To Modelling of Monoservice Multicast Queueing Systems with Overlapping Resource Requirements

In this paper we consider random resources queueing system with multicasting designed for the performance analysis of modern telecommunication systems. This is a monoservice loss queueing system with random resource requirements, a finite number of servers and limited amount of resources. The term "overlapping resource requirements" reflects the multicast principle: all the customers in th system are served at the same amount of resourses dedicated to the first customer after idle period, as against unicast with providing individual amount for each subscriber accepted in the system. A newcomer never decreases the amount of resources occupied in the system but it can increase this amount in case when its random requirement exeeds the amount of resourses allocated to all its predecessors on the current busy period. Busy period starts when the first customer joins the sytem. When the service time of the first customer ends all the customers leave the system and the idle period starts. For this queueing system the stationary probabilities are obtained as a solution of the stationary equilibrium equations. We also propose the main performance characteristics of the system, i.e. the blocking probability and the mean number of customers in the system.