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Optimal policy for controlling two-server queueing systems with jockeying 认领 引用
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作者 LIN Bing LIN Yuchen BHATNAGAR Rohit 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2022年第1期144-155,共12页
This paper studies the optimal policy for joint control of admission, routing, service, and jockeying in a queueing system consisting of two exponential servers in parallel.Jobs arrive according to a Poisson process.U... This paper studies the optimal policy for joint control of admission, routing, service, and jockeying in a queueing system consisting of two exponential servers in parallel.Jobs arrive according to a Poisson process.Upon each arrival, an admissionouting decision is made, and the accepted job is routed to one of the two servers with each being associated with a queue.After each service completion, the servers have an option of serving a job from its own queue, serving a jockeying job from another queue, or staying idle.The system performance is inclusive of the revenues from accepted jobs, the costs of holding jobs in queues, the service costs and the job jockeying costs.To maximize the total expected discounted return, we formulate a Markov decision process(MDP) model for this system.The value iteration method is employed to characterize the optimal policy as a hedging point policy.Numerical studies verify the structure of the hedging point policy which is convenient for implementing control actions in practice. 展开更多
关键词 queueing system jockeying optimal policy Markov decision process(MDP) dynamic programming
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SUBGEOMETRIC RATES OF CONVERGENCE OF THE GI/G/1 QUEUEING SYSTEM 认领 引用
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作者 李晓花 侯振挺 《Acta Mathematica Scientia》 SCIE CSCD 2012年第5期1983-1996,共14页
The article deals with the waiting time process of the GI/G/1 queueing system.We shall give that the rate of convergence to the stationary distribution and the decay of the stationary tail only depend on the tail of t... The article deals with the waiting time process of the GI/G/1 queueing system.We shall give that the rate of convergence to the stationary distribution and the decay of the stationary tail only depend on the tail of the service distribution,but not on the interarrival distribution.We shall also give explicit criteria for the rate of convergence and decay of stationary tail for three specific types of subgeometric cases（Case 1：the rate function r（n）=exp（sn1/1＋α）,α〉0,s〉0;Case 2：polynomial rate function r（n）=nα,α〉0;Case 3：logarithmic rate function r（n）=logαn,α〉0）. 展开更多
关键词 GI/G/1 queueing system subgeometric rate of convergence polynomial rate of convergence logarithmic rate of convergence
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An Algorithm for Estimating the Expected Number of Customers for a Class of Markovian Queueing Systems 认领 引用
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作者 Hung-Yuan Tu Hillel Kumin 《American Journal of Operations Research》 2020年第4期132-137,共6页
An algorithm is presented for estimating the expected number of customers for a class of Markovian queueing systems. The class is characterized by those systems whose transition matrix for the underlying customer arri... An algorithm is presented for estimating the expected number of customers for a class of Markovian queueing systems. The class is characterized by those systems whose transition matrix for the underlying customer arrival and departure process is finite, irreducible, and aperiodic. The algorithm does not depend on a closed-form solution for the limiting behavior of the queue. The expected number of customers is frequently used as a measure of effectiveness to describe the behavior of the system or to optimize its design or control. To calculate such a quantity one must usually obtain a closed-form expression for the steady-state probabilities. Unfortunately, of the myriad of Markovian queueing systems, only a few have known closed-form expressions for their steady-state probabilities. The most well-known, using Kendall’s notation, are the M/M/1 and the M/M/c system. The algorithm described below estimates the expected number in the system under steady-state without a need for closed form steady-state probabilities. All that is needed is the transition matrix for the underlying Markov chain. 展开更多
关键词 Queueing Systems Markov Chain Expected Number in System
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Development and Investigation of the Program Model of Multichannel Queueing System with Unreliable Recoverable Servers in Matlab Environment 认领 引用 被引量：2
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作者 Ramaz R. Shamugia 《International Journal of Communications, Network and System Sciences》 2018年第11期229-237,共9页
In real life, in different industries, we often deal with systems designed for multiple use for performing single-type tasks. Processes taking place at this time are called service of requirements, and the systems the... In real life, in different industries, we often deal with systems designed for multiple use for performing single-type tasks. Processes taking place at this time are called service of requirements, and the systems themselves—Queueing Systems. This article is dedicated to computer software modelling of processes taking place in the systems in question, Markov processes in particular. In this article, by means of Matlab environment, software realization of one of the typical models of queueing service theory-multichannel QS with unreliable recoverable servers and limited number of requirements in the system, is fulfilled. The results of this research are important because it gives the possibility to use received results to determine optimality degree of some real queueing systems that possess Markov property. 展开更多
