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On a BMAP/G/1 G-queue with Setup Times and multiple vacations

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Acta Mathematicae Applicatae Sinica 2011年第4期27卷 625-638页

作者： Yi PENG Xiang-qun YANG School of Mathematical Science and Computing Technology Central South University Changsha 410075 Hunan China College of Mathematics and Computer Science Hunan Normal University Changsha 410081 China

In this paper, we consider a BMAP/G/1 G-queue with setup times and multiple vacations. Arrivals of positive customers and negative customers follow a batch Markovian arrival process （BMAP） and Markovian arrival process （MAP） respectively. The arrival of a negative customer removes all the customers in the system when the server is working. The server leaves for a vacation as soon as the system empties and is allowed to take repeated （multiple） vacations. By using the supplementary variables method and the censoring technique, we obtain the queue length distributions. We also obtain the mean of the busy period based on the renewal theory.

关键词： G-queues batch Markovian arrival process (BMAP) setup times multiple vacations censoring technique Markov chains

Transient Analysis of a Two-Heterogeneous Severs Queue with Impatient Behaviour and multiple vacations

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Journal of Systems Science and Information 2018年第1期9卷 69-84页

作者： Jia XU Liwei LIU Taozeng ZHU School of Science Nanjing University of Science and Technology School of Management University of Science and Technology of China

We consider an M/M/2 queueing system with two-heterogeneous servers and multiple vacations. Customers arrive according to a Poisson process. However, customers become impatient when the system is on vacation. We obtain explicit expressions for the time dependent probabilities,mean and variance of the system size at time t by employing probability generating functions, continued fractions and properties of the modified Bessel functions. Finally, two special cases are provided.

关键词： M/M/2 queueing system multiple vacations probability generating functions continued fractions modified Bessel functions

Cold standby repairable system with working vacations and vacation interruption

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Journal of Systems Engineering and Electronics 2015年第5期26卷 1127-1134页

作者： Baoliang Liu Lirong Cui Yanqing Wen College of Mathematics and Computer Science Shanxi Datong University School of Management and Economics Beijing Institute of Technology

This paper studies a cold standby repairable system with working vacations and vacation interruption. The repairman’s multiple vacations policy, the working vacations policy and the vacation interruption are considered simultaneously. The lifetime of components follows a phase-type(PH) distribution. The repair time in the regular repair period and the working vacation period follow other two PH distributions at different rates. For this system, the vector-valued Markov process governing the system is constructed. We obtain several important performance measures for the system in transient and stationary regimes applying matrixanalytic methods. Finally, a numerical example is given to illustrate the results obtained.

关键词： reliability phase-type(PH) distribution multiple vacations working vacations vacation interruption rate of occurrence of failure

Product Form Solution of a Queuing-Inventory System with Lost Sales and Server Vacation

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Journal of Systems Science & Complexity 2024年第2期37卷 729-758页

作者： YUE Dequan ZHANG Yuying XU Xiuli YUE Wuyi School of Science Yanshan UniversityQinhuangdao 066004China School of Economics and Management Yanshan UniversityQinhuangdao 066004China The Kyoto College of Graduate Studies for Informatics Kyoto City 606-8225Japan

In this study,the authors consider an M/M/1 queuing system with attached inventory under an(s,S)control *** server takes multiple vacations whenever the inventory is *** is assumed that the lead time and the vacation time follow exponential *** authors formulate the model as a quasi-birth-and-dearth(QBD)process and derive the stability condition of the ***,the stationary distribution in product form for the joint process of the queue length,the inventory level,and the server’s status is ***,the conditional distributions of the inventory level when the server is on and operational,and when it is off due to a vacation,are *** the stationary distribution,the authors obtain some performance measures of the *** authors investigate analytically the effect of the server’s vacation on the performance ***,several numerical examples are presented to investigate the effects of some parameters on the performance measures,the optimal policy,and the optimal cost.

关键词： Cost function multiple vacations product form solution queuing-inventory system (s S)control policy

PERFORMANCE ANALYSIS OF POWER SAVING CLASS OF TYPE Ⅲ IN IEEE 802.16E WITH USER INITIATED TRAFFIC

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Journal of Electronics(China) 2010年第1期27卷 127-133页

作者： Gao Jie Jin Shunfu Tian Naishuo Han Li College of Information Science and Engineering Yanshan University Qinhuangdao 056004 China

A novel method for analysing the performance of power saving class of Type III in IEEE 802.16e is proposed, which is applicable to design, maintenance and management for mobile wireless metropolitan area network. Considering the memoryless nature of user initiated packet arrival, a Geom/G/1 queue model with multiple vacations and setup period is built to capture the principle for the power saving class of Type III. By using an embedded Markov chain method and the boundary state variable theory, we obtain the queueing measures such as queueing length, waiting time and busy cycle in steady state. Correspondingly, we derive explicitly the performance measures for the power saving class of Type III in terms of handover ratio, energy saving ratio, and average packet response time. Based on numerical results, we develop a cost function to determine numerically the optimal length of sleep window and the minimal cost with different offered loads.

关键词： system IEEE 802.16e Power saving class of Type III Sleep mode multiple vacations Queueing