Hybrid performance modelling of opportunistic networks

We demonstrate the modelling of opportunistic networks using the process algebra stochastic HYPE. Network traffic is modelled as continuous flows, contact between nodes in the network is modelled stochastically, and instantaneous decisions are modelled as discrete events. Our model describes a network of stationary video sensors with a mobile ferry which collects data from the sensors and delivers it to the base station. We consider different mobility models and different buffer sizes for the ferries. This case study illustrates the flexibility and expressive power of stochastic HYPE. We also discuss the software that enables us to describe stochastic HYPE models and simulate them.Comment: In Proceedings QAPL 2012, arXiv:1207.055

On Leveraging Partial Paths in Partially-Connected Networks

Mobile wireless network research focuses on scenarios at the extremes of the network connectivity continuum where the probability of all nodes being connected is either close to unity, assuming connected paths between all nodes (mobile ad hoc networks), or it is close to zero, assuming no multi-hop paths exist at all (delay-tolerant networks). In this paper, we argue that a sizable fraction of networks lies between these extremes and is characterized by the existence of partial paths, i.e. multi-hop path segments that allow forwarding data closer to the destination even when no end-to-end path is available. A fundamental issue in such networks is dealing with disruptions of end-to-end paths. Under a stochastic model, we compare the performance of the established end-to-end retransmission (ignoring partial paths), against a forwarding mechanism that leverages partial paths to forward data closer to the destination even during disruption periods. Perhaps surprisingly, the alternative mechanism is not necessarily superior. However, under a stochastic monotonicity condition between current v.s. future path length, which we demonstrate to hold in typical network models, we manage to prove superiority of the alternative mechanism in stochastic dominance terms. We believe that this study could serve as a foundation to design more efficient data transfer protocols for partially-connected networks, which could potentially help reducing the gap between applications that can be supported over disconnected networks and those requiring full connectivity.Comment: Extended version of paper appearing at IEEE INFOCOM 2009, April 20-25, Rio de Janeiro, Brazi

Adaptive stochastic radio access selection scheme for cellular-WLAN heterogeneous communication systems

This study proposes a novel adaptive stochastic radio access selection scheme for mobile users in heterogeneous cellular-wireless local area network (WLAN) systems. In this scheme, a mobile user located in dual coverage area randomly selects WLAN with probability of ω when there is a need for downloading a chunk of data. The value of ω is optimised according to the status of both networks in terms of network load and signal quality of both cellular and WLAN networks. An analytical model based on continuous time Markov chain is proposed to optimise the value of ω and compute the performance of proposed scheme in terms of energy efficiency, throughput, and call blocking probability. Both analytical and simulation results demonstrate the superiority of the proposed scheme compared with the mainstream network selection schemes: namely, WLAN-first and load balancing

Incremental Stochastic Subgradient Algorithms for Convex Optimization

In this paper we study the effect of stochastic errors on two constrained incremental sub-gradient algorithms. We view the incremental sub-gradient algorithms as decentralized network optimization algorithms as applied to minimize a sum of functions, when each component function is known only to a particular agent of a distributed network. We first study the standard cyclic incremental sub-gradient algorithm in which the agents form a ring structure and pass the iterate in a cycle. We consider the method with stochastic errors in the sub-gradient evaluations and provide sufficient conditions on the moments of the stochastic errors that guarantee almost sure convergence when a diminishing step-size is used. We also obtain almost sure bounds on the algorithm's performance when a constant step-size is used. We then consider \ram{the} Markov randomized incremental subgradient method, which is a non-cyclic version of the incremental algorithm where the sequence of computing agents is modeled as a time non-homogeneous Markov chain. Such a model is appropriate for mobile networks, as the network topology changes across time in these networks. We establish the convergence results and error bounds for the Markov randomized method in the presence of stochastic errors for diminishing and constant step-sizes, respectively

The Strength of Arcs and Edges in Interaction Networks: Elements of a Model-Based Approach

When analyzing interaction networks, it is common to interpret the amount of interaction between two nodes as the strength of their relationship. We argue that this interpretation may not be appropriate, since the interaction between a pair of nodes could potentially be explained only by characteristics of the nodes that compose the pair and, however, not by pair-specific features. In interaction networks, where edges or arcs are count-valued, the above scenario corresponds to a model of independence for the expected interaction in the network, and consequently we propose the notions of arc strength, and edge strength to be understood as departures from this model of independence. We discuss how our notion of arc/edge strength can be used as a guidance to study network structure, and in particular we develop a latent arc strength stochastic blockmodel for directed interaction networks. We illustrate our approach studying the interaction between the Kolkata users of the myGamma mobile network.Comment: 23 pages, 5 figures, 4 table

