Martingale optimal transport duality

We obtain a dual representation of the Kantorovich functional defined for functions on the Skorokhod space using quotient sets. Our representation takes the form of a Choquet capacity generated by martingale measures satisfying additional constraints to ensure compatibility with the quotient sets. These sets contain stochastic integrals defined pathwise and two such definitions starting with simple integrands are given. Another important ingredient of our analysis is a regularized version of Jakubowski's $S$-topology on the Skorokhod space.Comment: 29 page

Modeling and Analysis of Content Caching in Wireless Small Cell Networks

Network densification with small cell base stations is a promising solution to satisfy future data traffic demands. However, increasing small cell base station density alone does not ensure better users quality-of-experience and incurs high operational expenditures. Therefore, content caching on different network elements has been proposed as a mean of offloading he backhaul by caching strategic contents at the network edge, thereby reducing latency. In this paper, we investigate cache-enabled small cells in which we model and characterize the outage probability, defined as the probability of not satisfying users requests over a given coverage area. We analytically derive a closed form expression of the outage probability as a function of signal-to-interference ratio, cache size, small cell base station density and threshold distance. By assuming the distribution of base stations as a Poisson point process, we derive the probability of finding a specific content within a threshold distance and the optimal small cell base station density that achieves a given target cache hit probability. Furthermore, simulation results are performed to validate the analytical model.Comment: accepted for publication, IEEE ISWCS 201