A Note on Some Mathematical Models of Time-Sharing Systems

This note deals with time-sharing disciplines where the arrival process is homogeneous Poisson and service requirements are exponentially distributed. The investigated regimes are: (A) ordinary round-robin (R.R.), (B) R.R. with the quantum allocated to a customer is a function of the number of quanta he has already received. These models were studied by Shemer, who derived for both models mathematical expressions for the expected total response time of a customer whose service requirement is given. Shemer's results are in disagreement with those of other authors and may only serve as a good approximation. His method is utilized here in a more general case of model (A) (with the discrepancies eliminated), and it also yields, after some improvement, a better approximation for model (B). © 1971, ACM. All rights reserved.