Analytic properties of two-carousel systems

We present analytic results for warehouse systems involving pairs of carousels. Specifically, for various picking strategies, we show that the sojourn time of the picker satisfies an integral equation that is a contraction mapping. As a result, numerical approximations for performance measures such as the throughput of the system are extremely accurate and converge fast (e.g.\ within 5 iterations) to their real values. We present simulation results validating our results and examining more complicated strategies for pairs of carousels.