Study on Ecological Footprint of Sightseeing Tourists and Vacation Tourists in Sanya City

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.

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.

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.

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.

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.

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.

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.

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.

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.

Machine Interference Problem with Reliable Server under Single Vacation

The machine interference problem with reliable server under single vacation is considered here. There are M similar machines that are subject to fail or breaks down with a single server who is responsible for repairing or maintaining the failed machines. The machine fails completely at random with rate 2 and they are serviced in order of breaks down. More so, the machines operate independently but are subject to fail or break down. The service time distributions of the failed machines are assumed to be exponentially distributed with state dependent service rate #n, where n is the number of failed machines. By state dependent service rate we mean a situation where the rate of service depends on the number of failed machines present in the system. The Chapman-Kolmogorov differential equations obtained for the reliable server under single vacation model is solved through ODE45 （Runge-Kutta algorithm of order 4 and 5） in MATLAB programming language. The transient probabilities obtained are used to compute the operational measures of performance for the systems. The following time dependent operational measures of performance for the system are obtained： expected number of failed machines, expected number of operating machines, machine availability, expected idle period, expected busy period, operational utilization of the machine, the variance of the expected number of failed machine and variance of expected number of operating machine in the system. The effects of failure rate of machines, service rate of failed machines and the number of operating machines are investigated; it is observe that the rate at which machine fails and is serviced, affect the expected number of failed and operating machines in the system. The CPU time for obtaining the transient results for the systems and the variance of the systems are reported in this work.

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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Customer Joining Behavior and Regulation Strategy in Visible Multi-Server Queues with Synchronous Vacations of Partial Servers

This paper studies customer joining behavior and system regulation strategy in nonexhaustive visible M/M/m queues with synchronous vacations of a part of the servers.Once this part of the servers are idle,they take multiple vacations simultaneously(vacation period).Until there are customers waiting in the queue,they are reactivated and all servers are busy or idle(busy period).The authors call this part of the servers as“partial servers”.In view of the fully visible queue and the almost visible queue,the authors obtain customers’equilibrium joining threshold strategies and their socially optimal joining threshold strategies,respectively,and observe that customer joining behavior in equilibrium generally makes the system overcrowded,which makes the equilibrium social welfare lower than the optimal social welfare.After regulation,interestingly,for optimizing social welfare,the system manager hopes not only customers arriving in vacation period pay attention to the number of partial servers,but also customers arriving in busy period should care about it rather than ignore.Moreover,arranging more servers for vacation does not necessarily lead to the decrease of social welfare on condition that the number of partial servers is close to m.As for the information advantage of the fully visible case,it is not obvious for increasing social welfare and even unfavorable to servers’profit unless the number of partial servers is big enough.Furthermore,given the different composition of social welfare,there exists the optimal number of partial servers and the optimal arrival rate of customers for maximizing social welfare.

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 M/M/1 QUEUE WITH WORKING VACATIONS AND VACATION INTERRUPTIONS

In this paper, we study the M/M/1 queue with working vacations and vacation interruptions. The working vacation is introduced recently, during which the server can still provide service on the original ongoing work at a lower rate. Meanwhile, we introduce a new policy：, the server can come back from the vacation to the normal working level once some indices of the system, such as the number of customers, achieve a certain value in the vacation period. The server may come back from the vacation without completing the vacation. Such policy is called vacation interruption. We connect the above mentioned two policies and assume that if there are customers in the system after a service completion during the vacation period, the server will come back to the normal working level. In terms of the quasi birth and death process and matrix-geometric solution method, we obtain the distributions and the stochastic decomposition structures for the number of customers and the waiting time and provide some indices of systems.

THE M/PH/1 QUEUE WITH WORKING VACATIONS AND VACATION INTERRUPTION

We study an M/PH/1 queue with phase type working vacation and vacation interruption where the vacation time follows a phase type distribution. The server serves the customers at a lower rate in a vacation period. The server comes back to the regular busy period at a service completion without completing the vacation. Such policy is called vacation interruption. In terms of quasi birth and death process and matrix-geometric solution method, we obtain the stationary queue length distribution. Moreover we obtain the conditional stochastic decomposition structures of queue length and waiting time when the service time distribution in the regular busy period is exponential.