THE QUEUE-LENGTH DISTRIBUTION FOR M^x/G/1 QUEUE WITH SINGLE SERVER VACATION

This paper studies the bulk-arrival M-x/G/1 queue with single server vacation. By introducing the server busy period and using the Laplace transform, the recursion expression of the Laplace transform of the transient queue-length distribution is derived. Furthermore, the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are obtained. Especially some results for the single-arrival M/G/1 queue with single server vacation and bulk-arrival M-x/G/1 queue but with no server vacation can be derived directly by the results obtained in this paper.

THE TRANSIENT SOLUTION FOR M/G/1 QUEUEWITH SERVER VACATIONS

In this paper, the transient solutions for M/G/1 queues with single server vacation and multiple server vacations are firstly studied, and the recursion expressions of their Laplace transform are given. Further the distribution and stochastic decomposition result of the queue length at a random point in equilibrium are directly obtained from the transient solution. As will be seen this paper provides a intuitive and elegant method for studying transient solutions for M/G/1 queues with single server.

M/G/1 Vacation Queueing Systems with Server Timeout

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=∞and c=0, respectively. The model is extended to the N-policy vacation queueing system.

Effects of Reneging, Server Breakdowns and Vacation on a Batch Arrival Single Server Queueing System with Three Fluctuating Modes of Service

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.

The M^X/M/1 Queue with Multiple Working Vacation

We study a batch arrival MX/M/1 queue with multiple working vacation. The server serves customers at a lower rate rather than completely stopping service during the service period. Using a quasi upper triangular transition probability matrix of two-dimensional Markov chain and matrix analytic method, the probability generating function (PGF) of the stationary system length distribution is obtained, from which we obtain the stochastic decomposition structure of system length which indicates the relationship with that of the MX/M/1 queue without vacation. Some performance indices are derived by using the PGF of the stationary system length distribution. It is important that we obtain the Laplace Stieltjes transform (LST) of the stationary waiting time distribution. Further, we obtain the mean system length and the mean waiting time. Finally, numerical results for some special cases are presented to show the effects of system parameters.

The M//M//1 Queue with Controlled Multiple Working Vacations

In this paper, we study an M/M/1 queue with multiple working vacations under following Bernoulli control policy: at the instants of the completion of a service in vacation, the server will interrupt the vacation and enter regular busy period with probability 1 p (if there are customers in the queue) or continue the vacation with probability p. For this model, we drive the analytic expression of the stationary queue length and demonstrate stochastic decomposition structures of the stationary queue length and waiting time, also we obtain the additional queue length and the additional delay of this model. The results we got agree with the corresponding results for working vacation model with or without vacation interruption if we set p = 0 or p = 1, respectively.

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

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.

Assessment on the component pattern of mountain vacation potential suitability in Hunan Province, China

In China,mountain destinations offer more opportunities for vacation than beaches and springs,with a larger national coverage,richer landscapes and various diverse folk cultures.Hunan Province,for example,serves as a typical mountain tourism destination.Our research aims to assess the potential suitability and component pattern of holidaymaking in Hunan Province to support for scientific endeavors and sustainable use of mountain resources in Hunan.An approach for mapping potential suitability was constructed based on Weighted Linear Combination(WLC)of six primary factors including terrain,climate suitability period,biology and environment,human activity culture,hydrological landscape,and road infrastructure,which is calculated on the base of eleven secondary factors used as suitability criteria.Analytic hierarchy process(AHP)and geographic information system(GIS)were also integrated into the evaluation models to prepare six single and complex factor suitability maps for mountain vacation.Multivariate clustering was used to clarify the component pattern of single factor combinations in each mountain vacation suitability index(MVSI)class.The results have shown that:1)Regions with high suitability are distributed with characteristics of significant dispersion and limited aggregation;2)15.89%of the sample mountains are highly suitable,30.78%are moderately suitable,42.61%are marginally suitable and 10.72%are poorly suitable;3)The complexity of index combination corresponding to each level is different;4)Different combinations emphasize different destination needs.The study reveals the suitability class,characteristics,and limiting factors of mountain vacation in different geographical locations on the provincial scale.These elements play an instructive role in scientific decision-making and orderly exploitation of resources among Hunan’s Mountain destinations.Furthermore,the study can also be used as a basis for the suitability evaluation of mountain vacation in other areas.

