Discovery of nodes and content in large-scale distributed systems is generally based on Kademlia, today. Understanding Kademlia-type systems to improve their performance is essential for maintaining a high service quality for an increased number of participants, particularly when those systems are adopted by latency-sensitive applications. This paper contributes to the understanding of Kademlia by studying the impact of neighbours' identifiers within each routing table bucket on the lookup performance. We propose a new, yet backward-compatible, neighbour selection scheme that attempts to maximize the aforementioned diversity. The scheme does not cause additional overhead except negligible computations for comparing the diversity of identifiers. We present a theoretical model for the actual impact of the new scheme on the lookup's hop count and validate it against simulations of three exemplary Kademlia-type systems. We also measure the performance gain enabled by a partial deployment for the scheme in the real KAD system. The results confirm the superiority of the systems that incorporate our scheme.
In this paper, we propose to improve the lookup performance, in form of reduction in the average hop count, by adapting the standard neighbour selection scheme. Although the approach differs from earlier improvements, it is orthogonal and hence compatible with them. The model that we present in this paper extends on a prior model of Kademlia-type systems @cite_28 , which allows a very accurate prediction of the routing overhead. Though theoretical analysis of P2P routing performance is widely studied, traditionally only asymptotic bounds have been derived (e.g. @cite_29 @cite_36 @cite_18 @cite_19 ). The few studies deriving exact formulas commonly only consider the average routing length, special cases such as bijective mapping from identifiers to nodes, and are of limited accuracy when compared to measurements or simulations (e.g. @cite_11 @cite_27 @cite_32 ). In particular, @cite_27 @cite_32 model P2P routing using a Markov chain approach similar to the one suggested in @cite_28 , but are restricted to systems without parallelism.
@cite_18 @cite_28 @cite_36 @cite_29 @cite_32 @cite_19 @cite_27 @cite_11
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Recent work has focused on increasing availability in the face of Internet path failures. To date, proposed solutions have relied on complex routing and path-monitoring schemes, trading scalability for availability among a relatively small set of hosts. This paper proposes a simple, scalable approach to recover from Internet path failures. Our contributions are threefold. First, we conduct a broad measurement study of Internet path failures on a collection of 3,153 Internet destinations consisting of popular Web servers, broad-band hosts, and randomly selected nodes. We monitored these destinations from 67 PlanetLab vantage points over a period of seven days, and found availabilities ranging from 99.6 for servers to 94.4 for broadband hosts. When failures do occur, many appear too close to the destination (e.g., last-hop and end-host failures) to be mitigated through alternative routing techniques of any kind. Second, we show that for the failures that can be addressed through routing, a simple, scalable technique, called one-hop source routing, can achieve close to the maximum benefit available with very low overhead. When a path failure occurs, our scheme attempts to recover from it by routing indirectly through a small set of randomly chosen intermediaries. Third, we implemented and deployed a prototype one-hop source routing infrastructure on PlanetLab. Over a three day period, we repeatedly fetched documents from 982 popular Internet Web servers and used one-hop source routing to attempt to route around the failures we observed. Our results show that our prototype successfully recovered from 56 of network failures. However, we also found a large number of server failures that cannot be addressed through alternative routing. Our research demonstrates that one-hop source routing is easy to implement, adds negligible overhead, and achieves close to the maximum benefit available to indirect routing schemes, without the need for path monitoring, history, or a-priori knowledge of any kind. We study a fundamental tradeoff issue in designing a distributed hash table (DHT) in peer-to-peer (P2P) networks: the size of the routing table versus the network diameter. Observing that existing DHT schemes have either 1) a routing table size and network diameter both of O(log sub 2 n), or 2) a routing table of size d and network diameter of O(n sup 1 d ), S. (2001) asked whether this represents the best asymptotic "state-efficiency" tradeoffs. We show that some straightforward routing algorithms achieve better asymptotic tradeoffs. However, such algorithms all cause severe congestion on certain network nodes, which is undesirable in a P2P network. We rigorously define the notion of "congestion" and conjecture that the above tradeoffs are asymptotically optimal for a congestion-free network. The answer to this conjecture is negative in the strict sense. However, it becomes positive if the routing algorithm is required to eliminate congestion in a "natural" way by being uniform. We also prove that the tradeoffs are asymptotically optimal for uniform algorithms. Furthermore, for uniform algorithms, we find that the routing table size of O(log sub 2 n) is a magic threshold point that separates two different "state-efficiency" regions. Our third result