144 citations · 255 across the 7 of their papers we have counts for
7 papers
Continuity and monotonicity of solutions to a greedy maximization problem
Lukasz Kruk
Motivated by an application to resource sharing network modelling, we consider a problem of greedy maximization (i.e., maximization of the consecutive minima) of a vector in ,…
Heavy traffic analysis for EDF queues with reneging
Łukasz Kruk, John Lehoczky, Kavita Ramanan +1
This paper presents a heavy-traffic analysis of the behavior of a single-server queue under an Earliest-Deadline-First (EDF) scheduling policy in which customers have deadlines and…
Diffusion limits for shortest remaining processing time queues
H. Christian Gromoll, Łukasz Kruk, Amber L. Puha
We present a heavy traffic analysis for a single server queue with renewal arrivals and generally distributed i.i.d. service times, in which the server employs the Shortest Remaini…
An explicit formula for the Skorokhod map on
Lukasz Kruk, John Lehoczky, Kavita Ramanan +1
The Skorokhod map is a convenient tool for constructing solutions to stochastic differential equations with reflecting boundary conditions. In this work, an explicit formula for th…
Heavy traffic limit for a processor sharing queue with soft deadlines
H. Christian Gromoll, Łukasz Kruk
This paper considers a GI/GI/1 processor sharing queue in which jobs have soft deadlines. At each point in time, the collection of residual service times and deadlines is modeled u…
Accuracy of state space collapse for earliest-deadline-first Queues
Łukasz Kruk, John Lehoczky, Steven Shreve
This paper presents a second-order heavy traffic analysis of a single server queue that processes customers having deadlines using the earliest-deadline-first scheduling policy. Fo…