关键词 Queueing System Simulation Queue Modeling Imitation Complex System
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M/G/1 Vacation Queueing Systems with Server Timeout 认领 引用 被引量：4
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作者 Oliver C. Ibe 《American Journal of Operations Research》 2015年第2期77-88,共12页
We consider a single-server vacation queueing system that operates in the following manner. When the server returns from a vacation, it observes the following rule. If there is at least one customer in the system, the... We consider a single-server vacation queueing system that operates in the following manner. When the server returns from a vacation, it observes the following rule. If there is at least one customer in the system, the server commences service and serves exhaustively before taking another vacation. If the server finds the system empty, it waits a fixed time c. At the expiration of this time, the server commences another vacation if no customer has arrived;otherwise, it serves exhaustively before commencing another vacation. Analytical results are derived for the mean waiting time in the system. The timeout scheme is shown to be a generalized scheme of which both the single vacation and multiple vacations schemes are special cases, with c=&infin;and c=0, respectively. The model is extended to the N-policy vacation queueing system. 展开更多
关键词 Vacation Queueing Systems Timeout Policies Performance Analysis N-Policy with Timeout
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Effects of Reneging, Server Breakdowns and Vacation on a Batch Arrival Single Server Queueing System with Three Fluctuating Modes of Service 认领 引用 被引量：1
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作者 Samuel Ugochukwu Enogwe H. Onyebuchi Obiora-Ilouno 《Open Journal of Optimization》 2020年第4期105-128,共24页
This article examines the effects of reneging, server breakdown and server vacation on the various states of the batch arrivals queueing system with single server providing service to customers in three fluctuating mo... This article examines the effects of reneging, server breakdown and server vacation on the various states of the batch arrivals queueing system with single server providing service to customers in three fluctuating modes. In this queueing system, any batch arrival joins the queue if the server is busy or on vacation or under repair. However, if the server is free, one customer from the arriving batch joins the service immediately while others join the queue. In case of server breakdown, the customer whose service is interrupted returns back to the head of the queue. As soon as the server has is repaired, the server attends to the customer in mode 1. For this queueing system, customers that are impatient due to breakdown and server vacation may renege (leave the queue without getting service). Due to fluctuating modes of service delivery, the system may provide service with complete or reduced efficiency. Consequently, we construct the mathematical model and derive the probability generating functions of the steady state probabilities of several states of the system including the steady state queue size distribution. Further, we discuss some particular cases of the proposed queueing model. We present numerical examples in order to demonstrate the effects of server vacation and reneging on the various states of the system. The study revealed that an increase in reneging and a decrease in server vacation results in a decrease in server utilization and an increase in server’s idle time provided rates of server breakdown and repair completion are constant. In addition, the probability of server vacation, the probability of system is under repair and the probabilities that the server provides service in three fluctuating modes decreases due to an increase in reneging and a decrease in vacation completion rates. 展开更多
关键词 Queueing Reneging Server Vacation Server Breakdowns Fluctuating Modes of Service
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A Non-Preemptive Priority Queueing System with a Single Server Serving Two Queues M/G/1 and M/D/1 with Optional Server Vacations Based on Exhaustive Service of the Priority Units 认领 引用
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作者 Kailash C. Madan 《Applied Mathematics》 2011年第6期791-799,共9页
We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson stream... We study a vacation queueing system with a single server simultaneously dealing with an M/G/1 and an M/D/1 queue. Two classes of units, priority and non-priority, arrive at the system in two independent Poisson streams. Under a non-preemptive priority rule, the server provides a general service to the priority units and a deterministic service to the non-priority units. We further assume that the server may take a vacation of random length just after serving the last priority unit present in the system. We obtain steady state queue size distribution at a random epoch. Corresponding results for some special cases, including the known results of the M/G/1 and the M/D/1 queues, have been derived. 展开更多
关键词 Non Preemptive Priority Queueing System Modified Server Vacations Combination of General Service and Deterministic Service Steady State Queue Size Distribution
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Equilibrium Joining Strategies of Retrial Queueing Systems with Two-phase Service and Priority-purchasing 认领 引用
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作者 Fan XU Rui-ling TIAN Qi SHAO 《Acta Mathematicae Applicatae Sinica》 SCIE CSCD 2026年第2期489-511,共23页