is to study the exact (instead of asymptotic) optimal tradeoffs for uniform algorithms. We propose a new routing algorithm that reduces the routing table size and the network diameter of Chord both by 21.4 without introducing any other protocol overhead, based on a novel number-theory technique. Our final result is to present Ulysses, a congestion-free nonuniform algorithm that achieves a better asymptotic "state-efficiency" tradeoff than existing schemes in the probabilistic sense, even under dynamic node joins leaves. We address the problem of balancing the traffic load in multi-hop wireless networks. We consider a point-to-point communicating network with a uniform distribution of source-sink pairs. When routing along shortest paths, the nodes that are centrally located forward a disproportionate amount of traffic. This translates into increased congestion and energy consumption. However, the maximum load can be decreased if the packets follow curved paths. We show that the optimum such routing scheme can be expressed in terms of geometric optics and computed by linear programming. We then propose a practical solution, which we call Curveball Routing which achieves results not much worse than the optimum. We evaluate our solution at three levels of fidelity: a Java high-level simulator, the ns2 simulator, and the Intel Mirage Sensor Network Testbed. Simulation results using the high-level simulator show that our solution successfully avoids the crowded center of the network, and reduces the maximum load by up to 40 . At the same time, the increase of the expected path length is minimal, i.e., only 8 on average. Simulation results using the ns2 simulator show that our solution can increase throughput on moderately loaded networks by up to 15 , while testbed results show a reduction in peak energy usage by up to 25 . Our prototype suggests that our solution is easily deployable. The lack of an accurate representation of the Internet topology at the Autonomous System (AS) level is a limiting factor in the design, simulation, and modeling efforts in inter-domain routing protocols. In this paper, we design and implement a framework for identifying AS links that are missing from the commonly-used Internet topology snapshots. We apply our framework and show that the new links that we find change the current Internet topology model in a non-trivial way. First, in more detail, our framework provides a large-scale comprehensive synthesis of the available sources of information. We cross-validate and compare BGP routing tables, Internet Routing Registries, and traceroute data, while we extract significant newinformation from the less-studied Internet Exchange Points (IXPs). We identify 40 more edges and approximately 300 more peer-to-peer edges compared to commonly used data sets. Second, we identify properties of the new edges and quantify their effects on important topological properties. Given the new peer-to-peer edges, we find that for some ASes more than 50 of their paths stop going through their ISP providers assuming policy-aware routing. A surprising observation is that the degree of a node may be a poor indicator of which ASes it will peer with: the two degrees differ by a factor of four or more in 50 of the peer-to-peer links. Finally, we attempt to estimate the number of edges we may still be missing. We propose a routing strategy to improve the transportation efficiency on complex networks. Instead of using the routing strategy for shortest path, we give a generalized routing algorithm to find the so-called efficient path, which considers the possible congestion in the nodes along actual paths. Since the nodes with the largest degree are very susceptible to traffic congestion, an effective way to improve traffic and control congestion, as our strategy, can be redistributing traffic load in central nodes to other noncentral nodes. Simulation results indicate that the network capability in processing traffic is improved more than 10 times by optimizing the efficient path, which is in good agreement with the analysis. DOI: 10.1103 PhysRevE.73.046108 PACS numbers: 89.75.Hc Since the seminal work on scale-free networks by Barabasi and Albert BA model1 and on the small-world phenomenon by Watts and Strogatz 2, the structure and dynamics of complex networks have recently attracted a tremendous amount of interest and attention from the physics community see the review papers 3‐5 and references therein. The increasing importance of large communication networks such as the Internet 6, upon which our society survives, calls for the need for high efficiency in handling and delivering information. In this light, to find optimal strategies for traffic routing is one of the important issues we have to address. There have been many previous studies to understand and control traffic congestion on networks, with a basic assumption that the network has a homogeneous structure 7‐11. However, many real networks display both scale-free and small-world features, and thus it is of great interest to study the effect of network topology on traffic flow and the effect of traffic on network evolution. present a formalism that can cope simultaneously with the searching and traffic dynamics in parallel transportation systems 12. This formalism can be used to optimize network structure under a local search algorithm, while to obtain the formalism one should know the global information of the whole networks. Holme and Kim provide an in-depth analysis on the vertex edge overload cascading breakdowns based