The Impact of Setup Times on the Performance of Multiclass Service and Production Systems

We characterize the impact of the means and distributions of setup times in polling systems. Starting with cyclic systems with exhaustive service, we show that the vector of average setup times affects the complete distribution of waiting times and queue sizes only via its sum. In addition, all moments of all waiting times and queue sizes are reduced if the higher order moments of one or more of the setup times is reduced while maintaining their means. We also obtain a fundamental decomposition result of the queue sizes at polling instants which is reminiscent of those obtained in vacation models. We show that the above results continue to apply under more general and more efficient protocols, e.g., general polling tables, systems with gated service, and systems with mixed service.