113 citations · 178 across the 8 of their papers we have counts for
8 papers · 1 filter
Optimal cash management using impulse control
Peter Lakner, Josh Reed
We consider the impulse control of Levy processes under the infinite horizon, discounted cost criterion. Our motivating example is the cash management problem in which a controller…
Reflected Brownian Motion with Drift in a Wedge
Peter Lakner, Ziran Liu, Josh Reed
We study reflecting Brownian motion with drift constrained to a wedge in the plane. Our first set of results provide necessary and sufficient conditions for existence and uniquenes…
A Dirichlet Process Characterization of RBM in a Wedge
Peter Lakner, Josh Reed, Bert Zwart
Reflected Brownian motion (RBM) in a wedge is a 2-dimensional stochastic process Z whose state space in R^2 is given in polar coordinates by S={(r,theta): r >= 0, 0 <= theta <= xi}…
Scaling limit of a limit order book model via the regenerative characterization of Lévy trees
Peter Lakner, Josh Reed, Florian Simatos
We consider the following Markovian dynamic on point processes: at constant rate and with equal probability, either the rightmost atom of the current configuration is removed, or a…
Fluid Limits for Bandwidth-Sharing Networks with Rate Constraints
Maria Frolkova, Josh Reed, Bert Zwart
Bandwidth-sharing networks as introduced by Massoulié & Roberts (1998) model the dynamic interaction among an evolving population of elastic flows competing for several links. With…
On many-server queues in heavy traffic
Anatolii A. Puhalskii, Josh E. Reed
We establish a heavy-traffic limit theorem on convergence in distribution for the number of customers in a many-server queue when the number of servers tends to infinity. No critic…
The queue in the Halfin--Whitt regime
Josh Reed
In this paper, we study the queue in the Halfin--Whitt regime. Our first result is to obtain a deterministic fluid limit for the properly centered and scaled numb…
Distribution-valued heavy-traffic limits for the queue
Josh Reed, Rishi Talreja
We study the queue in heavy-traffic using tempered distribution-valued processes which track the age and residual service time of each customer in the system…