on evolving networks, and suggest a method to avoid We study approximate distributed solutions to the weighted all-pairs shortest-paths (APSP) problem in the CONGEST model. We obtain the following results. A deterministic (1+epsilon)-approximation to APSP with running time O(e-2n log n) rounds. The best previously known algorithm was randomized and slower by a Theta(log n) factor. In many cases, routing schemes involve relabeling, i.e., assigning new names to nodes and that are used in distance and routing queries. It is known that relabeling is necessary to achieve running times of o(n log n). In the relabeling model, we obtain the following results. A randomized O(k)-approximation to APSP, for any integer k>1, running in O(n1 2+1 k+D) rounds, where D is the hop diameter of the network. This algorithm simplifies the best previously known result and reduces its approximation ratio from O(k log k) to O(k). Also, the new algorithm uses O(log n)-bit labels, which is asymptotically optimal. A randomized O(k)-approximation to APSP, for any integer k>1, running in time O((nD)1 2 n1 k+D) and producing compact routing tables of size O(n1 k). The node labels consist of O(k log n) bits. This improves on the approximation ratio of Theta(k2) for tables of that size achieved by the best previously known algorithm, which terminates faster, in O(n1 2+1 k+D) rounds. In addition, we improve on the time complexity of the best known deterministic algorithm for distributed approximate Steiner forest. A number of distributed hash table (DHT)-based protocols have been proposed to address the issue of scalability in peer-to-peer networks. In this paper, we present Ulysses, a peer-to-peer network based on the butterfly topology that achieves the theoretical lower bound of log n log log n on network diameter when the average routing table size at nodes is no more than log n. Compared to existing DHT-based schemes with similar routing table size, Ulysses reduces the network diameter by a factor of log log n, which is 2–4 for typical configurations. This translates into the same amount of reduction on query latency and average traffic per link node. In addition, Ulysses maintains the same level of robustness in terms of routing in the face of faults and recovering from graceful ungraceful joins and departures, as provided by existing DHT-based schemes. The performance of the protocol has been evaluated using both analysis and simulation. Copyright © 2004 AEI We adapt the compact routing scheme by Thorup and Zwick to optimize it for power-law graphs. We analyze our adapted routing scheme based on the theory of unweighted random power-law graphs with fixed expected degree sequence by Aiello, Chung, and Lu. Our result is the first theoretical bound coupled to the parameter of the power-law graph model for a compact routing scheme. In particular, we prove that, for stretch 3, instead of routing tables with O(n1 2) bits as in the general scheme by Thorup and Zwick, expected sizes of O(nγ log n) bits are sufficient, and that all the routing tables can be constructed at once in expected time O(n1 + γ log n), with γ = τ - 2 2τ - 3 + Ɛ, where τ ∈ (2, 3) is the power-law exponent and Ɛ > 0. Both bounds also hold with probability at least 1 - 1 n (independent of Ɛ). The routing scheme is a labeled scheme, requiring a stretch-5 handshaking step and using addresses and message headers with O(log n log log n) bits, with probability at least 1 - o(1). We further demonstrate the effectiveness of our scheme by simulations on real-world graphs as well as synthetic power-law graphs. With the same techniques as for the compact routing scheme, we also adapt the approximate distance oracle by Thorup and Zwick for stretch 3 and obtain a new upper bound of expected O(n1+γ) for space and preprocessing. This paper considers max-min fair rate allocation and routing in energy harvesting networks where fairness is required among both the nodes and the time slots. Unlike most previous work on fairness, we focus on multihop topologies and consider different routing methods. We assume a predictable energy profile and focus on the design of efficient and optimal algorithms that can serve as benchmarks for distributed and approximate algorithms. We first develop an algorithm that obtains a max-min fair rate assignment for any given (time-variable or time-invariable) unsplittable routing or a routing tree. For time-invariable unsplittable routing, we also develop an algorithm that finds routes that maximize the minimum rate assigned to any node in any slot. For fractional routing, we study the joint routing and rate assignment problem. We develop an algorithm for the time-invariable case with constant rates. We show that the time-variable case is at least as hard as the 2-commodity feasible flow problem and design an FPTAS to combat the high running time. Finally, we show that finding a max-min fair unsplittable routing or a routing tree is NP-hard, even for a time horizon of a single slot. Our analysis provides insights into the problem structure and can be applied to other related fairness problems. Compact routing addresses the tradeoff between table sizes and stretch, which is the worst-case ratio between the length of the path a packet is routed through by the scheme and the length of an actual shortest path from source to destination. We adapt the compact routing scheme by Thorup and Zwick [2001] to optimize it for power-law graphs. We analyze our adapted routing scheme based on the theory of unweighted random power-law graphs with