Processor sharing system with non-homogeneous customers and limitations

Abstract

We investigate a processor sharing system in which each customer has three interdependent random characteristics: the required number of homogeneous discrete resourse units, capacity (volume) and service time (length). The total capacity of customers and the total number of discrete resourse units are limited. The type of a customer is defined by the number of resourse units required for his servise. We determine a stationary distribution of the number of customers present in the system, as well as the loss probability for a customer of each type.