带有负顾客且具有反馈的M/M/1/N工作休假排队

研究带反馈的且具有正、负两类顾客的M/M/1/N工作休假排队模型.工作休假策略为空竭服务多重工作休假.负顾客一对一抵消队首正在接受服务的正顾客(若有),若系统中无正顾客时,到达的负顾客自动消失,负顾客不接受服务.完成服务的正顾客以概率p(0相似文献   

带有负顾客且具有Bernoulli反馈的M/M/1工作休假排队

本文研究带反馈的具有正、负两类顾客的M/M/1工作休假排队模型.工作休假策略为空竭服务多重工作休假.负顾客一对一抵消队尾的正顾客(若有),若系统中无正顾客时,到达的负顾客自动消失,负顾客不接受服务.完成服务的正顾客以概率p(0相似文献   

一类带负顾客和反馈的M/G/1休假排队系统

将负顾客和反馈相结合研究了一类带负顾客和反馈M/G/1的休假排队系统,正顾客服务完后以概率1-θ反馈到队尾等待下次服务,以概率θ(0θ≤1)离开系统。负顾客抵消正在接受服务的正顾客,休假策略为单重休假。给出了它们稳态存在的充分必要条件,利用补充变量法和状态转移分析模型,得到了系统主要排队指标和稳态队长概率母函数及概率母函数的随机分解结果。     

带有负顾客的N策略工作休假M/M/1排队

考虑带有正、负顾客的N策略工作休假M/M/1排队。负顾客一对一抵消队尾的正顾客(若有),若系统中无正顾客,到达的负顾客自动消失,负顾客不接受服务。在休假期间,服务员并未完全停止工作而是以较低的服务率为顾客服务。用拟生灭过程和矩阵几何解方法,我们给出了稳态队长和稳态等待时间的分布。此外,我们也证明了稳态条件下的队长和等待时间的条件随机分解并得到了附加队长和附加延迟的分布。     

Bernoulli控制下的带有负顾客和启动时间的M/M/1休假排队

研究在Bernoulli控制下的带有负顾客和启动时间的M/M/1休假排队系统,负顾客抵消队首正在接受服务的正顾客.在正规期,若系统中没有正顾客,服务员以概率α(0≤α≤1)进入普通休假,或以概率β(β=1-α)进入工作休假.利用拟生灭过程和矩阵几何解的方法,得到了系统的稳态队长.最后,通过数值例子来说明-些参数对系统队长的影响.     

带RCE抵消策略的负顾客M/M/1工作休假排队系统

考虑服务员在休假期间不是完全停止工作,而是以相对于正常工作时低些的速率服务顾客的M/M/1工作休假排队模型.在此模型基础上,笔者针对现实的M/M/1排队模型中可能出现的外来干扰因素,提出了带RCE(Removal of Customers at the End)抵消策略的负顾客M/M/1工作休假排队这一新的模型.服务规则为先到先服务.工作休假策略为空竭服务多重工作休假.抵消原则为负顾客一对一抵消队尾的正顾客,若系统中无正顾客时,到达的负顾客自动消失,负顾客不接受服务.使用拟生灭过程和矩阵几何解方法给出了系统队长的稳态分布,证明了系统队长和等待时间的随机分解结果并给出稳态下系统中正顾客的平均队长和顾客在系统中的平均等待时间.     

具有负顾客和抢占反馈的M/G/1随机休假排队系统

本文研究了具有负顾客和抢占反馈机制的非空竭服务随机休假的M/G/1排队系统.正顾客以某种概率抢占和反馈.负顾客移除一个正在接受服务的正顾客.通过构造一个具有吸收态的马尔可夫链求得了系统稳态存在的充分必要条件.利用补充变量法求得了在稳态下系统队长的概率母函数,进而计算出稳态下系统的平均队长.最后我们还给出了一个数值实例.     

带负顾客且具有Bernoulli反馈的Geom/Geom/1休假排队

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.     

带有负顾客的M/M/c多重工作休假排队

考虑服务台在休假期间不是完全停止工作,而是以相对于正常服务期低些的服务率服务顾客的M/M/c工作休假排队模型.在此模型基础上,针对现实的M/M/c排队模型中可能出现的外来干扰因素,提出了带有负顾客的M/M/c工作休假排队这一新的模型.服务规则为先到先服务.工作休假策略为空竭服务异步多重工作休假.抵消原则为负顾客一对一抵消处于正常服务期的正顾客,若系统中无处于正常服务期的正顾客时,到达的负顾客自动消失,负顾客不接受服务.首先,由该多重休假模型得到其拟生灭过程及生成元矩阵,然后运用矩阵几何方法给出系统队长的稳态分布表达式和若干系统指标.     

