Evaluation of memory capacity for heavily loaded systems with priorities

Abstract

Subject of Research. The paper deals with the models of computer networks represented by queuing systems with heterogeneous flow of requests. The models show processing and transmission of packets of different classes. Requirements for the quality indicators of packet transmission for each class are implemented by the use of the priority service disciplines. Operation in high load conditions is a distinctive feature of modern telecommunication systems, leading to probability increase of packets (requests) loss. This necessitates the use of models with limited memory capacity. Analytic study of such models is accompanied by complex and bulky mathematical calculations with explicit results only in special cases under certain assumptions. For example, with regard to the probability laws, describing the processes of receiving and serving of requests that limits the usage of such models. Method. The study of such systems with simulation methods is also problematic in view of statistical instability of operation characteristics for high load conditions. We propose an approach to the study of heavily loaded systems with priorities based on the models with unlimited memory capacity. Main Results. Analytical results for service characteristics with two moments of distribution were obtained. The distribution laws approximation of the number of requests in system is based on these results. Practical Relevance. We have shown the possibility of approximation of continuous multi-exponential distributions that enable to assess memory capacity for given probability of losses for different classes of requests.