Mathematical problems in the theory of shared-processor systems

This article considers new approaches in queuing theory associated with mathematical modelling and analysis of contemporary computer systems and networks using shared processors. Emphasis is placed on results concerning exact determination of probability distributions for such characteristics as sojourn times and waiting times. Various methods of analyzing shared-processor systems are considered, their characteristics analyzed, and special attention is devoted to the broad class of $M|GI|1$ queuing disciplines that result in Poisson throughput. Several limit theorems for heavyload conditions are described.