Development Strategies of Rural Vacation in Puqian Town, Heyuan City

Puqian Town, Heyuan City has beautiful natural environment and agricultural landscape and unique hot spring resources, so it is very suitable for the development of rural vacation industry. At present, there were only two vacation projects of Bavaria Manor and Ketianxia Hot Spring Resort in the town, and the radiation driving effect is not obvious. In this paper, literature research and interview methods were used to collect data. After 15 interviewees were effectively interviewed and hundreds of data were collected, the PEST theory model and balanced points card theory were used to measure the development factors of rural vacation in Puqian Town, Heyuan City. SWOT matrix matching analysis method was adopted to determine the development strategies of local rural vacation industry.

My Summer Vacation Plan

I have a summer vacation plan.I’m going to the USA with my family.Because it’s very far from Zhongshan,I’m going to America by plane.First, I’d like to go to Washington D.C.There, I will be able to see the White House.It’s said that it is very beautiful.But I only saw it on TV or in the newspapers or on the magazines before.When I get there, I’ll take some nice photos.When I come back to Zhongshan, I’ll share them with my classmates.

A Meaningful Summer Vacation

Meaningful Summer Vacation I'll be a senior high school student after this summer vacation, so my parents and I decided making①this summer vacation a special and memorable one for me.

My Vacation

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Grid Side Distributed Energy Storage Cloud Group End Region Hierarchical Time-Sharing Configuration Algorithm Based onMulti-Scale and Multi Feature Convolution Neural Network

There is instability in the distributed energy storage cloud group end region on the power grid side.In order to avoid large-scale fluctuating charging and discharging in the power grid environment and make the capacitor components showa continuous and stable charging and discharging state,a hierarchical time-sharing configuration algorithm of distributed energy storage cloud group end region on the power grid side based on multi-scale and multi feature convolution neural network is proposed.Firstly,a voltage stability analysis model based onmulti-scale and multi feature convolution neural network is constructed,and the multi-scale and multi feature convolution neural network is optimized based on Self-OrganizingMaps(SOM)algorithm to analyze the voltage stability of the cloud group end region of distributed energy storage on the grid side under the framework of credibility.According to the optimal scheduling objectives and network size,the distributed robust optimal configuration control model is solved under the framework of coordinated optimal scheduling at multiple time scales;Finally,the time series characteristics of regional power grid load and distributed generation are analyzed.According to the regional hierarchical time-sharing configuration model of“cloud”,“group”and“end”layer,the grid side distributed energy storage cloud group end regional hierarchical time-sharing configuration algorithm is realized.The experimental results show that after applying this algorithm,the best grid side distributed energy storage configuration scheme can be determined,and the stability of grid side distributed energy storage cloud group end region layered timesharing configuration can be improved.

重庆市大学生暑期饮酒模式及其相关因素研究

目的分析重庆市大学生暑假期间的饮酒模式和主要影响因素,为进行针对性健康生活方式干预提供一定理论依据。方法采用分层整群抽样的方法,招募到487名大学生,对其中420名饮酒者进行暑期饮酒行为调查。使用频数和百分比进行一般描述,百分率的比较采用χ^(2)检验。使用单因素和多因素二元逻辑回归分析重庆市大学生暑期饮酒的主要影响因素。结果487名大学生中,饮酒率为86.24%(420/487),暑期饮酒率为29.57%(144/487),暑期饮酒量为4(4.0~16.5)标准杯。暑期饮酒者中91.67%(132/144)饮啤酒,56.25%(81/144)在餐馆饮酒。性别[调整比值比(AOR)=4.659,95%可信区间(95%CI)2.998~7.238]、父亲和母亲的饮酒行为(AOR=1.934,95%CI 1.151~3.251;AOR=2.341,95%CI 1.403~3.907)是大学生暑期饮酒行为的影响因素。结论重庆市大学生暑期饮酒较普遍,是健康一级预防的潜在风险点。在进行暑期饮酒一级预防时应重点关注女性和父母不饮酒的大学生。

基于启动时间和完全故障的双阶段休假排队系统的流体模型性能分析

基于风力发电路灯的能量转化机制,该文构建并分析了具有启动时间和完全故障策略的M/M/1排队系统驱动的流体模型.首先,对驱动系统进行模型描述,运用矩阵几何解方法得到驱动系统的稳态概率分布.其次,引入流体模型的净输入率结构,并利用概率分析方法得到流体库存水平在稳态条件下的微分差分方程组,进而运用Laplace-Stieltjes transform(LST)方法得到稳态条件下库存量的均值及空库概率.根据性能指标构建系统的费用函数,在数值分析中给出系统参数对性能指标和费用的影响.