When nodes in a mobile network cluster together or move according to common external factors (e.g., cars that follow the road network), the resulting contact patterns become correlated. In this work we address the question of modelling such correlated mobility movements for the analysis of intermittently connected networks. We propose to use the concept of node colouring time to characterise dynamic node contact patterns. We analyse how this model compares to existing work, and demonstrate how to extract the relevant data from actual trace files. Moreover, we show how this information can be used to derive the latency distribution of DTN routing protocols. Our model achieves a very good fit to simulated results based on real vehicular mobility traces, whereas models which assumes independent contacts do not.
There is a rich body of work discussing detailed analytic models for latency and delivery ratio in delay-tolerant networks. The work ranges from experimentally grounded papers aiming to find models and frameworks that fit to observed data to more abstract models dealing with asymptotic bounds on information propagation. Many of these approaches are based on or inspired by epidemiological models @cite_25 . We have previously characterised the worst-case latency of broadcast for such networks using expander graph techniques @cite_15 . In a preliminary version of this paper we developed the basic framework for deriving the latency of ideal epidemic routing @cite_11 . This paper extends the latter work by incorporating an analysis of multi-copy routing as well as presenting a more rigrorous matematical basis with a hierarchy of connectivity models.
@cite_15 @cite_25 @cite_11
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In this paper, we present a framework for analyzing routing performance in delay tolerant networks (DTNs). Differently from previous work, our framework is aimed at characterizing the exact distribution of relevant performance metrics, which is a substantial improvement over existing studies characterizing either the expected value of the metric, or an asymptotic approximation of the actual distribution. In particular, the considered performance metrics are packet delivery delay, and communication cost, expressed as number of copies of a packet circulating in the network at the time of delivery. Our proposed framework is based on a characterization of the routing process as a stochastic coloring process and can be applied to model performance of most stateless delay tolerant routing protocols, such as epidemic, two-hops, and spray and wait. After introducing the framework, we present examples of its application to derive the packet delivery delay and communication cost distribution of two such protocols, namely epidemic and two-hops routing. Characterizing packet delivery delay and communication cost distribution is important to investigate fundamental properties of delay tolerant networks. As an example, we show how packet delivery delay distribution can be used to estimate how epidemic routing performance changes in presence of different degrees of node cooperation within the network. More specifically, we consider fully cooperative, noncooperative, and probabilistic cooperative scenarios, and derive nearly exact expressions of the packet delivery rate (PDR) under these scenarios based on our proposed framework. The comparison of the obtained packet delivery rate estimation in the various cooperation scenarios suggests that even a modest level of node cooperation (probabilistic cooperation with a low probability of cooperation) is sufficient to achieve 2-fold performance improvement with respect to the most pessimistic scenario in which all potential forwarders drop packets. Worst-case latency is an important characteristic of information dissemination protocols. However, in sparse mobile ad hoc networks where end-to-end connectivity cannot be achieved and store-carry-forward algorithms are needed, such worst-case analyses have not been possible to perform on real mobility traces due to lack of suitable models. We propose a new metric called delay expansion that reflects connectivity and reachability properties of intermittently connected networks. Using the delay expansion, we show how bounds on worst-case latency can be derived for a general class of broadcast protocols and a wide range of real mobility patterns. The paper includes theoretical results that show how worst-case latency can be related with delay expansion for a given mobility scenario, as well as simulations to validate the theoretical model. We introduce a unifying model to study the impact of worst-case latency deviations in non-atomic selfish routing games. In our model, latencies are subject to (bounded) deviations which are taken into account by the players. The quality deterioration caused by such deviations is assessed by the Deviation Ratio, i.e., the worst case ratio of the cost of a Nash flow with respect to deviated latencies and the cost of a Nash flow with respect to the unaltered latencies. This notion is inspired by the Price of Risk Aversion recently studied by Nikolova and Stier-Moses [9]. Here we generalize their model and results. In particular, we derive tight bounds on the Deviation Ratio for multi-commodity instances with a common source and arbitrary non-negative and non-decreasing latency functions. These bounds exhibit a linear dependency on the size of the network (besides other parameters). In contrast, we show that for general multi-commodity networks an exponential dependency is inevitable. We also improve recent smoothness results to bound the Price of Risk Aversion. We consider the problem of routing in a delay tolerant network (DTN) in the presence of path failures. Previous work on DTN routing has focused on using precisely known network dynamics, which does not account for message losses due to link failures, buffer overruns, path selection errors, unscheduled delays, or other problems. We show how to split, replicate, and erasure code message fragments over multiple delivery paths to optimize the probability of successful message delivery. We provide a formulation of this problem and solve it for two cases: a 0 1 (Bernoulli) path delivery model where messages are either fully lost or delivered, and a Gaussian path delivery model where only a fraction of a message may be delivered. Ideas from the modern portfolio theory literature are borrowed to solve the underlying optimization problem. Our approach is directly relevant to solving similar problems that arise in replica placement in distributed file systems and virtual node placement in DHTs. In three different simulated DTN scenarios covering a wide range of applications, we show the effectiveness of our approach in handling failures.