On Capacity Dimensioning in Dynamic Scenarios: The Key Role of Peak Values

Abstract—This paper analyzes queueing behavior in queues with a random number of parallel flows, and not static as typically assumed. By deriving upper and lower bounds on the queue size distribution, the paper identifies extremal properties in such dynamic queues. The extremal best-case distribution (minimizing the queue) is simply the constant, whereas the worst-case distri-bution (maximizing the queue) has a bimodal structure. From a more practical point of view, this paper highlights an idiosyncrasy of dynamic queues: unlike in static queues whereby capacity dimensioning is dominated by average-values (subject to certain safety margins), in dynamic queues the capacity dimensioning is dominated instead by peak-values. I