Discrete-time queues with zero-regenerative arrivals: moments and examples

In this paper we investigate a single-server discrete-time queueing system with single-slot service times. The stationary ergodic arrival process this queueing system is subject to, satisfies a regeneration property when there are no arrivals during a slot. Expressions for the mean and the variance of the queue content in steady state are obtained for this broad class which includes among others autoregressive arrival processes and M/G/infinity-input or train arrival processes. To illustrate our results, we then consider a number of numerical examples

Deep space experiment to measure GG

Responding to calls from the National Science Foundation (NSF) for new proposals to measure the gravitational constant $G$, we offer an interesting experiment in deep space employing the classic gravity train mechanism. Our setup requires three bodies: a larger layered solid sphere with a cylindrical hole through its center, a much smaller retroreflector which will undergo harmonic motion within the hole and a host spacecraft with laser ranging capabilities to measure round trip light-times to the retroreflector but ultimately separated a significant distance away from the sphere-retroreflector apparatus. Measurements of the period of oscillation of the retroreflector in terms of host spacecraft clock time using existing technology could give determinations of $G$ nearly three orders of magnitude more accurate than current measurements here on Earth. However, significant engineering advances in the release mechanism of the apparatus from the host spacecraft will likely be necessary. Issues with regard to the stability of the system are briefly addressed.Comment: 13 pp, 3 figs, accepted CQ