On Space-Time Capacity Limits in Mobile and Delay Tolerant Networks

We investigate the fundamental capacity limits of space-time journeys of information in mobile and Delay Tolerant Networks (DTNs), where information is either transmitted or carried by mobile nodes, using store-carry-forward routing. We define the capacity of a journey (i.e., a path in space and time, from a source to a destination) as the maximum amount of data that can be transferred from the source to the destination in the given journey. Combining a stochastic model (conveying all possible journeys) and an analysis of the durations of the nodes' encounters, we study the properties of journeys that maximize the space-time information propagation capacity, in bit-meters per second. More specifically, we provide theoretical lower and upper bounds on the information propagation speed, as a function of the journey capacity. In the particular case of random way-point-like models (i.e., when nodes move for a distance of the order of the network domain size before changing direction), we show that, for relatively large journey capacities, the information propagation speed is of the same order as the mobile node speed. This implies that, surprisingly, in sparse but large-scale mobile DTNs, the space-time information propagation capacity in bit-meters per second remains proportional to the mobile node speed and to the size of the transported data bundles, when the bundles are relatively large. We also verify that all our analytical bounds are accurate in several simulation scenarios.Comment: Part of this work will be presented in "On Space-Time Capacity Limits in Mobile and Delay Tolerant Networks", P. Jacquet, B. Mans and G. Rodolakis, IEEE Infocom, 201

Modelling and performance analysis of mobile ad hoc networks

PhD ThesisMobile Ad hoc Networks (MANETs) are becoming very attractive and useful in many kinds of communication and networking applications. This is due to their efficiency, relatively low cost, and flexibility provided by their dynamic infrastructure. Performance evaluation of mobile ad hoc networks is needed to compare various architectures of the network for their performance, study the effect of varying certain network parameters and study the interaction between various parameters that characterise the network. It can help in the design and implementation of MANETs. It is to be noted that most of the research that studies the performance of MANETs were evaluated using discrete event simulation (DES) utilising a broad band of network simulators. The principle drawback of DES models is the time and resources needed to run such models for large realistic systems, especially when results with a high accuracy are desired. In addition, studying typical problems such as the deadlock and concurrency in MANETs using DES is hard because network simulators implement the network at a low abstraction level and cannot support specifications at higher levels. Due to the advantage of quick construction and numerical analysis, analytical modelling techniques, such as stochastic Petri nets and process algebra, have been used for performance analysis of communication systems. In addition, analytical modelling is a less costly and more efficient method. It generally provides the best insight into the effects of various parameters and their interactions. Hence, analytical modelling is the method of choice for a fast and cost effective evaluation of mobile ad hoc networks. To the best of our knowledge, there is no analytical study that analyses the performance of multi-hop ad hoc networks, where mobile nodes move according to a random mobility model, in terms of the end-to-end delay and throughput. This work ii presents a novel analytical framework developed using stochastic reward nets and mathematical modelling techniques for modelling and analysis of multi-hop ad hoc networks, based on the IEEE 802.11 DCF MAC protocol, where mobile nodes move according to the random waypoint mobility model. The proposed framework is used to analysis the performance of multi-hop ad hoc networks as a function of network parameters such as the transmission range, carrier sensing range, interference range, number of nodes, network area size, packet size, and packet generation rate. The proposed framework is organized into several models to break up the complexity of modelling the complete network and make it easier to analyse each model as required. This is based on the idea of decomposition and fixed point iteration of stochastic reward nets. The proposed framework consists of a mathematical model and four stochastic reward nets models; the path analysis model, data link layer model, network layer model and transport layer model. These models are arranged in a way similar to the layers of the OSI protocol stack model. The mathematical model is used to compute the expected number of hops between any source-destination pair; and the average number of carrier sensing, hidden, and interfering nodes. The path analysis model analyses the dynamic of paths in the network due to the node mobility in terms of the path connection availability and rate of failure and repair. The data link layer model describes the behaviour of the IEEE 802.11 DCF MAC protocol. The actions in the network layer are modelled by the network layer model. The transport layer model represents the behaviour of the transport layer protocols. The proposed models are validated using extensive simulations