied. (c) 2006 Elsevier Inc. All rights reserved.
Optimal management for a finite M/M/R queueing system with two arrival modes
(2007)
Wang, Kuo-Hsiung
;
Ke, Jyh-Bin
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Pearn, W. L.
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
We consider an M/M/R queueing system with finite capacity N, where customers have two arrival modes under steady-state conditions. It is assumed that each arrival mode is serviced by one or more servers, and that the two arrival modes have equal probabilities of receiving service. Arrival times of the customers and service times of the severs follow an exponential distribution. A cost model is developed to determine the optimal number of servers and the optimal system capacity. The minimum expected cost, the optimal number of servers, the optimal system capacity, and various system characteristics are obtained for some designated system parameters' values. Sensitivity for the minimal cost is also investigated.
Optimal management of the machine repair problem with working vacation: Newton's method
(2009-11-15)
Wang, Kuo-Hsiung
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Chen, Wei-Lun
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Yang, Dong-Yuh
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工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper studies the M/M/1 machine repair problem with working vacation in which the server works with different repair rates rather than completely terminating the repair during a vacation period. We assume that the server begins the working vacation when the system is empty. The failure times, repair times, and vacation times are all assumed to be exponentially distributed. We use the MAPLE software to compute steady-state probabilities and several system performance measures. A cost model is derived to determine the optimal values of the number of operating machines and two different repair rates simultaneously, and maintain the system availability at a certain level. We use the direct search method and Newton's method for unconstrained optimization to repeatedly find the global minimum value until the system availability constraint is satisfied. Some numerical examples are provided to illustrate Newton's method. (C) 2009 Published by Elsevier B.V.
Optimal randomized control policy of an unreliable server system with second optional service and startup
(2008)
Yang, Dong-Yuh
;
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.
Optimization and sensitivity analysis of controlling arrivals in the queueing system with single working vacation
(2010-05-15)
Yang, Dong-Yuh
;
Wang, Kuo-Hsiung
;
Wu, Chia-Huang
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper analyzes the F-policy M/M/1/K queueing system with working vacation and an exponential startup time. The F-policy deals with the issue of controlling arrivals to a queueing system, and the server requires a startup time before allowing customers to enter the system. For the queueing systems with working vacation, the server can still provide service to customers rather than completely stop the service during a vacation period. The matrix-analytic method is applied to develop the steady-state probabilities, and then obtain several system characteristics. We construct the expected cost function and formulate an optimization problem to find the minimum cost. The direct search method and Quasi-Newton method are implemented to determine the optimal system capacity K, the optimal threshold F and the optimal service rates (mu(B), mu(V)) at the minimum cost. A sensitivity analysis is conducted to investigate the effect of changes in the system parameters on the expected cost function. Finally, numerical examples are provided for illustration purpose. (C) 2010 Elsevier B.V. All rights reserved.
Optimization of the T policy M/G/1 queue with server breakdowns and general startup times
(2009-06-01)
Wang, Tsung-Yin
;
Wang, Kuo-Hsiung
;
Pearn, Wen Lea
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper investigates the T policy M/G/1 queue with server breakdowns, and startup times. Customers arrive at the system according to a Poisson process. Service times, repair times, and startup times are assumed to be generally distributed. The server is turned on after a fixed length of time T repeatedly until at least one customer is present in the waiting line. The server needs a startup time before starting the service. We analyze various system performance measures and develop the total expected cost function per unit time in which T is a decision variable. We determine the optimum threshold T* and derive analytical results for sensitivity investigations. The sensitivity analysis is particularly valuable to the system analyst when evaluating future conditions. We also present extensive numerical computation for illustration purpose. (c) 2008 Elsevier B.V. All rights reserved.
The Interrelationship Between N-policy M/G/1/K and F-policy G/M/1/K Queues with Startup Time
(2011-09-01)
Kuo, Ching-Chang
;
Wang, Kuo-Hsiung
;
Pearn, W. L.
;
工業工程與管理學系
;
Department of Industrial Engineering and Management
This paper studies the interrelationship between the N-policy M/G/1/K queue and the F-policy G/M/1/K queue. The N-policy queuing problem investigates the most common issue of controlling service. The F-policy queuing problem deals with the most common issue of controlling arrivals. We provide a recursive method, using the supplementary variable technique and treating the supplementary variable as the remaining service time, to develop the solution algorithm for the N-policy M/G/1/K queue with startup time. We have demonstrated that the N-policy M/G/1/K queue with startup time has been effectively used to derive the solution algorithm to the F-policy G/M/1/K queue with startup time. The interrelationship between the N-policy and the F-policy queueing problems are illustrated analytically for 3-stage Erlang (service or interarrival) time distribution.