fixed expected degree sequence by [2000]. Our result is the first analytical bound coupled to the parameter of the power-law graph model for a compact routing scheme. Let n denote the number of nodes in the network. We provide a labeled routing scheme that, after a stretch--5 handshaking step (similar to DNS lookup in TCP IP), routes messages along stretch--3 paths. We prove that, instead of routing tables with O(n1 2) bits (O suppresses factors logarithmic in n) as in the general scheme by Thorup and Zwick, expected sizes of O(nγ log n) bits are sufficient, and that all the routing tables can be constructed at once in expected time O(n1+γ log n), with γ = τ-22 τ-3 + e, where τ∈(2,3) is the power-law exponent and e 0 (which implies e With the same techniques as for the compact routing scheme, we also adapt the approximate distance oracle by Thorup and Zwick [2001, 2005] for stretch-3 and we obtain a new upper bound of expected O(n1+γ) for space and preprocessing for random power-law graphs. Our distance oracle is the first one optimized for power-law graphs. Furthermore, we provide a linear-space data structure that can answer 5--approximate distance queries in time at most O(n1 4+e) (similar to γ, the exponent actually depends on τ and lies between e and 1 4 + e). We consider a network where each route comprises a backlogged source, a number of relays and a destination at a finite distance. The locations of the sources and the relays are realizations of independent Poisson point processes. Given that the nodes observe a TDMA ALOHA MAC protocol, our objective is to determine the number of relays and their placement such that the mean end-to-end delay in a typical route of the network is minimized.We first study an idealistic network model where all routes have the same number of hops, the same distance per hop and their own dedicated relays. Combining tools from queueing theory and stochastic geometry, we provide a precise characterization of the mean end-to-end delay. We find that the delay is minimized if the first hop is much longer than the remaining hops and that the optimal number of hops scales sublinearly with the source-destination distance. Simulating the original network scenario reveals that the analytical results are accurate, provided that the density of the relay process is sufficiently large. We conclude that, given the considered MAC protocol, our analysis provides a delay-minimizing routing strategy for random, multihop networks involving a small number of hops. Several peer-to-peer networks are based upon randomized graph topologies that permit efficient greedy routing, e. g., randomized hypercubes, randomized Chord, skip-graphs and constructions based upon small-world percolation networks. In each of these networks, a node has out-degree Θ(log n), where n denotes the total number of nodes, and greedy routing is known to take O(log n) hops on average. We establish lower-bounds for greedy routing for these networks, and analyze Neighbor-of-Neighbor (NoN)- greedy routing. The idea behind NoN, as the name suggests, is to take a neighbor's neighbors into account for making better routing decisions.The following picture emerges: Deterministic routing networks like hypercubes and Chord have diameter Θ(log n) and greedy routing is optimal. Randomized routing networks like randomized hypercubes, randomized Chord, and constructions based on small-world percolation networks, have diameter Θ(log n log log n) with high probability. The expected diameter of Skip graphs is also Θ(log n log log n). In all of these networks, greedy routing fails to find short routes, requiring Ω(log n) hops with high probability. Surprisingly, the NoN- greedy routing algorithm is able to diminish route-lengths to Θ(log n log log n) hops, which is asymptotically optimal. It is well known that in a network with arbitrary (convex) latency functions that are a function of edge traffic, the worst-case ratio, over all inputs, of the system delay caused due to selfish behavior versus the system delay of the optimal centralized solution may be unbounded even if the system consists of only two parallel links. This ratio is called the price of anarchy (PoA). In this paper, we investigate ways by which one can reduce the performance degradation due to selfish behavior. We investigate two primary methods (a) Stackelberg routing strategies, where a central authority, e.g., network manager, controls a fixed fraction of the flow, and can route this flow in any desired way so as to influence the flow of selfish users; and (b) network tolls, where tolls are imposed on the edges to modify the latencies of the edges, and thereby influence the induced Nash equilibrium. We obtain results demonstrating the effectiveness of both Stackelberg strategies and tolls in controlling the price of anarchy. For Stackelberg strategies, we obtain the first results for nonatomic routing in graphs more general than parallel-link graphs, and strengthen existing results for parallel-link graphs, (i) In series-parallel graphs, we show that Stackelberg routing reduces the PoA to a constant (depending on the fraction of flow controlled). (ii) For general graphs, we obtain latency-class specific bounds on the PoA with Stackelberg routing, which give a continuous trade-off between the fraction of flow controlled and the price of anarchy, (iii) In parallel-link graphs, we show that for any given class L of latency functions, Stackelberg routing reduces the PoA to at most α + (1 - α) · ρ(L), where α is the fraction of flow controlled and