This paper considers the customer's equilibrium joining-balking behavior in a retrial queue with two-phase service and priority-purchasing.If the arriving customer finds the server busy,the customer can make three... This paper considers the customer's equilibrium joining-balking behavior in a retrial queue with two-phase service and priority-purchasing.If the arriving customer finds the server busy,the customer can make three choices(joining the orbit,purchasing the priority or balking)based on different levels of the system information.We consider two cases:the partially observable case and the fully unobservable case.The customer's equilibrium strategy for the partially observable case and the fully unobservable case are derived.Then,an algorithm is developed to solve the optimal fee that maximizes the service provider's profit.Finally,the influence of system parameters on performance measures,equilibrium joining strategies and the service provider's profits is illustrated by numerical examples. 展开更多
关键词 queueing system retrial customers priority-purchasing equilibrium strategy two-phase service
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Transient and Comparative Analysis of a Single-Server Queueing System with Preventive Maintenance,Bernoulli Feedback and Randomized Vacation Strategy 认领 引用
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作者 Wenlong CHEN Shaojun LAN 《Journal of Systems Science and Information》 CSCD 2026年第2期350-382,共33页
This paper investigates an M/G/1 queueing system that integrates preventive maintenance,randomized vacation policy,and Bernoulli feedback mechanism.By applying the law of total probability decomposition and Laplace tr... This paper investigates an M/G/1 queueing system that integrates preventive maintenance,randomized vacation policy,and Bernoulli feedback mechanism.By applying the law of total probability decomposition and Laplace transform(LT)technique,we derive explicit expressions for the LT of the transient queue length distribution starting from arbitrary initial states.Based on the transient results,the steady-state queue length distribution and the corresponding additional queue length distribution are also obtained.Furthermore,we show that the proposed model reduces to several classical systems under specific parameter settings.Finally,numerical experiments are conducted to compare the proposed model with classical vacation models,to examine the system capacity optimization design under loss constraints,and to illustrate the transient behavior of the system.These findings verify the validity and practical relevance of the considered model. 展开更多
关键词 M/G/1 queueing system randomized vacation strategy preventive maintenance stochastic decomposition property Bernoulli feedback
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A NEW AND DIRECT METHOD OF ANALYSIS THE DEPARTURE PROCESSES OF SINGLE SERVER QUEUEING SYSTEMS 认领 引用 被引量：4
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作者 唐应辉 《Acta Mathematica Scientia》 SCIE 1996年第S1期131-138,共8页
In this paper, using the stochastic decomposition and renewal theory we provide the direct method for analysis the departure process of single sever M/G/1 queueing system, and further discuss the departure process of ... In this paper, using the stochastic decomposition and renewal theory we provide the direct method for analysis the departure process of single sever M/G/1 queueing system, and further discuss the departure process of GI/G/1 queueing system. The method provided in this paper is new and concise, which make us see dearly the structure of the departure process of a single server queueing system. 展开更多
关键词 Queue M/G/1 GI/G/1 departure decomposition
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Bayesian inference and prediction in multi-server Markovian queueing system with reverse balking:A simulation-based approach 认领 引用
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作者 Asmita Tamuli Dhruba Das 《Statistical Theory and Related Fields》 CSCD 2025年第4期367-383,共17页
This article presents an in-depth exploration of classical and Bayesian inference methods to estimate the traffic intensity parameter,providing a comprehensive comparison of these two statistical paradigms in a novel ... This article presents an in-depth exploration of classical and Bayesian inference methods to estimate the traffic intensity parameter,providing a comprehensive comparison of these two statistical paradigms in a novel multiserver Markovian queueing model(M/M/s)incorporating the phenomenon of reverse balking.The classical inference relies on maximum likelihood(ML)estimation,while the Bayesian approach leverages prior distributions and posterior analysis to enhance estimates.The results indicate that Bayesian methods offer better flexibility and precision compared to traditional ML estimates.Additionally,the predictive probabilities for the number of customers in the system are calculated for different hyper-parameter values of the prior through extensive simulation techniques.The results provide valuable insights for optimizing queue management and improving service efficiency in systems where reverse balking occurs.Moreover,a real-life example is presented to demonstrate the practical implementation of the proposed methodology.This work not only advances the theoretical understanding of queueing dynamics,but also offers practical implications for industries relying on efficient service mechanisms. 展开更多
关键词 M/M/s queueing system reverse balking maximum likelihood estimation Bayesian estimation prediction
A GATED SERVICE SINGLE VACATION M/G/1 QUEUE SYSTEM WITH SETUP AND CLOSEDOWN TIMES AND DIFFERENT CUSTOMER ARRIVAL RATES 认领 引用
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作者 Ying SUN Zhanyou MA Tongyu XU 《Acta Mathematica Scientia》 SCIE CSCD 2026年第1期407-426,共20页
