The total capacity of customers in the MMPP/GI/∞ queueing system

In the paper, the infinite-server queueing system with a random capacity of customers is considered. In this system, the total capacity of customers is analysed by means of the asymptotic analysis method with high-rate Markov Modulated Poisson Process arrivals. It is obtained that the stationary probability distribution of the total customer capacity can be approximated by the Gaussian distribution. Parameters of the approximation is also derived in the pape

Resource retrial queue with two orbits and negative customers

In this paper, a multi-server retrial queue with two orbits is considered. There are two arrival processes of positive customers (with two types of customers) and one process of negative customers. Every positive customer requires some amount of resource whose total capacity is limited in the system. The service time does not depend on the customer’s resource requirement and is exponentially distributed with parameters depending on the customer’s type. If there is not enough amount of resource for the arriving customer, the customer goes to one of the two orbits, according to his type. The duration of the customer delay in the orbit is exponentially distributed. A negative customer removes all the customers that are served during his arrival and leaves the system. The objects of the study are the number of customers in each orbit and the number of customers of each type being served in the stationary regime. The method of asymptotic analysis under the long delay of the customers in the orbits is applied for the study. Numerical analysis of the obtained results is performed to show the influence of the system parameters on its performance measure

Resource queueing system with feedback as a model for servicing two types of traffic

The resource multi-server queue with two arrival processes is considered. The analytical expressions for the means of the number of customers in the orbits are found. The stationary distribution of the two-dimensional stochastic process of numbers of customers in the service block is found, which allows calculating the main probability and numerical characteristics. A numerical example is considered, where the applicability area of approximation was obtained

Multi-service resource queue with the multy-component Poisson arrivals

In many papers devoted to telecommunication systems, multiservice queueing models with heterogeneous customer arrivals are given. As a rule, there is streaming traffic, corresponding to the audio and video conference, and elastic traffic, corresponding to the data and file transmission. Different types of traffic require different quality of service, therefore the multi-service systems are also differentiated service systems. Such papers are aimed at developing a framework for estimating the quality of service indicators in new generation multi-service networks. This paper considers a multiservice resource queueing system with three Poisson arrivals, one of which is splitting. The equation for the probabilities distribution of the total resource amounts on the system blocks is compiling by the dynamic screening method, and using the characteristic function of the stationary distribution, the solution is obtaining. The numerical characteristics of the system performance are obtained by the method of moments using characteristic function. A numerical example shows that arrivals intensity growing increases optimal total resource amounts on system blocks in the system with limited resources, and the splitting arrivals affect the correlation between total resource amounts

Resource Retrial Queue with Two Orbits and Negative Customers

In this paper, a multi-server retrial queue with two orbits is considered. There are two arrival processes of positive customers (with two types of customers) and one process of negative customers. Every positive customer requires some amount of resource whose total capacity is limited in the system. The service time does not depend on the customer’s resource requirement and is exponentially distributed with parameters depending on the customer’s type. If there is not enough amount of resource for the arriving customer, the customer goes to one of the two orbits, according to his type. The duration of the customer delay in the orbit is exponentially distributed. A negative customer removes all the customers that are served during his arrival and leaves the system. The objects of the study are the number of customers in each orbit and the number of customers of each type being served in the stationary regime. The method of asymptotic analysis under the long delay of the customers in the orbits is applied for the study. Numerical analysis of the obtained results is performed to show the influence of the system parameters on its performance measures

Имитационное моделирование системы массового обслуживания требований случайного объема

В работе получен алгоритм имитационного моделирования бесконечнолинейной системы массового обслуживания требований случайного объема. Также проведено сравнение эмпирических и теоретических результатов для функции распределения числа заявок в системе и для функции распределения суммарного объема требований в системе. Показано, что полученная имитационная модель имеет широкую область применимости