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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.
This paper gives an overview of recent research on the performance evaluation and design of carousel systems. We discuss picking strategies for problems involving one carousel, consider the throughput of the system for problems involving two carousel
We show that at any location away from the spectral edge, the eigenvalues of the Gaussian unitary ensemble and its general beta siblings converge to Sine_beta, a translation invariant point process. This process has a geometric description in term of
We study distributions of random vectors whose components are second order polynomials in Gaussian random variables. Assuming that the law of such a vector is not absolutely continuous with respect to Lebesgue measure, we derive some interesting cons
We prove the existence of non-trivial phase transitions for the intersection of two independent random interlacements and the complement of the intersection. Some asymptotic results about the phase curves are also obtained. Moreover, we show that at
We study the scattering of photons from periodically modulated quantum-optical systems. For excitation-number conserving quantum optical systems, we connect the analytic structure of the frequency-domain N-photon scattering matrix of the system to th