On the M/G/1 foreground-background processor-sharing queue (Q1825530)

The authors give a new derivation of the distribution of the equilibrium system state of a service system with Poisson batch arrivals and general service time requirement distribution. The discipline is such that customers whose attained service is x units receive service only when no customers are present with smaller attained service. Those present with least attained service receive service at a rate inversely proportional to their number. The application of the model is to processor-sharing systems.