The M/G/infinity system revisited: finiteness, summability, long range dependence, and reverse engineering
We explore M/G/infinity systems 'fed' by Poissonian inflows with infinite arrival rates. Three processes-corresponding to the system's state, workload, and queue-size-are studied and analyzed. Closed form formulae characterizing the system's stationary structure and correlation structure are derived. And, the issues of queue finiteness, workload summability, and Long Range Dependence are investigated. We then turn to devise a 'reverse engineering' scheme for the design of the system's correlation structure. Namely: how to construct an M/G/infinity system with a pre-desired 'target' workload/queue auto-covariance function. The 'reverse engineering' scheme is applied to various examples, including ones with infinite queues and non-summable workloads.
m/g/infinity systems reverse engineering infinite arrival rates poisson point processes levy inflows workload processes long range dependence (lrd)