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

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

Asymptotic analysis of mathematical model of subscriber communication network based on IAB technology

The mathematical queue model of subscriber communication networks based on IAB technology is proposed. The approximation of the probability distribution of a two-dimensional random process for the number of users in the service unit is obtained. A numerical example is considered where the applicability area of the approximation was obtained