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

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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-control throttle, with and without a job buffer. Given a fixed total capacity in the throttle (and thus a fixed admission rate of the throttle) and given a fixed amount of buffer space for jobs to allocate to a downstream queue and a job buffer in the throttle, the maximum throughput of jobs occurs when all the buffer capacity is allocated to the downstream queue, even though the admitted stream from the throttle is not smoothed by a job buffer. Similar results hold for systems with non-discrete flow, such as regulated Brownian motion and Markov modulated fluid models.

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