Notice
Rare events in a polling system: Rays & Spirals
- document 1 document 2 document 3
- niveau 1 niveau 2 niveau 3
Descriptif
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 clear that backlog and so on. When stuck in a very long queue it is inevitable to wonder how did I get into this mess?
We study a polling model with a server having exponential service time with mean 1/μ alternating between two queues, emptying one queue before switching to the other. Customers arrive at queue one according to a Poisson process with rate λ1 and at queue two with rate λ2. We discuss how we get at a rare event with a large number of customers in the system. In fact this can happen in two different ways depending on the parameters. In one case one queue simply explodes and runs away without emptying. We call this the ray case. In the other spiral case the queues are successively emptied but in a losing battle as the system zigzags to the rare event. This dichotomy extends to the steady state distribution and leads to quite different asymptotic behavior in the two cases.
Thème
Dans la même collection
-
Combinatorial maps in high genus
LoufBaptisteCombinatorial maps are a model of discrete geometry: they are surfaces made by gluing polygons along their sides, or equivalently, graphs drawn on surfaces. In this talk, I'll focus on the study of
-
Do there exist expanders with non-negative curvature ?
SalezJustinIn this talk I will briefly recall the framework of local weak limits of finite graphs introduced by I. Benjamini and O. Schramm
-
Tail bounds for detection times in mobile hyperbolic graphs
MitscheDieterMotivated by Krioukov et al.'s model of random hyperbolic graphs for real-world networks, and inspired by the analysis of a dynamic model of graphs in Euclidean space by Peres et al., we introduce a
-
Online matching for the multiclass Stochastic Block Model
SOPRANO LOTONahuelA matching in a graph is a set of edges that do not share endpoints. Developing algorithms that find large matchings is an important problem. An algorithm is said to be online if it has to construct
-
Critical cluster cascades
KirchnerMatthiasWe consider a sequence of Poisson cluster point processes on $R^d$: At step $n\in\mathbb{N}_0$ of the construction, the cluster centers have intensity $c/(n+1)$ for some $c > 0$, and each cluster
-
Point processes on higher rank symmetric spaces and their cost
MellickSamuelCost is a natural invariant associated to group actions and invariant point processes on symmetric spaces (such as Euclidean space and hyperbolic space). Informally, it measures how difficult it is to
-
Parallel server systems in extended heavy traffic
CastielEyalThe standard setting for studying parallel server systems (PSS) at the diffusion scale is based on the heavy traffic condition (HTC)...
-
The Maximal Agreement Subtree problem for random trees
BudzinskiThomasConsider two binary trees whose leaves are labelled from 1 to n.
-
An Improved Lower Bound on the Largest Common Subtree of Random Leaf-Labeled Binary Trees
KhezeliAliIt is known that the size of the largest common subtree...
-
Reversible Markov decision processes
AnantharamVenkatA Markov decision process is called reversible if for every stationary Markov control strategy the resulting Markov chain is reversible.
-
The question of connectedness in the Free Uniform Spanning Forest
TimárÁdám DávidThe uniform measure on the set of all spanning trees of a finite graph is a classical object in probability.
-
Optimal Convex and Nonconvex Regularizers for a Data Source
O'ReillyElizaRegularization is a widespread technique used in statistical estimation problems that helps to capture low dimensional structure in the data and improve signal recovery.
Sur le même thème
-
Combinatorial maps in high genus
LoufBaptisteCombinatorial maps are a model of discrete geometry: they are surfaces made by gluing polygons along their sides, or equivalently, graphs drawn on surfaces. In this talk, I'll focus on the study of
-
Do there exist expanders with non-negative curvature ?
SalezJustinIn this talk I will briefly recall the framework of local weak limits of finite graphs introduced by I. Benjamini and O. Schramm
-
Tail bounds for detection times in mobile hyperbolic graphs
MitscheDieterMotivated by Krioukov et al.'s model of random hyperbolic graphs for real-world networks, and inspired by the analysis of a dynamic model of graphs in Euclidean space by Peres et al., we introduce a
-
Sofic entropy of processes on infinite random trees
BordenaveCharlesThis is a joint work with Agnes Backhausz et Balasz Szegedy. We define a natural notion of micro-state entropy...
-
Online matching for the multiclass Stochastic Block Model
SOPRANO LOTONahuelA matching in a graph is a set of edges that do not share endpoints. Developing algorithms that find large matchings is an important problem. An algorithm is said to be online if it has to construct
-
Critical cluster cascades
KirchnerMatthiasWe consider a sequence of Poisson cluster point processes on $R^d$: At step $n\in\mathbb{N}_0$ of the construction, the cluster centers have intensity $c/(n+1)$ for some $c > 0$, and each cluster
-
Point processes on higher rank symmetric spaces and their cost
MellickSamuelCost is a natural invariant associated to group actions and invariant point processes on symmetric spaces (such as Euclidean space and hyperbolic space). Informally, it measures how difficult it is to
-
Parallel server systems in extended heavy traffic
CastielEyalThe standard setting for studying parallel server systems (PSS) at the diffusion scale is based on the heavy traffic condition (HTC)...
-
The Maximal Agreement Subtree problem for random trees
BudzinskiThomasConsider two binary trees whose leaves are labelled from 1 to n.
-
An Improved Lower Bound on the Largest Common Subtree of Random Leaf-Labeled Binary Trees
KhezeliAliIt is known that the size of the largest common subtree...
-
Reversible Markov decision processes
AnantharamVenkatA Markov decision process is called reversible if for every stationary Markov control strategy the resulting Markov chain is reversible.
-
The question of connectedness in the Free Uniform Spanning Forest
TimárÁdám DávidThe uniform measure on the set of all spanning trees of a finite graph is a classical object in probability.
