343 research outputs found
When is a network epidemic hard to eliminate?
We consider the propagation of a contagion process (epidemic) on a network
and study the problem of dynamically allocating a fixed curing budget to the
nodes of the graph, at each time instant. For bounded degree graphs, we provide
a lower bound on the expected time to extinction under any such dynamic
allocation policy, in terms of a combinatorial quantity that we call the
resistance of the set of initially infected nodes, the available budget, and
the number of nodes n. Specifically, we consider the case of bounded degree
graphs, with the resistance growing linearly in n. We show that if the curing
budget is less than a certain multiple of the resistance, then the expected
time to extinction grows exponentially with n. As a corollary, if all nodes are
initially infected and the CutWidth of the graph grows linearly, while the
curing budget is less than a certain multiple of the CutWidth, then the
expected time to extinction grows exponentially in n. The combination of the
latter with our prior work establishes a fairly sharp phase transition on the
expected time to extinction (sub-linear versus exponential) based on the
relation between the CutWidth and the curing budget
Qualitative Properties of alpha-Weighted Scheduling Policies
We consider a switched network, a fairly general constrained queueing network
model that has been used successfully to model the detailed packet-level
dynamics in communication networks, such as input-queued switches and wireless
networks. The main operational issue in this model is that of deciding which
queues to serve, subject to certain constraints. In this paper, we study
qualitative performance properties of the well known -weighted
scheduling policies. The stability, in the sense of positive recurrence, of
these policies has been well understood. We establish exponential upper bounds
on the tail of the steady-state distribution of the backlog. Along the way, we
prove finiteness of the expected steady-state backlog when , a
property that was known only for . Finally, we analyze the
excursions of the maximum backlog over a finite time horizon for . As a consequence, for , we establish the full state space
collapse property.Comment: 13 page
An efficient curing policy for epidemics on graphs
We provide a dynamic policy for the rapid containment of a contagion process
modeled as an SIS epidemic on a bounded degree undirected graph with n nodes.
We show that if the budget of curing resources available at each time is
, where is the CutWidth of the graph, and also of order
, then the expected time until the extinction of the epidemic
is of order , which is within a constant factor from optimal, as well
as sublinear in the number of nodes. Furthermore, if the CutWidth increases
only sublinearly with n, a sublinear expected time to extinction is possible
with a sublinearly increasing budget
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