A gated service single vacation M/G/1 queue with setup and closedown periods,and different customer arrival rates,is studied in this paper.The probability generating function of the number of systems for customers who... A gated service single vacation M/G/1 queue with setup and closedown periods,and different customer arrival rates,is studied in this paper.The probability generating function of the number of systems for customers who are at the initial moment of service period is analyzed by using a total probability theorem,and the stability condition of the system is obtained.The stationary distribution of the queue length is solved by the regeneration cycle method.The stochastic decomposition of queue length in the steady state is calculated,and the service cycle is obtained.Moreover,classified discussions are established in order to solve the steady-state distribution for the waiting time.The variation of system performance indicators with parameters is analyzed by performing numerical experiments. 展开更多
关键词 different arrival rates regeneration cycle method stochastic decomposition theorem stationary queue length
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Markov Skeleton Processes and Applications to Queueing Systems 认领 引用 被引量：13
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作者 Zhen-ting HouSchool of Mathematical Sciences and Computing Technology, Central South University. Changsha 410075, China 《Acta Mathematicae Applicatae Sinica》 2002年第4期537-552,共16页
In this paper, we apply the backward equations of Markov skeleton processes to qucueing systems. The transient distribution of the waiting time of a GI/G/1 queueing system, the transient distribution of the length of ... In this paper, we apply the backward equations of Markov skeleton processes to qucueing systems. The transient distribution of the waiting time of a GI/G/1 queueing system, the transient distribution of the length of a GI/G/N queueing system and the transient distribution of the length of queueing networks are obtained. 展开更多
关键词 Markov skeleton process (MSP) queueing system (H,Q)-pair backward equation
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On the M/G/1 queueing system with multiclass customers and fixed feedback 认领 引用 被引量：2
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作者 ZHANG Qi-zhi 《The Journal of China Universities of Posts and Telecommunications》 EI 2008年第2期114-121,共8页
The M/G/1 queueing system with multiclass customer arrivals, fixed feedback, and first come first served policy is considered, where different classes of customers have different arrival rates, service-time distributi... The M/G/1 queueing system with multiclass customer arrivals, fixed feedback, and first come first served policy is considered, where different classes of customers have different arrival rates, service-time distributions, and feedback numbers. The joint probabifity generation function of queue size of each class and the Laplace-Stieltjes transform of the total sojourn time of a customer in each class are presented, which extended the results obtained by Choi B D. The mean queue size of each class and mean total sojourn time of a customer in each class are obtained with this result. The results can be used in computer and communication networks for their performance analysis. 展开更多
关键词 M/G/1 queueing system feedback multiclasscustomers queue size sojourn time
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MATCHED QUEUEING SYSTEMS WITH A DOUBLE INPUT 认领 引用
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作者 徐光辉 何启明 刘西锁 《Acta Mathematicae Applicatae Sinica》 1993年第1期50-62,共13页
In this paper, we study the matched queueing system with a double input, MoM/PH/1,where the two inputs are two independent Poisson processes, and the service time is of PH-distribution.The L.S. transforms and the expe... In this paper, we study the matched queueing system with a double input, MoM/PH/1,where the two inputs are two independent Poisson processes, and the service time is of PH-distribution.The L.S. transforms and the expectations of the distributions of occupation time and virtual waiting time of the type-Ⅰ customer are derived.The probability that the server is working, the mean non-idle period, and the mean busy period are also derived. The related algorithms are given with numerical results. 展开更多
关键词 MATCHED QUEUEING SYSTEMS WITH A DOUBLE INPUT
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RELIABILITY INDICES OF DISCRETE-TIME Geo^X/G/1 QUEUEING SYSTEM WITH UNRELIABLE SERVICE STATION AND MULTIPLE ADAPTIVE DELAYED VACATIONS 认领 引用 被引量：10
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作者 Yinghui TANG Miaomiao YU +1 位作者 Xi YUN Shujuan HUANG 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2012年第6期1122-1135,共14页
This paper considers the discrete-time GeoX/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the perspective of reliability research. Following problems will be discussed... This paper considers the discrete-time GeoX/G/1 queueing model with unreliable service station and multiple adaptive delayed vacations from the perspective of reliability research. Following problems will be discussed： 1） The probability that the server is in a ＂generalized busy period＂ at time n; 2） The probability that the service station is in failure at time n, i.e., the transient unavailability of the service station, and the steady state unavailability of the service station; 3） The expected number of service station failures during the time interval （0, hi, and the steady state failure frequency of the service station; 4） The expected number of service station breakdowns in a server＇s ＂generalized busy period＂. Finally, the authors demonstrate that some common discrete-time queueing models with unreliable service station are special cases of the model discussed in this paper. 展开更多
关键词 Delayed vacation policy discrete-time queueing model failure frequency reliability index total probability decomposition unavailability unreliable.
