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1.
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.  相似文献   

2.
研究偏微分方程形式的M/M/1排队模型的主算子在左半复平面中的谱,证明集合{γ∈C|Rγ≤-(λ+μ)}包含于该模型主算子的连续谱与剩余谱的并集.由此指出偏微分方程形式的M/M/1排队模型和常微分方程形式的M/M/1排队模型的本质区别.  相似文献   

3.
证明当.M=1,λ(μ+b)μb时,(-6λ~2+μb-λ(b+μ)-|μb-λ(b+μ)-2λ~2|)/(8λ)是服务员强制休假的M/M/1排队模型的主算子的几何重数为1的特征值.  相似文献   

4.
研究服务员强制休假的M/M/1排队模型的主算子在左半复平面中的特征值,证明(λ-μ-b)-√(b+μ)2-3λ2-μb/2是该主算子的几何重数为1的特征值.  相似文献   

5.
当λ(μ1+μ2)<μ1μ2时,证明-λ是具有可选服务的M/M/1排队模型的主算子的几何重数为1的特征值.  相似文献   

6.
研究偏微分方程形式的M/M/1排队模型的主算子在左半复平面中的谱,证明当顾客的到达率λ,服务员的服务率μ和非零实数b满足一定的条件时,-μ+ib不是该主算子的特征值,其中i~2=-1.  相似文献   

7.
M/M/1排队模型的l~1动态解及其稳定性   总被引:1,自引:1,他引:0  
运用算子半群理论证明了 M/M/1排队模型的 l1动态解的稳定性和正等距性 .  相似文献   

8.
本文研究当顾客的到达率λ,必选服务的服务率μ1,可选服务的服务率μ2以及顾客选择可选服务的概率r满足条件λ/u1+rλ/μ2时,具有可选服务的M/M/1排队模型的主算子在左半实轴上的特征值,证明该条件下模型主算子的点谱包含左半实轴上的区间(max{-λ,-μ1μ2-λ(μ1r+μ2)/|μ1(1-r)-λ|},0).  相似文献   

9.
运用Mathematica软件包模拟一个M/M/1队列问题,显现该软件包对于数学研究与教学的重要价值.通过对问题的分析制定模拟方案,利用计算机仿真形象地展示排队过程.其方法适用于一般队列问题.  相似文献   

10.
M/M/1排队系统四个指标的渐近性质   总被引:1,自引:0,他引:1  
应用 C0 -半群理论研究 M/M/1排队系统中四个指标 :系统中顾客的平均等待时间 ,顾客的平均逗留时间 ,顾客总数和等待服务的顾客总数的渐近性质 ,得到这四个指标的渐近稳定性结果 .  相似文献   

11.
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 pn(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 pn(t) and (ii) applying the ray method to a scaled form of the forward Kolmogorov equation which describes the time evolution of pn(t).  相似文献   

12.
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.  相似文献   

13.
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.  相似文献   

14.
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.  相似文献   

15.
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.  相似文献   

16.
M/M/1/m系统算子的本征值特性(m=1,2,3,4)   总被引:2,自引:1,他引:1  
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.  相似文献   

17.
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.  相似文献   

18.
��ǿռ��������ȨM/M/n/m�Ŷ�ϵͳ   总被引:1,自引:0,他引:1  
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.  相似文献   

19.
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.  相似文献   

20.
证明2√λμ-λ-μ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.  相似文献   

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