Risk sensitive optimal control framework applied to delay tolerant networks

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 state-dependent 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. INTRODUCTION 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 towards 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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Eitan Altman, Veeraruna Kavitha, Francesco de Pellegrini, Vijay Kamble, Vivek Borkar. Risk sensitive optimal control framework applied to delay tolerant networks. INFOCOM, 2011 Proceedings IEEE , Apr 2011, Shanghai, China. ⟨10.1109/INFCOM.2011.5935161⟩. ⟨hal-01314379⟩

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