ρ(L) is the PoA of class L (when α = 0). For network tolls, motivated by the known strong results for nonatomic games, we consider the more general setting of atomic splittable routing games. We show that tolls inducing an optimal flow always exist, even for general asymmetric games with heterogeneous users, and can be computed efficiently by solving a convex program. Furthermore, we give a complete characterization of flows that can be induced via tolls. These are the first results on the effectiveness of tolls for atomic splittable games. We consider the problem of designing an overlay network and routing mechanism that permits finding resources efficiently in a peer-to-peer system. We argue that many existing approaches to this problem can be modeled as the construction of a random graph embedded in a metric space whose points represent resource identifiers, where the probability of a connection between two nodes depends only on the distance between them in the metric space. We study the performance of a peer-to-peer system where nodes are embedded at grid points in a simple metric space: a one-dimensional real line. We prove upper and lower bounds on the message complexity of locating particular resources in such a system, under a variety of assumptions about failures of either nodes or the connections between them. Our lower bounds in particular show that the use of inverse power-law distributions in routing, as suggested by Kleinberg [5], is close to optimal. We also give heuristics to efficiently maintain a network supporting efficient routing as nodes enter and leave the system. Finally, we give some experimental results that suggest promising directions for future work. Abstract This paper proposes a state-of-the-art branch-cut-and-price algorithm for the vehicle routing problem with stochastic demands (VRPSD). We adapt the model of Christiansen and Lysgaard [6] and formulate the VRPSD as a set partitioning model with additional constraints. Feasible routes are generated using a dynamic programming algorithm executed over a state-space graph. Our method combines 2-cycle elimination with ng -routes. In addition, our pricing problem is significantly accelerated by the introduction of a new aggregate dominance rule. To speed up the generation of negative reduced cost columns, we use a tabu search heuristic and a bidirectional labeling algorithm. We also add capacity and subset-row inequalities dynamically in order to strengthen the linear relaxation of the master problem. As extensive computational tests illustrate, our algorithm is very competitive with the one of [6] . We solve 20 additional instances from the 40-instance set considered by these authors and we considerably improve the computing times for instances already closed. We also solve 17 new instances from the literature. We describe a distributed randomized algorithm to construct routing tables. Given 0< e <= 1 2, the algorithm runs in time O(n1 2+e + HD), where n is the number of nodes and HD denotes the diameter of the network in hops (i.e., as if the network is unweighted). The weighted length of the produced routes is at most O(e-1log e-1) times the optimal weighted length. This is the first algorithm to break the Omega(n) complexity barrier for computing weighted shortest paths even for a single source. Moreover, the algorithm nearly meets the Omega(n1 2 + HD) lower bound for distributed computation of routing tables and approximate distances (with optimality, up to polylog factors, for e=1 log n). The presented techniques have many applications, including improved distributed approximation algorithms for Generalized Steiner Forest, all-pairs distance estimation, and estimation of the weighted diameter. In this paper, a novel joint transmit power and resource allocation approach for enabling ultra-reliable low-latency communication (URLLC) in vehicular networks is proposed. The objective is to minimize the network-wide power consumption of vehicular users (VUEs) while ensuring high reliability in terms of probabilistic queuing delays. In particular, a reliability measure is defined to characterize extreme events (i.e., when vehicles' queue lengths exceed a predefined threshold with non-negligible probability) using extreme value theory (EVT). Leveraging principles from federated learning (FL), the distribution of these extreme events corresponding to the tail distribution of queues is estimated by VUEs in a decentralized manner. Finally, Lyapunov optimization is used to find the joint transmit power and resource allocation policies for each VUE in a distributed manner. The proposed solution is validated via extensive simulations using a Manhattan mobility model. It is shown that FL enables the proposed distributed method to estimate the tail distribution of queues with an accuracy that is very close to a centralized solution with up to 79 reductions in the amount of data that need to be exchanged. Furthermore, the proposed method yields up to 60 reductions of VUEs with large queue lengths, without an additional power consumption, compared to an average queue-based baseline. Compared to systems with fixed power consumption and focusing on queue stability while minimizing average power consumption, the reductions in extreme events of the proposed method is about two orders of magnitude. This paper studies the problem of constructing a minimum-weight spanning tree (MST) in a distributed network. This is one of the most important problems in the area of distributed computing. There is a long line of gradually improving