Mathematical Model of Information Processing with Relative Priority and Different Service Intensity

This paper proposes a model of information processing with priorities. The peculiarity of the model is that the system receives two flows of different types of data of different intensity. Thus we may operate with two classes of customers. The first class of the customers are priority. In this paper, we consider a system with a relative priority. It means that the arrived priority customer does not push out a customer of the second class, if the last one is servicing by a server. The service time of customers is random with an exponential probability distribution. Each type of customer has its own service duration. It is supposed that each class of customers has its own queue. The queue sizes are the same. Limiting the length of queues is the reason for the system to work with losses. It means that if at the time of receipt of a customer the server is idle, then a customer immediately gets up for service; if the server is busy servicing another customer, and there is a place in the queue, the newly received customer enters the waiting queue, otherwise it is lost. We suggest a system of equations for stationary probabilities and an original numerical implementation of finding the system's probability distribution. We also obtain the characteristics of the QoS parameters of customers - the probability of receiving a customer for instant service, the probability of getting into the system regardless of priority, the loss probability for priority customers, the loss probability for non-priority customers, the probability of refusing to service a customer of any class, the probability that the server is currently serves the customer of the first class, the probability that the server is currently servicing the customer of the second class.