排序方式: 共有13条查询结果,搜索用时 15 毫秒
1.
Multi-dimensional asymptotically quasi-Toeplitz Markov chains with discrete and continuous time are introduced. Ergodicity
and non-ergodicity conditions are proven. Numerically stable algorithm to calculate the stationary distribution is presented.
An application of such chains in retrial queueing models with Batch Markovian Arrival Process is briefly illustrated.
AMS Subject Classifications Primary 60K25 · 60K20 相似文献
2.
3.
This paper deals with the single server queueing system with a Batch Markovian Arrival Process (BMAP), the semi-Markovian
(SM) service process, and the retrial process of a MMPP (Markov Modulated Poisson Process) type. The stationary distribution
of orbit size at the embedded and arbitrary epochs is the subject of research.
We appreciate the INTAS program for the financial support of this research via project #96-828. 相似文献
4.
A retrial queueing system with the batch Markovian arrival process and semi-Markovian service is investigated. We suppose that the intensity of retrials linearly depends on the number of repeated calls. The distribution of the number of calls in the system is the subject of research. Asymptotically quasi-Toeplitz 2-dimensional Markov chains are introduced into consideration and applied for solving the problem. 相似文献
5.
Che Soong Kim Moon Ho Lee Alexander Dudin Valentina Klimenok 《Annals of Operations Research》2008,162(1):57-68
In this paper, we consider an N-server queueing model with homogeneous servers in which customers arrive according to a stationary Poisson arrival process.
The service times are exponentially distributed. Two new customer’s service disciplines assuming simultaneous service of arriving
customer by all currently idle servers are discussed. The steady state analysis of the queue length and sojourn time distribution
is performed by means of the matrix analytic methods. Numerical examples, which illustrate advantage of introduced disciplines
comparing to the classical one, are presented. 相似文献
6.
Valentina Klimenok Chesoong Kim Olga Dudina Alexander Dudin 《Applied Mathematical Modelling》2013,37(10-11):6809-6820
Tandem queues are widely used in mathematical modeling of random processes describing the operation of manufacturing systems, supply chains, computer and telecommunication networks. Although there exists a lot of publications on tandem queueing systems, analytical research on tandem queues with non-Markovian input is very limited. In this paper, the results of analytical investigation of two-node tandem queue with arbitrary distribution of inter-arrival times are presented. The first station of the tandem is represented by a single-server queue with infinite waiting room. After service at the first station, a customer proceeds to the second station that is described by a single-server queue without a buffer. Service times of a customer at the first and the second server have PH (Phase-type) distributions. A customer, who completes service at the first server and meets a busy second server, is forced to wait at the first server until the second server becomes available. During the waiting period, the first server becomes blocked, i.e., not available for service of customers. We calculate the joint stationary distribution of the system states at the embedded epochs and at arbitrary time. The Laplace–Stieltjes transform of the sojourn time distribution is derived. Key performance measures are calculated and numerical results presented. 相似文献
7.
Che Soong Kim Valentina Klimenok Alexander Birukov Alexander Dudin 《Annals of Operations Research》2006,141(1):193-210
A single server retrial system having several operation modes is considered. The modes are distinguished by the transition
rate of the batch Markovian arrival process (BMAP), kernel of the semi-Markovian (SM) service process and the intensity of
retrials. Stationary state distribution is calculated under the fixed value of the multi-threshold control strategy. Dependence
of the cost criterion, which includes holding and operation cost, on the thresholds is derived. Numerical results illustrating
the work of the computer procedure for calculation of the optimal values of thresholds are presented. 相似文献
8.
We consider optimal admission control of the GI/PH/1-type queueing system. The problem is then reduced to that of determining multi-threshold strategies. Some numerical examples are presented. The results have applications in the optimal input control of information flow in a computer communication network with heterogeneous traffic. 相似文献
9.
A multi-server retrial queueing model with Batch Markovian Arrival Process and phase-type service time distribution is analyzed. The continuous-time multi-dimensional Markov chain describing the behavior of the system is investigated by means of reducing it to the corresponding discrete-time multi-dimensional Markov chain. The latter belongs to the class of multi-dimensional quasi-Toeplitz Markov chains in the case of a constant retrial rate and to the class of multi-dimensional asymptotically quasi-Toeplitz Markov chains in the case of an infinitely increasing retrial rate. It allows to obtain the existence conditions for the stationary distribution and to elaborate the algorithms for calculating the stationary state probabilities. 相似文献
10.