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.

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.

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.

Performance Assessment and Configuration Analysis in the Study of SCADA System (Supervisory Control and Data Acquisition)

Queuing models are used to assess the functionality and aesthetics of SCADA systems for supervisory control and data collection.Here,the main emphasis is on how the queuing theory can be used in the system’s design and analysis.The analysis’s findings indicate that by using queuing models,cost-performance ratios close to the ideal might be attained.This article discusses a novel methodology for evaluating the service-oriented survivability of SCADA systems.In order to evaluate the state of service performance and the system’s overall resilience,the framework applies queuing theory to an analytical model.As a result,the SCADA process is translated using the M^(X)/G/1 queuing model,and the queueing theory is used to evaluate this design’s strategy.The supplemental variable technique solves the queuing problem that comes with the subsequent results.The queue size,server idle time,utilization,and probabilistic generating factors of the distinct operating strategies are estimated.Notable examples were examined via numerical analysis using mathematical software.Because it is used frequently and uses a statistical demarcation method,this tactic is completely acceptable.The graphical representation of this perspective offers a thorough analysis of the alleged limits.

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

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

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 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.

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.

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.

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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Optimal Control Policy of M/G/1 Queueing System with Delayed Randomized Multiple Vacations Under the Modified Min(N,D)-Policy Control

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.

三亚市观光旅游者和度假旅游者生态足迹研究(英文)

Based on the theory of ecological footprint and tourists' consumption structure, the model of tourist ecological footprint was divided into six sub-models including catering, accommodation, shopping, sightseeing, shopping and entertainment, and ecological footprint of sightseeing tourists and vacation tourists in Sanya City was analyzed. The result showed that per capita ecological footprint of vacation tourists was higher than that of sightseeing tourists in Sanya City. The influential factor of the two kinds of tourists was slightly different in their proportion of sightseeing and entertainment factors. In the future, it should advocate sightseeing tourists to rationally make use of ecological resources, vacation tourists to have a healthy and ecological holiday, so as to ensure sustainable development of tourism.

Some Reliability Problems Arising in the M^x/G(M/G)/1 Repairable Queueing System with Single Delay Vacation

On the basis of Ref.\, the M x/G(M/G)/1 repairable queueing system with single delay vacation is discussed again. The following reliability problems of the service station are studied: (a) The probability that it fails at time t , i.e. its unavailability; (b) The expected failure number during the time interval (0,t\];; (c) The expected failure number during the ″server busy period″; (d) The expected downtime during the time interval (0,t\]. Some reliability results of the service station are obtained. These results would be interest to reliability analysts.

An M/G/1 Queueing System with Delay Server Vacations

In this paper we study the transient property of the queue length for the M/G/1 queueing system with delay server vacations.Using the server busy period and the Laplace transformation we directly obtain the recursion formula of the L transformation of the transient queue length distribution at time t , and also the recursion formula of the equilibrium distribution for calculating conveniently.As will be seen, this paper provides an intuitive and elegant method for studying transient properties of M/G/1 type queueing systems.