Risk sensitive optimal control framework applied to
delay tolerant networks
Eitan Altman, Veeraruna Kavitha, Francesco De Pellegrini, Vijay Kamble and Vivek Borkar
Abstract
—Epidemics dynamics can describe the dissemination
of
information
in
delay
tolerant
networks,
in
peer
to
peer
networks and in content delivery networks. The control of such
dynamics has thus gained a central role in all of these areas.
However, a major difficulty in this context is that the objective
functions to be optimized are often not additive in time but are
rather multiplicative. The classical objective function in DTNs,
i.e., the successful delivery probability of a message within a
given deadline, falls precisely in this category, because it takes
often the form of the expectation of the exponent of some
integral cost. So far, models involving such costs have been solved
by interchanging the order of expectation and the exponential
function. While reducing the problem to a standard optimal
control problem, this interchange is only tight in the mean field
limit obtained as the population tends to infinity.
In this paper we identify a general framework from optimal
control in finance, known as risk sensitive control, which let us
handle the original (multiplicative) cost and obtain solutions to
several novel control problems in DTNs. In particular, we can
derive the structure of statedependent controls that optimize
transmission power at the source node. Further, we can account
for the propagation loss factor of the wireless medium while
obtaining these controls, and, finally, we address power control
at the destination node, resulting in a novel threshold optimal
activation policy. Combined optimal power control at source and
destination nodes is also obtained.
Index
Terms
—Delay
Tolerant
Networks,
Markov
Decision
Process, Risk Sensitive Control
I. I
NTRODUCTION
Delay Tolerant Networks (DTNs) gained the interest of
the research community in recent past [2], [3]. They have
been identified as a promising mean to transport data in
intermittently connected networks. DTNs in particular, sustain
communications in a networked system where no continuous
connectivity guarantee can be assumed [4], [5]. Messages are
carried from source to destination via relay nodes adopting
store and carry type forwarding protocols; such protocols
basically rely on the underlying node mobility pattern. The
core problem in DTNs is to efficiently route messages to
wards the intended destination. We observe that traditional
techniques for routing perform very poorly in this context
due to frequent disruptions, and furthermore mobile nodes
rarely possess information on the upcoming encounters they
are going to experience [6], [7]. An intuitive and rather robust
solution is to disseminate multiple copies of the message in
the network. This is meant to ensure that at least some of them
will reach the destination node within some deadline [5], [8].
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 Spring '09
 R.Srikant
 Optimization, DTNs

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