Bounds for P(X + X ⩽ k2σ) are given where X1 and X2 are independent normal variables having zero means and variances σ, σ, respectively. This is generalized when X1 and X2 are dependent variables with known covariance matrix. 相似文献
This paper analyses the E/M/c queueing system and shows how to calculate the expected number in the system, both at a random epoch and immediately preceding an arrival. These expectations are expressed in terms of certain initial probabilities which are determined by linear equations. The advantages and disadvantages of this method are also discussed. 相似文献
We consider single-server queueing systems with the queue discipline “first come, first served,” interarrival times {uk, k ≥ l}, and service times {uk, k ≥ l}, where the {uk} and {uk} are independent sequences of non-negative random variables that are independently but not necessarily identically distributed. Let Xk = uk − uk (k ≥ 1), S0 0, Sn = X1 + X2 … + Xn(n≥1). It is known that the (possibly nonhomogeneous) random walk {Sn} determines the behavior of the system. In this paper we make stochastic comparisons of two such systems σ1,σ2 whose basic random variables X and X are stochastically ordered. The corresponding random walks are also similarly ordered, and this leads to stochastic comparisons of idle times, duration of busy period and busy cycles, number of customers served during a busy period, and output from the system. In the classical case of identical distributions of {uk} and {uk} we obtain further comparisons. Our results are for the transient behavior of the systems, not merely for steady state. 相似文献
A unifying survey of the literature related to the knapsack problem; that is, maximize \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_i {v_i x_{i,} } $\end{document}, subject to \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_j {w_i x_i W} $\end{document} and xi ? 0, integer; where vi, wi and W are known integers, and wi (i = 1, 2, …, N) and W are positive. Various uses, including those in group theory and in other integer programming algorithms, as well as applications from the literature, are discussed. Dynamic programming, branch and bound, search enumeration, heuristic methods, and other solution techniques are presented. Computational experience, and extensions of the knapsack problem, such as to the multi-dimensional case, are also considered. 相似文献
Let Xi be independent IFR random variables and let Yi be independent exponential random variables such that E[Xi]=E[Yi] for all i=1, 2, ? n. Then it is well known that E[min (Xi)] ≥E[min (Xi)]. Nevertheless, for 1≤i≤n exponentially distributed Xi's and for a decreasing convex function ?(.). it is shown that . 相似文献
For each n, X1(n),…Xn(n) are independent and identically distributed random variables, with common probability density function Where c, θ, α, and r(y) are all unknown. It is shown that we can make asymptotic inferences about c, θ, and α, when r(y) satisfies mild conditions. 相似文献
Let {Xi} be independent HNBUE (Harmonic New Better Than Used in Expectation) random variables and let {Yi} be independent exponential random variables such that E{Xi}=E{Yi} It is shown that \documentclass{article}\pagestyle{empty}\begin{document}$ E\left[{u\left({\mathop {\min \,X_i}\limits_{l \le i \le n}} \right)} \right] \ge E\left[{u\left({\mathop {\min \,Y_i}\limits_{l \le i \le n}} \right)} \right] $\end{document} for all increasing and concave u. This generalizes a result of Kubat. When comparing two series systems with components of equal cost, one with lifetimes {Xi} and the other with lifetimes {Yi}, it is shown that a risk-averse decision-maker will prefer the HNBUE system. Similar results are obtained for parallel systems. 相似文献
Let us assume that observations are obtained at random and sequentially from a population with density function In this paper we consider a sequential rule for estimating μ when σ is unknown corresponding to the following class of cost functions In this paper we consider a sequential rule for estimating μ when σ is unknown corresponding to the following class of cost functions Where δ(XI,…,XN) is a suitable estimator of μ based on the random sample (X1,…, XN), N is a stopping variable, and A and p are given constants. To study the performance of the rule it is compared with corresponding “optimum fixed sample procedures” with known σ by comparing expected sample sizes and expected costs. It is shown that the rule is “asymptotically efficient” when absolute loss (p=-1) is used whereas the one based on squared error (p = 2) is not. A table is provided to show that in small samples similar conclusions are also true. 相似文献
This paper considers the problem of the optimal redeployment of a resource among different geographical locations. Initially, it is assumed that at each location i, i = 1,…, n, the level of availability of the resource is given by a1 ≧ 0. At time t > 0, requirements Rf(t) ≧ 0 are imposed on each location which, in general, will differ from the a1. The resource can be transported from any one location to any other in magnitudes which will depend on t and the distance between these locations. It is assumed that ΣRj > Σat The objective function consideis, in addition to transportation costs incurred by reallocation, the degree to which the resource availabilities after redeployment differ from the requirements. We shall associate the unavailabilities at the locations with the unreadiness of the system and discuss the optimal redeployment in terms of the minimization of the following functional forms: \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_{j = 1}^n {kj(Rj - yj) + } $\end{document} transportation costs, Max \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop {Max}\limits_j \,[kj(Rj - yj)] + $\end{document} transportation costs, and \documentclass{article}\pagestyle{empty}\begin{document}$ \sum\limits_{j = 1}^n {kj(Rj - yj)^2 + } $\end{document} transportation costs. The variables yj represent the final amount of the resource available at location j. No benefits are assumed to accrue at any location if yj > Rj. A numerical three location example is given and solved for the linear objective. 相似文献
Let be a basic solution to the linear programming problem subject to: where R is the index set associated with the nonbasic variables. If all of the variables are constrained to be nonnegative integers and xu is not an integer in the basic solution, the linear constraint is implied. We prove that including these “cuts” in a specified way yields a finite dual simplex algorithm for the pure integer programming problem. The relation of these modified Dantzig cuts to Gomory cuts is discussed. 相似文献
For each n, X1(n),…, Xn(n) are independent and identically distributed random variables, each with cumulative distribution function F(x) which is known to be absolutely continuous but is otherwise unknown. The problem is to test the hypothesis that \documentclass{article}\pagestyle{empty}\begin{document}$ F(x) = G\left( {{\textstyle{{x - \theta _1 } \over {\theta _2 }}}} \right) $\end{document}, where the cumulative distribution function Gx is completely specified and satisfies certain regularity conditions, and the parameters θ1, θ2 are unknown and unspecified, except that the scale parameter θ2, is positive. Y1 (n) ≦ Y2 (n) ≦ … ≦ Yn (n)are the ordered values of X1(n),…, Xn(n). A test based on a certain subset of {Yi(n)} is proposed, is shown to have asymptotically a normal distribution when the hypothesis is true, and is shown to be consistent against all alternatives satisfying a mild regularity condition. 相似文献