This work focuses on a class of distributed storage systems whose content may evolve over time. Each component or node of the storage system is mobile and the set of all nodes forms a delay tolerant (ad hoc) network (DTN). The goal of the paper is to study efficient ways for distributing evolving files within DTNs and for managing dynamically their content. We specify to dynamic files where not only the latest version is useful but also previous ones; we restrict however to files where a file has no use if another more recent version is available. The DTN is composed of fixed number of nodes including a single source. At some points in time the source makes available a new version of a single file F. We consider both the cases when (a) nodes do not cooperate and (b) nodes cooperate. In case (a) only the source may transmit a copy of F to a node that it meets, while in case (b) any node may transmit a copy of F to a node that it meets. Scenario (a) is studied under the assumption that the source updates F at discrete times t = 0,1,.. .. Within each slot [t,t + 1) there is a fixed probability that a node meets the source. A file management policy is a set of rules specifying when the source transmits a copy of F to a node (say node i) that it meets; this decision only depends on the age of the version of F (if any) that node i is carrying, where the age is k if this version was created k-1 slots ago. We And the optimal static (resp. dynamic) policy which maximizes a general utility function under a constraint on the number of transmissions within a slot. In particular, we show the existence of a threshold dynamic policy. In scenario (b) F is updated at random points in time. Similar to scenerio (a) we assume that each node knows the age of the file it carries (the case where nodes only know the date of creation of a file is studied in (E. Altman et al., 2008)). Under Markovian assumptions regarding nodes mobility and update frequency of F, we study the stability of the system (aging of the nodes) and derive an (approximate) optimal static policy. We then revisit scenario (a) when the source does not know the number of nodes and the probability that the source meets a node in a slot, and we derive a stochastic approximation algorithm which we show to converge to the optimal static policy found in the complete information setting. Numerical results illustrate the respective performance of optimal static and dynamic policies as well as the benefit of node cooperation.

A major contribution of biology to competitive decision making is the area of evolutionary games. It describes the evolution of sizes of large populations as a result of many local interactions, each involving a small number of randomly selected individuals. An individual plays only once; it plays in a one shot game against another randomly selected player with the goal of maximizing its utility (fitness) in that game. We introduce here a new more general type of games: a Stochastic Evolutionary Game where each player may be in different states; the player may be involved in several local interactions during his life time and his actions determine not only the utilities but also the transition probabilities and his life duration. This is used to study a large population of mobiles forming a sparse ad-hoc network, where mobiles compete with their neighbors on the access to a radio channel. We study the impact of the level of energy in the battery on the aggressiveness of the access policy of mobiles at equilibrium. We obtain properties of the ESS (Evolutionary Stable Strategy) equilibrium which, Unlike the Nash equilibrium concept, is robust against deviations of a whole positive fraction of the population. We further study dynamical properties of the system when it is not in equilibrium.

We consider the situation where N nodes share a common access point. With each node i there is an associated buffer and channel state that change in time. Node i dynamically chooses both the power and the admission control to be adopted so as to maximize the expected capacity, which depends on the actions and states of all the players, given its power and delay constraints. The information structure that we consider is such that each player knows the state of its own buffer and channel and its own actions. It does not know the states of, and the actions taken by other players. Using Markov Decision Processes we analyze the single player optimal policies under different model parameters. In the context of stochastic games we study the equilibria of the N player scenario.

A major contribution of biology to competitive decision making is the development of the discipline of evolutionary games. Its ESS (evolutionary stable strategy) equilibrium concept, well adapted to large populations of players, describes robustness against deviations of a whole fraction of the population (in contrast to Nash equilibrium that requires robustness against a single user's deviation). The second appealing element of evolutionary games, the replicator dynamics, describes the evolution of strategies in time. Under suitable conditions, this (and some other) dynamics, converge to an ESS. In this paper we study the effect of slow time scale delays on the convergence of various dynamics. We apply this to an evolutionary game describing competition between mobile terminals over the access to a common channel.