Probability (2nd ed.)
A new heavy-tailed discrete distribution for LRD M/G/∞ sample generation
Performance Evaluation
Tail probabilities for M/G/\infty input processes (I): Preliminary asymptotics
Queueing Systems: Theory and Applications
M|G|Infinity Input Processes: A Versatile Class of Models for Network Traffic
INFOCOM '97 Proceedings of the INFOCOM '97. Sixteenth Annual Joint Conference of the IEEE Computer and Communications Societies. Driving the Information Revolution
General applications 1: a highly efficient M/G/∞ model for generating self-similar traces
Proceedings of the 34th conference on Winter simulation: exploring new frontiers
The M/G/∞ system revisited: finiteness, summability, long range dependence, and reverse engineering
Queueing Systems: Theory and Applications
Semi-linear Stochastic Difference Equations
Discrete Event Dynamic Systems
Fast simulation of self-similar and correlated processes
Mathematics and Computers in Simulation
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The discrete-time G/GI/∞ 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↦ Y and X↦ 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 L2 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 L2 structure of general stationary G/GI/∞ systems.