带有止步和中途退出的成批到达的Mx/M/1/N多重休假排队系统的性能分析

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。     

On the Transient Behavior of the M/M/1 and M/M/1/M Queues

This paper gives a transient analysis of the classic M/M/1 and M/M/1/K queues. Our results are asymptotic as time and queue length become simultaneously large for the infinite capacity queue, and as the system’s storage capacity K becomes large for the finite capacity queue. We give asymptotic expansions for p_n(t), which is the probability that the system contains n customers at time t. We treat several cases of initial conditions and different traffic intensities. The results are based on (i) asymptotic expansion of an exact integral representation for p_n(t) and (ii) applying the ray method to a scaled form of the forward Kolmogorov equation which describes the time evolution of p_n(t).     

非强占优先权下的M/M/1排队

分析带有两个优先权的非强占M/M/1系统的性能,用补充变量法构造向量马尔可夫过程对此排队系统的状态转移方程进行分析,得到两类顾客在非强占优先权的队长联合分布的母函数,进一步讨论,得出了服务台被两类顾客占有和闲置的概率以及两类信元各自的平均队长.     

The M/M/c with critical jobs

We consider theM/M/c queue, where customers transfer to a critical state when their queueing (sojourn) time exceeds a random time. Lower and upper bounds for the distribution of the number of critical jobs are derived from two modifications of the original system. The two modified systems can be efficiently solved. Numerical calculations indicate the power of the approach.     

M/M/1 Queueing systems with inventory

We derive stationary distributions of joint queue length and inventory processes in explicit product form for various M/M/1-systems with inventory under continuous review and different inventory management policies, and with lost sales. Demand is Poisson, service times and lead times are exponentially distributed. These distributions are used to calculate performance measures of the respective systems. In case of infinite waiting room the key result is that the limiting distributions of the queue length processes are the same as in the classical M/M/1/∞-system. All authors were supported by DAAD/KBN grant number D/02/32206.     

The M/M/1+M queue with a utility-maximizing server

We consider an M/M/1+M queue with a human server, who is influenced by incentives. Specifically, the server chooses his service rate by maximizing his utility function. Our objective is to guarantee the existence of a unique maximum. The complication is that most sensible utility functions depend on the server utilization, a non-simple expression. We derive a property of the utilization that guarantees quasiconcavity of any utility function that multiplies the server’s concave (including linear) “value” of his service rate by the server utilization.     

Transient Behaviour of an M/M/1/N queue

For a simple queue with finite waiting space the difference equations satisfied by the Laplace transforms of the state probabilities at finite time are solved and the state probabilities have been obtained. The method economizes in algebra and the simple closed form of the state probabilities is used to obtain important parameters.     

M/M/1/m系统算子的本征值特性(m=1,2,3,4)

研究了m=1,2,3,4时,M/M/1/m算子本征值特性:每个模型的相应本征值的代数重均为1;相邻两个模型系统算子的非零本征值相互交替;随着m值的增大,相应的最大非零本征值逐渐靠近0点;给出了m=3,4时,相应的p_0(t)图像.     

M/M/1算子的其它特征值

证明对一切θ∈（0,1）,θ（2（λμ）~（1/2）-λ-μ）都是偏微分方程形式的M/M/1排队模型主算子的几何重数为1的特征值.     

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Concerning the problem that network congestion risk of computer network service system for some data frames having a full priority of transmission, a method about nonpreemptive limited-priority M/M/n/m queuing system model was proposed. Firstly, as the parameter r of limited-priority was introduced into the model, the data frame with full priority was converted to the one with limited priority. Secondly, in order to lower the risk of computer network service system and stabilize the network system further, the fairness among different priorities was studied in the model. Moreover, by making use of Total Probability Theorem, three results of the models, the average waiting time, the average dwelling time and the average queue length were obtained.     

Strategic joining in M/M/1 retrial queues

The equilibrium and socially optimal balking strategies are investigated for unobservable and observable single-server classical retrial queues. There is no waiting space in front of the server. If an arriving customer finds the server idle, he occupies the server immediately and leaves the system after service. Otherwise, if the server is found busy, the customer decides whether or not to enter a retrial pool with infinite capacity and becomes a repeated customer, based on observation of the system and the reward–cost structure imposed on the system. Accordingly, two cases with respect to different levels of information are studied and the corresponding Nash equilibrium and social optimization balking strategies for all customers are derived. Finally, we compare the equilibrium and optimal behavior regarding these two information levels through numerical examples.