Related papers: Many-Server Asymptotics for Join-the-Shortest-Queu…
In our companion work \cite{Stojnicl1RegPosasymldp} we revisited random under-determined linear systems with sparse solutions. The main emphasis was on the performance analysis of the $\ell_1$ heuristic in the so-called asymptotic regime,…
We prove a sample path Large Deviation Principle (LDP) for a class of jump processes whose rates are not uniformly Lipschitz continuous in phase space. Building on it we further establish the corresponding Wentzell-Freidlin (W-F) (infinite…
We study a queueing network with a strictly upper-triangular routing matrix, where each column contains at most one non-negative entry, and the root node receives input from a spectrally positive L\'{e}vy process. Our aim is to characterize…
We study an open discrete-time queueing network that models the collection of data in a multi-hop sensor network. We assume data is generated at the sensor nodes as a discrete-time Bernoulli process. All nodes in the network maintain a…
The event of large losses plays an important role in credit risk. As these large losses are typically rare, and portfolios usually consist of a large number of positions, large deviation theory is the natural tool to analyze the tail…
Quasi-birth-and-death (QBD) processes with infinite ``phase spaces'' can exhibit unusual and interesting behavior. One of the simplest examples of such a process is the two-node tandem Jackson network, with the ``phase'' giving the state of…
In the standard formulation of the occupancy problem one considers the distribution of r balls in n cells, with each ball assigned independently to a given cell with probability 1/n. Although closed form expressions can be given for the…
Let $L = (L(t))_{t\geq 0}$ be a multivariate L\'evy process with L\'evy measure $\nu(dy) = \exp(-f(|y|)) dy$ for a smoothly regularly varying function $f$ of index $\alpha>1$. The process $L$ is renormalized as $X^\varepsilon(t) =…
Consider a system with $K$ parallel queues in which the server for each queue processes jobs at rate $n$ and the total arrival rate to the system is $nK-\upsilon \sqrt{n}$ where $\upsilon \in (0, \infty)$ and $n$ is large. We study…
In this paper, we study a large system of $N$ servers each with capacity to process at most $C$ simultaneous jobs and an incoming job is routed to a server if it has the lowest occupancy amongst $d$ (out of N) randomly selected servers. A…
We consider a system of parallel queues where tasks are assigned (dispatched) to one of the available servers upon arrival. The dispatching decision is based on the full state information, i.e., on the sizes of the new and existing jobs. We…
In this paper, we exploit results obtained in an earlier study for the Laplace transform of the sojourn time $\Omega$ of an entire batch in the $M^{[X]}/M/1$ Processor Sharing (PS) queue in order to derive the asymptotic behavior of the…
We consider the supermarket model in the usual Markovian setting where jobs arrive at rate $n \lambda_n$ for some $\lambda_n > 0$, with $n$ parallel servers each processing jobs in its queue at rate 1. An arriving job joins the shortest…
We establish large deviation principles (LDPs) for empirical measures associated with a sequence of Gibbs distributions on $n$-particle configurations, each of which is defined in terms of an inverse temperature $% \beta_n$ and an energy…
We consider scheduling in a quantum switch with stochastic entanglement generation, finite quantum memories, and decoherence. The objective is to design a scheduling algorithm with polynomial-time computational complexity that stabilizes a…
In this paper, we present large deviation theory that characterizes the exponential estimate for rare events of stochastic dynamical systems in the limit of weak noise. We aim to consider next-to-leading-order approximation for more…
Consider a countably infinite collection of interacting queues, with a queue located at each point of the $d$-dimensional integer grid, having independent Poisson arrivals, but dependent service rates. The service discipline is of the…
An overview of rare events algorithms based on large deviation theory (LDT) is presented. It covers a range of numerical schemes to compute the large deviation minimizer in various setups, and discusses best practices, common pitfalls, and…
A multiclass queueing system is considered, with heterogeneous service stations, each consisting of many servers with identical capabilities. An optimal control problem is formulated, where the control corresponds to scheduling and routing,…
We consider continuous state branching processes (CSBP) with additional multiplicative jumps modeling dramatic events in a random environment. These jumps are described by a L\'evy process with bounded variation paths. We construct a…