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1.
有Bernoulli休假和可选服务的M/G/1重试反馈排队模型   总被引:1,自引:0,他引:1  
考虑具有可选服务的M/G/1重试反馈排队模型,其中服务台有Bernoulli休假策略.系统外新到达的顾客服从参数为λ的泊松过程.重试区域只允许队首顾客重试,重试时间服从一般分布.所有的顾客都必须接受必选服务,然而只有其中部分接受可选服务.每个顾客每次被服务完成后可以离开系统或者返回到重试区域.服务台完成一次服务以后,可以休假也可以继续为顾客服务.通过嵌入马尔可夫链法证明了系统稳态的充要条件.利用补充变量的方法得到了稳态时系统和重试区域中队长分布.我们还得到了重试期间服务台处于空闲的概率,重试区域为空的概率以及其他各种指标.并证出在系统中服务员休假和服务台空闲的时间定义为广义休假情况下也具有随机分解特征.  相似文献   

2.
讨论了有Bernoulli休假策略和可选服务的离散时间Geo/G/1重试排队系统.假定一旦顾客发现服务台忙或在休假就进入重试区域,重试时间服从几何分布.顾客在进行第一阶段服务结束后可以离开系统或进一步要求可选服务.服务台在每次服务完毕后,可以进行休假,或者等待服务下一个顾客.还研究了在此模型下的马尔可夫链,并计算了在稳态条件下的系统的各种性能指标以及给出一些特例和系统的随机分解.  相似文献   

3.
研究了带有止步和中途退出的M~x/M/1/N单重工作休假排队系统.顾客成批到达,到达后每批中的顾客,或者以概率b决定进入队列等待服务,或者以概率1-b止步(不进入系统).顾客进入系统后可能因为等待的不耐烦而在没有接受服务的情况下离开系统(中途退出).系统中一旦没有顾客,服务员立即进入单重工作休假.首先,利用马尔科夫过程理论建立了系统稳态概率满足的方程组.其次利用矩阵解法求出了稳态概率的矩阵解并得到了系统的平均队长、平均等待队长以及顾客的平均消失概率等性能指标.最后通过数值例子分析了工作休假时的低服务率η和休假率θ这两个参数对系统平均队长的影响.  相似文献   

4.
A retrial queue accepting two types of positive customers and negative arrivals, mixed priorities, unreliable server and multiple vacations is considered. In case of blocking the first type customers can be queued whereas the second type customers leave the system and try their luck again after a random time period. When a first type customer arrives during the service of a second type customer, he either pushes the customer in service in orbit (preemptive) or he joins the queue waiting to be served (non-preemptive). Moreover negative arrivals eliminate the customer in service and cause server’s abnormal breakdown, while in addition normal breakdowns may also occur. In both cases the server is sent immediately for repair. When, upon a service or repair completion, the server finds no first type customers waiting in queue remains idle and activates a timer. If timer expires before an arrival of a positive customer the server departs for multiple vacations. For such a system the stability conditions and the system state probabilities are investigated both in a transient and in a steady state. A stochastic decomposition result is also presented. Interesting applications are also discussed. Numerical results are finally obtained and used to investigate system performance.  相似文献   

5.
K. Farahmand 《Queueing Systems》1996,22(3-4):425-435
We analyze a model queueing system in which customers cannot be in continuous contact with the server, but must call in to request service. If the server is free, the customer enters service immediately, but if the server is occupied, the unsatisfied customer must break contact and reapply for service later. There are two types of customer present who may reapply. First transit customers who arrive from outside according to a Poisson process and if they find the server busy they join a source of unsatisfied customers, called the orbit, who according to an exponential distribution reapply for service till they find the server free and leave the system on completion of service. Secondly there are a number of recurrent customers present who reapply for service according to a different exponential distribution and immediately go back in to the orbit after each completion of service. We assume a general service time distribution and calculate several characterstic quantities of the system for both the constant rate of reapplying for service and for the case when customers are discouraged and reduce their rate of demand as more customers join the orbit.  相似文献   

6.
This paper investigates a batch arrival retrial queue with general retrial times, where the server is subject to starting failures and provides two phases of heterogeneous service to all customers under Bernoulli vacation schedules. Any arriving batch finding the server busy, breakdown or on vacation enters an orbit. Otherwise one customer from the arriving batch enters a service immediately while the rest join the orbit. After the completion of two phases of service, the server either goes for a vacation with probability p or may wait for serving the next customer with probability (1 − p). We construct the mathematical model and derive the steady-state distribution of the server state and the number of customers in the system/orbit. Such a model has potential application in transfer model of e-mail system.  相似文献   

7.
本文中研究了一个带有启动时间的Geom/Geom/1多重工作休假排队模型。服务台在休假期间,不停止服务,而是以较低的服务率为顾客提供服务。运用拟生灭过程和矩阵几何解的方法,给出了该模型的稳态队长分布,并求出了平均队长以及顾客的平均逗留时间。  相似文献   

8.
Crowdsourcing is getting popular after a number of industries such as food, consumer products, hotels, electronics, and other large retailers bought into this idea of serving customers. In this paper, we introduce a multi-server queueing model in the context of crowdsourcing. We assume that two types, say, Type 1 and Type 2, of customers arrive to a c-server queueing system. A Type 1 customer has to receive service by one of c servers while a Type 2 customer may be served by a Type 1 customer who is available to act as a server soon after getting a service or by one of c servers. We assume that a Type 1 customer will be available for serving a Type 2 customer (provided there is at least one Type 2 customer waiting in the queue at the time of the service completion of that Type 1 customer) with probability \(p, 0 \le p \le 1\). With probability \(q = 1 - p\), a Type 1 customer will opt out of serving a Type 2 customer provided there is at least one Type 2 customer waiting in the system. Upon completion of a service a free server will offer service to a Type 1 customer on an FCFS basis; however, if there are no Type 1 customers waiting in the system, the server will serve a Type 2 customer if there is one present in the queue. If a Type 1 customer decides to serve a Type 2 customer, for our analysis purposes that Type 2 customer will be removed from the system as Type 1 customer will leave the system with that Type 2 customer. Under the assumption of exponential services for both types of customers we study the model in steady state using matrix analytic methods and establish some results including explicit ones for the waiting time distributions. Some illustrative numerical examples are presented.  相似文献   

9.
本文研究了带有止步和中途退出的M^x/M/1/N多重休假排队系统。顾客成批到达,到达后每批中的顾客,或者以概率b决定进入队列等待服务,或者以概率1-b止步(不进入系统)。顾客进入系统后可能因为等待的不耐烦而在没有接受服务的情况下离开系统(中途退出)。系统中一旦没有顾客,服务员立即进行多重休假。首先,利用马尔科夫过程理论建立了系统稳态概率满足的方程组。其次,在利用高等代数相关知识证明了相关矩阵可逆性的基础上,利用矩阵解法求出了稳态概率的矩阵解,并得到了系统的平均队长、平均等待队长以及顾客的平均损失率等性能指标。  相似文献   

10.
研究带有反馈的具有正、负两类顾客的Geom/Geom/1离散时间休假排队模型.休假排队策略为单重休假,其中负顾客不接受服务,只起一对一抵消队首正在接受服务的顾客作用.完成服务的正顾客以概率σ(0≤σ≤1)等待下次服务,以概率σ离开系统.运用拟生灭过程和矩阵几何解方法得到队长的稳态分布的存在条件和表达式,进而求出系统队长稳态分布的随机分解.此外,我们利用了数值例子进一步反映参数对平均队长的影响.  相似文献   

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