protocols for this problem, and the state of the art today is a protocol with running time O(Λ(G)+n⋅log∗n) due to Kutten and Peleg [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27], where Λ(G) denotes the diameter of the graph G. Peleg and Rubinovich [D. Peleg, V. Rubinovich, A near-tight lower bound on the time complexity of distributed MST construction, in: Proc. 40th IEEE Symp. on Foundations of Computer Science, 1999, pp. 253–261] have shown that Ω˜(n) time is required for constructing MST even on graphs of small diameter, and claimed that their result “establishes the asymptotic near-optimality” of the protocol of [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27]. In this paper we refine this claim, and devise a protocol that constructs the MST in Ω˜(μ(G,ω)+n) rounds, where μ(G,ω) is the MST-radius of the graph. The ratio between the diameter and the MST-radius may be as large as Θ(n), and, consequently, on some inputs our protocol is faster than the protocol of [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27] by a factor of Ω˜(n). Also, on every input, the running time of our protocol is never greater than twice the running time of the protocol of [S. Kutten, D. Peleg, Fast distributed construction of k-dominating sets and applications, J. Algorithms 28 (1998) 40–66; preliminary version appeared in: Proc. of 14th ACM Symp. on Principles of Distributed Computing, Ottawa, Canada, August 1995, pp. 20–27]. As part of our protocol for constructing an MST, we develop a protocol for constructing neighborhood covers with a drastically improved running time. The latter result may be of independent interest. A natural generalization of the selfish routing setting arises when some of the users obey a central coordinating authority, while the rest act selfishly. Such behavior can be modeled by dividing the users into an α fraction that are routed according to the central coordinator’s routing strategy (Stackelberg strategy), and the remaining 1−α that determine their strategy selfishly, given the routing of the coordinated users. One seeks to quantify the resulting price of anarchy, i.e., the ratio of the cost of the worst traffic equilibrium to the system optimum, as a function of α. It is well-known that for α=0 and linear latency functions the price of anarchy is at most 4 3 (J. ACM 49, 236–259, 2002). If α tends to 1, the price of anarchy should also tend to 1 for any reasonable algorithm used by the coordinator. We analyze two such algorithms for Stackelberg routing, LLF and SCALE. For general topology networks, multicommodity users, and linear latency functions, we show a price of anarchy bound for SCALE which decreases from 4 3 to 1 as α increases from 0 to 1, and depends only on α. Up to this work, such a tradeoff was known only for the case of two nodes connected with parallel links (SIAM J. Comput. 33, 332–350, 2004), while for general networks it was not clear whether such a result could be achieved, even in the single-commodity case. We show a weaker bound for LLF and also some extensions to general latency functions. The existence of a central coordinator is a rather strong requirement for a network. We show that we can do away with such a coordinator, as long as we are allowed to impose taxes (tolls) on the edges in order to steer the selfish users towards an improved system cost. As long as there is at least a fraction α of users that pay their taxes, we show the existence of taxes that lead to the simulation of SCALE by the tax-payers. The extension of the results mentioned above quantifies the improvement on the system cost as the number of tax-evaders decreases. This paper is meant to be an illustration of the use of stochastic geometry for analyzing the performance of routing in large wireless ad hoc (mobile or mesh) networks. In classical routing strategies used in such networks, packets are transmitted on a pre-defined route that is usually obtained by a shortest-path routing protocol. In this paper we review some recent ideas concerning a new routing technique which is opportunistic in the sense that each packet at each hop on its (specific) route from an origin to a destination takes advantage of the actual pattern of nodes that captured its recent (re)transmission in order to choose the next relay. The paper focuses both on the distributed algorithms allowing such a routing technique to work and on the evaluation of the gain in performance it brings compared to classical mechanisms. On the algorithmic side, we show that it is possible to implement this opportunistic technique in such a way that the current transmitter of a given packet does not need to know its next relay a priori, but the nodes that capture this transmission (if any) perform a self-selection procedure to choose the packet relay node and acknowledge the transmitter. We also show that this routing technique works well with various medium access protocols (such as Aloha, CSMA, TDMA). Finally, we show that the above relay self-selection procedure can be optimized in the sense that it is the node that optimizes some given utility criterion (e.g. minimize the remaining distance to the final destination), which is chosen as the relay. The performance evaluation part is based on stochastic geometry and combines simulation as analytical models. The main result is that such opportunistic schemes very significantly outperform classical routing schemes when properly optimized and provided at least a small number of nodes in the network know their geographical positions exactly.