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1.
We study a system of two non-identical and separate M/M/1/? queues with capacities (buffers) C1 < ∞ and C2 = ∞, respectively, served by a single server that alternates between the queues. The server’s switching policy is threshold-based, and, in contrast to other threshold models, is determined by the state of the queue that is not being served. That is, when neither queue is empty while the server attends Qi (i = 1, 2), the server switches to the other queue as soon as the latter reaches its threshold. When a served queue becomes empty we consider two switching scenarios: (i) Work-Conserving, and (ii) Non-Work-Conserving. We analyze the two scenarios using Matrix Geometric methods and obtain explicitly the rate matrix R, where its entries are given in terms of the roots of the determinants of two underlying matrices. Numerical examples are presented and extreme cases are investigated. 相似文献
2.
M. Samanta 《Australian & New Zealand Journal of Statistics》1986,28(2):164-172
The probability density function (pdf) of a two parameter exponential distribution is given by f(x; p, s?) =s?-1 exp {-(x - ρ)/s?} for x≥ρ and 0 elsewhere, where 0 < ρ < ∞ and 0 < s?∞. Suppose we have k independent random samples where the ith sample is drawn from the ith population having the pdf f(x; ρi, s?i), 0 < ρi < ∞, 0 < s?i < s?i < and f(x; ρ, s?) is as given above. Let Xi1 < Xi2 <… < Xiri denote the first ri order statistics in a random sample of size ni, drawn from the ith population with pdf f(x; ρi, s?i), i = 1, 2,…, k. In this paper we show that the well known tests of hypotheses about the parameters ρi, s?i, i = 1, 2,…, k based on the above observations are asymptotically optimal in the sense of Bahadur efficiency. Our results are similar to those for normal distributions. 相似文献
3.
《随机性模型》2013,29(3):387-424
This paper considers a single server queue that handles arrivals from N classes of customers on a non-preemptive priority basis. Each of the N classes of customers features arrivals from a Poisson process at rate λ i and class-dependent phase type service. To analyze the queue length and waiting time processes of this queue, we derive a matrix geometric solution for the stationary distribution of the underlying Markov chain. A defining characteristic of the paper is the fact that the number of distinct states represented within the sub-level is countably infinite, rather than finite as is usually assumed. Among the results we obtain in the two-priority case are tractable algorithms for the computation of both the joint distribution for the number of customers present and the marginal distribution of low-priority customers, and an explicit solution for the marginal distribution of the number of high-priority customers. This explicit solution can be expressed completely in terms of the arrival rates and parameters of the two service time distributions. These results are followed by algorithms for the stationary waiting time distributions for high- and low-priority customers. We then address the case of an arbitrary number of priority classes, which we solve by relating it to an equivalent three-priority queue. Numerical examples are also presented. 相似文献
4.
《随机性模型》2013,29(1):1-24
A sufficient condition is proved for geometric decay of the steady-state probabilities in a quasi-birth-and-death process having a countable number of phases in each level. If there is a positive number η and positive vectors x = (x i) and y = (y j ) satisfying some equations and inequalities, the steady-state probability π mi decays geometrically with rate η in the sense π mi ~ cη m x i as m → ∞. As an example, the result is applied to a two-queue system with shorter queue discipline. 相似文献
5.
《随机性模型》2013,29(2-3):485-505
ABSTRACT We study the queue length distribution of a queueing system with BMAP arrivals under D-policy. The idle server begins to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We derive the vector generating functions of the queue lengths both at a departure and at an arbitrary point of time. Mean queue lengths are derived and a numerical example is presented. 相似文献
6.
We explicitly compute the sojourn time distribution of an arbitrary customer in an M/M/1 processor sharing (PS) queue with permanent customers. We notably exhibit the orthogonal structure associated with this queuing system and we show how sieved Pollaczek polynomials and their associated orthogonality measure can be used to obtain an explicit representation for the complementary cumulative distribution function of the sojourn time of a customer. This explicit formula subsequently allows us to compute the two first moments of this random variable and to study the asymptotic behavior of its distribution. The most salient result is that the decay rate depends on the load of the system and the number K of permanent customers. When the load is above a certain threshold depending on K, the decay rate is identical to that of a regular M/M/1 PS queue. 相似文献
7.
