An Introduction to Stochastic-Process Limits and their Application to Queues

By Ward Whitt. 2002

882 citations recorded by the source corpus.

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Citations in the corpus

Many-server diffusion limits for G/Ph/n+GI queues (2010, methodology): “3); readers are referred to Whitt (2004) for further discussion.”
Fluid limits of many-server queues with reneging (2010, background): “3 of [23], we have (F η s )−1 → (F ηs )−1 on [0,F ηs (H r−)) in the M1 topology.”
Heavy traffic analysis of open processing networks with complete resource pooling: Asymptotic optimality of discrete review policies (2005, background): “Since the one-dimensional regulator map commutes with scaling (see [50]), we immediately have, on the set N r , that”
Reflected Symmetric α-Stable Processes and Regional Fractional Laplacian (2006, background): “[2][3][4][18][29][33][ 37 ]). Because of the importance of processes in an open set instead of in the whole Euclidean space, in the last few years appeared also number of publications concerning the properties of α-stable processes in a bounded open set (see e.g.”
Limit theorems for the number of occupied boxes in the Bernoulli sieve (2010, methodology): “We refer the reader to the monograph [26] for a comprehensive exposition of the J1- and the M1-topologies as well as some other topologies on D[0, T ].”
An SPDE model for systemic risk with endogenous contagion (2018, unknown): “1 in [47] implies that the canonical projections πti : (DR,M1)→ R are continuous at each 〈νk , φλ〉 for λ ∈ N.”
Particle systems with singular interaction through hitting times: Application in systemic risk modeling (2017, background): “, [DIRT15b], [Sko56], [JS03], [Whi02] for a detailed discussion of the M1 topology).”
On the supremum of γ-reflected processes with fractional Brownian motion as input (2013, background): “(19) is established by comparing the last inequality with (22).”