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Optimal Control Policy of M/G/1 Queueing System with Delayed Randomized Multiple Vacations Under the Modified Min(N,D)-Policy Control 认领 引用 被引量：10
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作者 Le Luo Ying-Hui Tang +1 位作者 Miao-Miao Yu Wen-Qing Wu 《Journal of the Operations Research Society of China》 EI CSCD 2023年第4期857-874,共18页
Based on the number of customers and the server’s workload,this paper proposes a modified Min(N,D)-policy and discusses an M/G/1 queueing model with delayed randomized multiple vacations under such a policy.Applying ... Based on the number of customers and the server’s workload,this paper proposes a modified Min(N,D)-policy and discusses an M/G/1 queueing model with delayed randomized multiple vacations under such a policy.Applying the well-known stochastic decomposition property of the steady-state queue size,the probability generating function of the steady-state queue length distribution is obtained.Moreover,the explicit expressions of the expected queue length and the additional queue length distribution are derived by some algebraic manipulations.Finally,employing the renewal reward theorem,the explicit expression of the long-run expected cost per unit time is given.Furthermore,we analyze the optimal policy for economizing the expected cost and compare the optimal Min(N,D)-policy with the optimal N-policy and the optimal D-policy by using numerical examples. 展开更多
关键词 M/G/1 queue Modified Min(N,D)-policy Randomized multiple vacations Queue length generating function Optimal joint control policy
THE MATCHED QUEUEING SYSTEM GI。PH/PH/1 认领 引用
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作者 徐光煇 何启明 《Acta Mathematicae Applicatae Sinica》 1994年第1期34-47,共14页
We study the matched queueing system GIoPH/PH/1, where the type-I input is a renewal process, the type-II input is a PH renewal process, and the service times are i. i. d. random variables with PH-distributions. First... We study the matched queueing system GIoPH/PH/1, where the type-I input is a renewal process, the type-II input is a PH renewal process, and the service times are i. i. d. random variables with PH-distributions. First, a condition is given for the stationarity of the system. Then the distributions of the number of type-I customers at the arrival epoches of type-I customers and the number of type-I customers at an arbitrary epoch are derived. We also discuss the occupation time and the waiting time. Their L. S. transforms are derived. Finally, we discuss some problems in numerical computation. 展开更多
关键词 Queueing theory matched queueing system matrix-analytic method Markov renewal processes positive recurrent occupation time.
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MATCHED QUEUEING SYSTEM M·PH/G/1 认领 引用
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作者 徐光煇 何启明 《Acta Mathematicae Applicatae Sinica》 1993年第2期104-114,共11页
In this paper,we study the matched queueing system,MoPH/G/1,where the type-Ⅰ input is a Poisson process,the type-Ⅱ input is a PH renewal process, and the service times are i.i.d. random variables. A necessary and su... In this paper,we study the matched queueing system,MoPH/G/1,where the type-Ⅰ input is a Poisson process,the type-Ⅱ input is a PH renewal process, and the service times are i.i.d. random variables. A necessary and sufficient condition for the stationariness of the system is given.The expectations of the length of the non-idle period and the number of customers served in a non-idle period are obtained. 展开更多
关键词 MATCHED QUEUEING SYSTEM M PH/G/1 exp
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Improved Weighted Fair Queueing Scheduling Algorithm for Integrated Information Transmission in Power Systems 认领 引用
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作者 DONG Xueyuan WANG Xiaoru 《中国电机工程学报》 EI CSCD 北大核心 2012年第22期I0020-I0020,共1页
The sharing of operation and management information is required by smart grid.The amount of information transmitted in electric power communication systems will increase greatly in the near future.The integrated infor... The sharing of operation and management information is required by smart grid.The amount of information transmitted in electric power communication systems will increase greatly in the near future.The integrated information transmission technology is an important method for transmitting various kinds of information via the existing broadband channels and networks in power systems.To implement integrated information transmission in power systems,the problem about how to guarantee the quality of service(QoS)of the communication services must be dealt with. 展开更多
关键词 smart grid integrated information transmission service of quality differentiated services queue scheduling algorithm
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