This paper studies a system with multiple infinite-server queues that are modulated by a common background process. If this background process, being modeled as a finite-state continuous-time Markov chain, is in state j, then the arrival rate into the i-th queue is λi, j, whereas the service times of customers present in this queue are exponentially distributed with mean μ? 1i, j; at each of the individual queues all customers present are served in parallel (thus reflecting their infinite-server nature).Three types of results are presented: in the first place (i) we derive differential equations for the probability-generating functions corresponding to the distributions of the transient and stationary numbers of customers (jointly in all queues), then (ii) we set up recursions for the (joint) moments, and finally (iii) we establish a central limit theorem in the asymptotic regime in which the arrival rates as well as the transition rates of the background process are simultaneously growing large. 相似文献
8.
《随机性模型》2013,29(3):363-380
Abstract We study the queue length distribution of a queueing system with MAP arrivals under D-policy. The idle server begins to serve the customers only when the sum of the service times of all waiting customers exceeds some fixed threshold D. We derive the vector generating functions of the queue lengths both at a departure and at an arbitrary point of time. Mean queue lengths will be derived from these transform results. A numerical example is provided. 相似文献
9.
AbstractIn this article, customers’ strategic behavior and social optimation in a constant retrial queue with setup time and the N-policy are investigated. Customers who find the server isn’t idle either leave forever or enter an orbit. After a service, the server will seek a customer from the orbit at a constant rate. The server is closed whenever the system becomes empty, and is activated when the number of waitlisted customers reaches a threshold. We obtain the equilibrium arrival rates in different states. There exist both Follow-the-Crowd (FTC) and Avoid-the-Crowd (ATC) behaviors. Through the Particle Swarm Optimization (PSO) algorithm, we numerically obtain the optimal solution of the social welfare maximization problem. Finally, numerical examples are presented to illustrate the sensitivity of system performance measures. 相似文献
10.
《随机性模型》2013,29(1):185-213
ABSTRACT We consider a class of single server queueing systems in which customers arrive singly and service is provided in batches, depending on the number of customers waiting when the server becomes free. Service is independent of the batch size. This system could also be considered as a batch service queue in which a server visits the queue at arbitrary times and collects a batch of waiting customers for service, or waits for a customer to arrive if there are no waiting customers. A waiting server immediately collects and processes the first arriving customer. The system is considered in discrete time. The interarrival times of customers and the inter-visit times of the server, which we call the service time, have general distributions and are represented as remaining time Markov chains. We analyze this system using the matrix-geometric method and show that the resulting R matrix can be determined explicitly in some special cases and the stationary distributions are known semi-explicitly in some other special cases. 相似文献
11.
《随机性模型》2013,29(4):483-506
Abstract For a discrete‐time closed cyclic network of single server queues whose service rates are non‐decreasing in the queue length, we compute the queue‐length distribution at each node in terms of throughputs of related networks. For the asymptotic analysis, we consider sequences of networks where the number of nodes grows to infinity, service rates are taken only from a fixed finite set of non‐decreasing sequences, the ratio of customers to nodes has a limit, and the proportion of nodes for each possible service‐rate sequence has a limit. Under these assumptions, the asymptotic throughput exists and is calculated explicitly. Furthermore, the asymptotic queue‐length distribution at any node can be obtained in terms of the asymptotic throughput. The asymptotic throughput, regarded as a function of the limiting customer‐to‐node ratio, is strictly increasing for ratios up to a threshold value (possibly infinite) and is constant thereafter. For ratios less than the threshold, the asymptotic queue‐length distribution at each node has finite moments of all orders. However, at or above the threshold, bottlenecks (nodes with asymptotically‐infinite mean queue length) do occur, and we completely characterize such nodes. 相似文献
12.
Let X1,…,Xn be exchangeable normal variables with a common correlation p, and let X(1) > … > X(n) denote their order statistics. The random variable σni=n—k+1xi, called the selection differential by geneticists, is of particular interest in genetic selection and related areas. In this paper we give results concerning a conjecture of Tong (1982) on the distribution of this random variable as a function of ρ. The same technique used can be applied to yield more general results for linear combinations of order statistics from elliptical distributions. 相似文献
13.
Serkan Eryilmaz 《统计学通讯:理论与方法》2013,42(19):5628-5636
ABSTRACTLet (Xi, Yi), i = 1, …, n be a pair where the first coordinate Xi represents the lifetime of a component, and the second coordinate Yi denotes the utility of the component during its lifetime. Then the random variable Y[r: n] which is known to be the concomitant of the rth order statistic defines the utility of the component which has the rth smallest lifetime. In this paper, we present a dynamic analysis for an n component system under the above-mentioned concomitant setup. 相似文献
14.
