ON THE DISCRETE-TIME G/GI/∞ QUEUE

The discrete-time G/GI/infinity queue model is explored. Jobs arrive to an infinite-server queuing system following an arbitrary input process X; job sizes are general independent and identically distributed random variables. The system's output process Y (of job departures) and queue process N (tracking the number of jobs present in the system) are analyzed. Various statistics of the stochastic maps X bar right arrow Y and X bar right arrow N are explicitly obtained, including means, variances, autocovariances, cross-covariances, and multidimensional probability generating functions. In the case of stationary inputs, we further compute the spectral densities of the stochastic maps, characterize the fixed points (in the L-2 sense) of the input-output map, precisely determine when the output and queue processes display either short-ranged or long-ranged temporal dependencies, and prove a decomposition result regarding the intrinsic L-2` structure of general stationary G/GI/infinity systems.