44 citations · 90 across the 6 of their papers we have counts for
6 papers
Rare events in a polling system: Rays and Spirals
Robert D. Foley, David R. McDonald
It's a situation everyone dreads. A road is down to one lane for repairs. Traffic is let through one way until the backlog clears and then traffic is let through the other way to c…
Yaglom limits can depend on the starting state
R. D. Foley, D. R. McDonald
We construct a simple example, surely known to Harry Kesten, of an R-transient Markov chain on a countable state space S with cemetery state delta. The transition matrix K on S is…
Yaglom limits for R-transient chains with non-trivial Martin boundary
Robert Foley, David McDonald
We give conditions for the existence of a Yaglom limit for R-transient Markov chains with non-trivial rho-Martin entrance boundary (rho=1/R) and we characterize the rho-invariant l…
Mean field convergence of a model of multiple TCP connections through a buffer implementing RED
D. R. McDonald, J. Reynier
RED (Random Early Detection) has been suggested when multiple TCP sessions are multiplexed through a bottleneck buffer. The idea is to detect congestion before the buffer overflows…
Bridges and networks: Exact asymptotics
Robert D. Foley, David R. McDonald
We extend the Markov additive methodology developed in [Ann. Appl. Probab. 9 (1999) 110-145, Ann. Appl. Probab. 11 (2001) 596-607] to obtain the sharp asymptotics of the steady sta…
Large deviations of a modified Jackson network: stability and rough asymptotics
Robert D. Foley, David R. McDonald
Consider a modified, stable, two node Jackson network where server 2 helps server 1 when server 2 is idle. The probability of a large deviation of the number of customers at node o…