A Gaussian copula is widely used to define correlated random variables. To obtain a prescribed Pearson correlation coefficient of ρx between two random variables with given marginal distributions, the correlation coefficient ρz between two standard normal variables in the copula must take a specific value which satisfies an integral equation that links ρx to ρz. In a few cases, this equation has an explicit solution, but in other cases it must be solved numerically. This paper attempts to address this issue. If two continuous random variables are involved, the marginal transformation is approximated by a weighted sum of Hermite polynomials; via Mehler’s formula, a polynomial of ρz is derived to approximate the function relationship between ρx and ρz. If a discrete variable is involved, the marginal transformation is decomposed into piecewise continuous ones, and ρx is expressed as a polynomial of ρz by Taylor expansion. For a given ρx, ρz can be efficiently determined by solving a polynomial equation. 相似文献
15.
《随机性模型》2013,29(2):157-190
In this paper, we establish an explicit form of matrix decompositions for the queue length distributions of the MAP/G/1 queues under multiple and single vacations with N-policy. We show that the vector generating function Y (z) of the queue length at an arbitrary time and X (z) at departures are decomposed into Y (z) = p idle (z)ζ Y (z) and X (z) = p idle (z)ζ X (z) where p idle (z) is the vector generating function of the queue length at an arbitrary epoch at which the server is not in service, and ζ Y (z) and ζ X (z) are unidentified matrix generating functions. 相似文献
16.
This paper deals with a single server Poisson arrival queue with two phases of heterogeneous service along with a Bernoulli schedule vacation model, where after two successive phases service the server either goes for a vacation with probability p (0≤p≤1) or may continue to serve the next unit, if any, with probability q(=1−p). Further the concept of multiple vacation policy is also introduced here. We obtained the queue size distributions at a departure epoch and at a random epoch, Laplace Stieltjes Transform of the waiting time distribution and busy period distribution along with some mean performance measures. Finally we discuss some statistical inference related issues. 相似文献
17.
ABSTRACTWe consider a model consisting of two fluid queues driven by the same background continuous-time Markov chain, such that the rates of change of the fluid in the second queue depend on whether the first queue is empty or not: when the first queue is nonempty, the content of the second queue increases, and when the first queue is empty, the content of the second queue decreases.We analyze the stationary distribution of this tandem model using operator-analytic methods. The various densities (or Laplace–Stieltjes transforms thereof) and probability masses involved in this stationary distribution are expressed in terms of the stationary distribution of some embedded process. To find the latter from the (known) transition kernel, we propose a numerical procedure based on discretization and truncation. For some examples we show the method works well, although its performance is clearly affected by the quality of these approximations, both in terms of accuracy and run time. 相似文献
18.
《随机性模型》2013,29(1):31-42
Abstract We give a sufficient condition for the exponential decay of the tail of a discrete probability distribution π = (π n ) n≥0 in the sense that lim n→∞(1/n) log∑ i>n π i = ?θ with 0 < θ < ∞. We focus on analytic properties of the probability generating function of a discrete probability distribution, especially, the radius of convergence and the number of poles on the circle of convergence. Furthermore, we give an example of an M/G/1 type Markov chain such that the tail of its stationary distribution does not decay exponentially. 相似文献
19.
Qing Xiao 《统计学通讯:理论与方法》2017,46(4):1594-1605
For the issue of generating correlated random vector containing discrete variables, one major obstacle is to determine a suitable correlation coefficient ρz in normal space for a specified correlation coefficient ρx. This paper develops a method to solve this problem. First, the double integral evaluated for ρx is transformed into independent standard uniform space, then, a Quasi Monte Carlo method is introduced to calculate the double integral. For a given ρx, an appropriate ρz is determined by a false position method. Compared with existing methodologies, the proposed method is less efficient, but it is relatively easy to implement. 相似文献
20.
《随机性模型》2013,29(2-3):531-550
ABSTRACT In this paper, we consider a retrial queueing system consisting of a waiting line of infinite capacity in front of a single server subject to breakdowns. A customer upon arrival may join the queue (waiting line) or go to the retrial orbit (another queue) to retry for service after a random time. Only the customer at the head of the retrial orbit is allowed to retry for service. Upon retrial, the customer enters the service if the server is idle; otherwise, it may go back to the retrial orbit or leave the system (become impatient). All the interarrival times, service times, server up times, server down times and retrial times are exponential, and all the necessary independence conditions in these variables are assumed. For this system, we provide sufficient conditions under which, for any given number of customers in the orbit, the stationary probability of the number of customers in the waiting line decays geometrically. We also provide explicitly an expression for the decay parameter. 相似文献