18 citations · 71 across the 23 of their papers we have counts for
4 papers · 1 filter
Implicit Renewal Theorem for Trees with General Weights
Predrag R. Jelenkovic, Mariana Olvera-Cravioto
Consider distributional fixed point equations of the form R =d f(C_i, R_i, 1 <= i <= N), where f(.) is a possibly random real valued function, N in {0, 1, 2, 3,...} U {infty}, {C_i…
On the transition from heavy traffic to heavy tails for the M/G/1 queue: The regularly varying case
Mariana Olvera-Cravioto, Jose Blanchet, Peter Glynn
Two of the most popular approximations for the distribution of the steady-state waiting time, , of the M/G/1 queue are the so-called heavy-traffic approximation and hea…
Uniform Approximations for the M/G/1 Queue with Subexponential Processing Times
Mariana Olvera-Cravioto, Peter W. Glynn
This paper studies the asymptotic behavior of the steady-state waiting time, W_infty, of the M/G/1 queue with subexponenential processing times for different combinations of traffi…
Implicit Renewal Theory and Power Tails on Trees
Predrag R. Jelenković, Mariana Olvera-Cravioto
We extend Goldie's (1991) Implicit Renewal Theorem to enable the analysis of recursions on weighted branching trees. We illustrate the developed method by deriving the power tail a…