The impact of a job buffer in a token-bank rate-control throttle

Abstract

In this paper we study a rate-control throttle with a finite-capacity token bank and a finite-capacity job buffer. The primary purpose is to gain additional insight into the impact of the job buffer. We show that the overflow processes of jobs and tokens depend on the job-buffer and token-bank capacities only through their sum, in a very strong sense. Given two throttles with arbitrary token and job arrival processes, which differ only in their initial conditions and buffer capacities, having common total capacity, there exists a random time after which the overflow processes in these two systems coincide. For given total capacity, the job buffer smooths the stream of admitted jobs, but the reduced congestion is less than might be expected. For example, the heavy-traffic limiting behavior of a downstream infinite-capacity ^-server queue is unaffected by the job buffer in the throttle. We make a sample-path comparison of the throughputs at a downstream finite-capacity queue regulated by a token-bank rate-c...