Strong Stationary Duality for M\"obius Monotone Markov Chains: Unreliable Networks

For Markov chains with a partially ordered finite state space we show strong stationary duality under the condition of M\"obius monotonicity of the chain. We show relations of M\"obius monotonicity to other definitions of monotone chains. We give examples of dual chains in this context which have transitions only upwards. We illustrate general theory by an analysis of nonsymmetric random walks on the cube with an application to networks of queues

A Survey on Delay-Aware Resource Control for Wireless Systems --- Large Deviation Theory, Stochastic Lyapunov Drift and Distributed Stochastic Learning

In this tutorial paper, a comprehensive survey is given on several major systematic approaches in dealing with delay-aware control problems, namely the equivalent rate constraint approach, the Lyapunov stability drift approach and the approximate Markov Decision Process (MDP) approach using stochastic learning. These approaches essentially embrace most of the existing literature regarding delay-aware resource control in wireless systems. They have their relative pros and cons in terms of performance, complexity and implementation issues. For each of the approaches, the problem setup, the general solution and the design methodology are discussed. Applications of these approaches to delay-aware resource allocation are illustrated with examples in single-hop wireless networks. Furthermore, recent results regarding delay-aware multi-hop routing designs in general multi-hop networks are elaborated. Finally, the delay performance of the various approaches are compared through simulations using an example of the uplink OFDMA systems.Comment: 58 pages, 8 figures; IEEE Transactions on Information Theory, 201

Routing on trees

We consider three different schemes for signal routing on a tree. The vertices of the tree represent transceivers that can transmit and receive signals, and are equipped with i.i.d. weights representing the strength of the transceivers. The edges of the tree are also equipped with i.i.d. weights, representing the costs for passing the edges. For each one of our schemes, we derive sharp conditions on the distributions of the vertex weights and the edge weights that determine when the root can transmit a signal over arbitrarily large distances

Performance of ad hoc networks with two-hop relay routing and limited packet lifetime (extended version)

We consider a mobile ad hoc network consisting of three types of nodes (source, destination and relay nodes) and using the two-hop relay routing. This type of routing takes advantage of the mobility and the storage capacity of the nodes, called the relay nodes, in order to route packets between a source and a destination. Packets at relay nodes are assumed to have a limited lifetime in the network. Nodes are moving inside a bounded region according to some random mobility model. Closed-form expressions and asymptotic results when the number of nodes is large are provided for the packet delivery delay and for the energy needed to transmit a packet from the source to its destination. We also introduce and evaluate a variant of the two-hop relay protocol that limits the number of generated copies in the network. Our model is validated through simulations for two mobility models (random waypoint and random direction mobility models), and the performance of the two-hop routing and of the epidemic routing protocols are compared.\ud \u

A dynamic approach to rebalancing bike-sharing systems

Bike-sharing services are flourishing in Smart Cities worldwide. They provide a low-cost and environment-friendly transportation alternative and help reduce traffic congestion. However, these new services are still under development, and several challenges need to be solved. A major problem is the management of rebalancing trucks in order to ensure that bikes and stalls in the docking stations are always available when needed, despite the fluctuations in the service demand. In this work, we propose a dynamic rebalancing strategy that exploits historical data to predict the network conditions and promptly act in case of necessity. We use Birth-Death Processes to model the stations' occupancy and decide when to redistribute bikes, and graph theory to select the rebalancing path and the stations involved. We validate the proposed framework on the data provided by New York City's bike-sharing system. The numerical simulations show that a dynamic strategy able to adapt to the fluctuating nature of the network outperforms rebalancing schemes based on a static schedule