Related papers: A large deviation principle for join the shortest …
We discuss the approach toward equilibrium of an isolated quantum system. For a wide class of systems we argue that the time-averaged expectation value of a local operator in any initial state is bounded by the so-called deviation function,…
We study the matching of jobs to workers in a queue, e.g. a ridesharing platform dispatching drivers to pick up riders at an airport. Under FIFO dispatching, the heterogeneity in trip earnings incentivizes drivers to cherry-pick, increasing…
A large deviations principle is established for the joint law of the empirical measure and the flow measure of a renewal Markov process on a finite graph. We do not assume any bound on the arrival times, allowing heavy tailed distributions.…
The aim of this paper is to investigate the large deviations for a class of slow-fast mean-field diffusions, which extends some existing results to the case where the laws of fast process are also involved in the slow component. Due to the…
We prove a maximal-type large deviation principle for dynamical systems with arbitrarily slow polynomial mixing rates. Also several applications, particularly to billiard systems, are presented.
Large deviation principles are established for the Fleming-Viot processes with neutral mutation and selection, and the corresponding equilibrium measures as the sampling rate goes to 0. All results are first proved for the finite allele…
This paper is devoted to the problem of sample path large deviations for multidimensional queueing models with feedback. We derive a new version of the contraction principle where the continuous map is not well-defined on the whole space:…
This work studies queues in a Euclidean space. Consider $N$ servers that are distributed uniformly in $[0,1]^d$. Customers arrive at the servers according to independent stationary processes. Upon arrival, they probabilistically decide…
We consider optimal control of a stochastic network,where service is controlled to prevent buffer overflow. We use a risk-sensitive escape time criterion, which in comparison to the ordinary escape time criteria heavily penalizes exits…
We study a system, where a random flow of customers is served by servers (called agents) invited on-demand. Each invited agent arrives into the system after a random time; after each service completion, an agent returns to the system or…
Motivated by applications that involve setting proper staffing levels for multi-server queueing systems with batch arrivals, we present a thorough study of the queue-length process $\{Q(t); t \geq 0\}$, departure process $\{D(t); t \geq…
A parallel server system with $n$ identical servers is considered. The service time distribution has a finite mean $1/\mu$, but otherwise is arbitrary. Arriving customers are be routed to one of the servers immediately upon arrival.…
A trajectorial large deviation principle is established in a mean field thermodynamic limit for a multiclass loss network with diminishing rates, which may have several stable equilibria. The large deviation limit is identified as a unique…
We introduce the prioritising exclusion process, a stochastic scheduling mechanism for a priority queueing system in which high priority customers gain advantage by overtaking low priority customers. The model is analogous to a totally…
We introduce a novel single-server queue with general retrial times and event-dependent arrivals. This is a versatile model for the study of service systems, in which the server needs a non-negligible time to retrieve waiting customers upon…
We consider the problem of staffing large-scale service systems with multiple customer classes and multiple dedicated server pools under joint quality-of-service (QoS) constraints. We first analyze the case in which arrival rates are…
We consider the FCFS $GI/GI/n$ queue in the Halfin-Whitt heavy traffic regime, and prove bounds for the steady-state probability of delay (s.s.p.d.) for generally distributed processing times. We prove that there exist $\epsilon_1,…
The Adaptive Multilevel Splitting (AMS) algorithm is a powerful and versatile method for the simulation of rare events. It is based on an interacting (via a mutation-selection procedure) system of replicas, and depends on two integer…
Queueing networks are typically modelled assuming that the arrival process is exogenous, and unaffected by admission control, scheduling policies, etc. In many situations, however, users choose the time of their arrival strategically,…
Arrival processes to service systems often display (i) larger than anticipated fluctuations, (ii) a time-varying rate, and (iii) temporal correlation. Motivated by this, we introduce a specific non-homogeneous Poisson process that…