Analysis of Two Time-Sharing Queueing Models

Two time-sharing models are described. One is the conventional round-robin model in which each customer receives at most q seconds of service at a time. If this completes his service requirement, he leaves the system; otherwise he joins the end of the queue to await his next turn. The second model is a modification of the round-robin system in which the amount of service per pass depends on the rate at which programs arrive in the system. The models are analyzed under the assumption of constant, non-zero overhead when the processor swaps one program for another. Expressions are derived for the mean waiting time in queue as a function of service requirement and for the mean system cost due to waiting time in queue