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The Nominal Capacity of Wireless Mesh Networks Jangeun Jun and Mihail L

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The Nominal Capacity of Wireless Mesh Networks Jangeun Jun and Mihail L MERGING IP AND WIRELESS NETWORKS THE NOMINAL CAPACITY OF WIRELESS MESH NETWORKS JANGEUN JUN AND MIHAIL L. SICHITIU, NORTH CAROLINA STATE UNIVERSITY broadband Internet access using seven gate- GW ABSTRACT ways (the larger red nodes) connected to the 1 Wireless mesh networks are an alternative Internet. In WMNs, each user node operates technology for last-mile broadband Internet not only as a host but also as a wireless router, access. In WMNs, similar to ad hoc networks, forwarding packets on behalf of other nodes 2 each user node operates not only as a host but that may not be within direct wireless transmis- also as a router; user packets are forwarded to sion range of a gateway. The gateways are con- 4 and from an Internet-connected gateway in nected to the Internet (the backhaul multihop fashion. The meshed topology pro- connection itself may also be wireless). The vides good reliability, market coverage, and network is dynamically self-organizing and self- 7 scalability, as well as low upfront investments. configuring, with the nodes in the network 5 Despite the recent startup surge in WMNs, automatically establishing and maintaining much research remains to be done before routes among themselves. Users can be station- Wireless mesh WMNs realize their full potential. This article ary or comparatively mobile [3]. The main dif- tackles the problem of determining the exact ference between a WMN and an ad hoc networks (WMNs) capacity of a WMN. The key concept we intro- network is perhaps the traffic pattern: in duce to enable this calculation is the bottleneck WMNs, practically all traffic is either to or are an alternative collision domain, defined as the geographical from a gateway, while in ad hoc networks the area of the network that bounds from above the traffic flows between arbitrary pairs of nodes. technology for amount of data that can be transmitted in the If desired, repeater nodes (pure wireless network. We show that for WMNs the through- routers) may be used to extend the coverage or last-mile broadband put of each node decreases as O(1/n), where n improve the performance of the network. A is the total number of nodes in the network. In repeater node is a layer 3 device, similar to a Internet access. contrast with most existing work on ad hoc net- client node except that it is never the source or work capacity, we do not limit our study to the destination of a traffic flow. Despite the recent asymptotic case. In particular, for a given topol- The gateways in WMNs are added one at a ogy and the set of active nodes, we provide time as needed. Adding more gateways will start-up surge in exact upper bounds on the throughput of any increase not only the capacity of the network but node. The calculation can be used to provision also its reliability. The mesh structure ensures WMNs, much the network, to ensure quality of service and the availability of multiple paths for each node fairness. The theoretical results are validated by in the network. If one or multiple nodes fail, the research remains to detailed simulations. packets will be rerouted around the failed node(s). Similarly, if one gateway fails, the oth- be done before NTRODUCTION ers will take over its traffic, while the network as I a whole will continue to function with (slightly) WMNs realize their The wireless mesh network (WMN) [1, 2] is a reduced performance. This provides a very new broadband Internet access technology draw- appealing “graceful degradation” feature. Mobile full potential. ing significant attention these days. The competi- users can connect to the WMN and have unteth- tion with other broadband technologies, ered connectivity as they roam within the cover- including cable, digital subscriber line (xDSL), age area of the WMN. broadband wireless local loop ,and satellite It is conceivable, and in fact quite desirable, Internet access, is stiff, but WMNs have signifi- that quality of service (QoS) guarantees can be cant advantages, making them a viable alterna- offered to customers. If the network is designed tive. Upfront investments are minimal, because carefully and enough Internet gateways are the technology can be installed incrementally, placed at key points, each customer can enjoy one node at a time, just as needed. As more guaranteed bandwidth and/or delay (at least in This work was supported nodes are installed, the reliability and network the access network). The guarantees enable mul- by the Center for coverage increase. timedia applications such as voice over IP and Advanced Computing and Figure 1 depicts a possible scenario where video on demand. Moreover, different classes of Communication. users (the small gray nodes) are provided with service (e.g., premium, enhanced, and basic) can 8 1536-1284/03/$17.00 © 2003 IEEE IEEE Wireless Communications • October 2003 be offered, each with different priorities and guarantees. Because the network is built one node at a time, the technology allows providers to better Internet match incoming revenues to outgoing expenses — a major challenge in DSL and cable-based services (and seemingly an insurmountable one for low Earth orbit, LEO, satellite services), especially at this time. Furthermore, many ver- sions of WMNs are largely deployable by con- sumers themselves. The technology is “radio agnostic” [3] (i.e., independent of the underlying radio technology). Fixed nodes can act as triangulation beacons for mobile users, and a Global Positioning System (GPS)-less geolocation feature can be imple- mented within the coverage area of a WMN. Several vendors have recently offered WMN products. Some of the most experienced in the business are Mesh Networks [3] and Nokia Rooftop. There are more than 20 other startup companies that plan to offer similar I Figure 1. A wireless mesh network for broadband Internet access. products. A comparison of the product offer- ings of these companies reveals that the research needed to back up the products was computation is the bottleneck collision domain, largely passed over in the rush to capture the which is the geographical area that limits the market. While the technology is sound, more overall throughput of the network. We analyze research is needed before WMNs can reach the capacity of WMNs based on traffic behavior their full potential. at the medium access control (MAC) layer. One of the most hyped ideas is that the Since our approach is not limited to a specific capacity of a WMN exceeds the capacity of a MAC scheme, we can compute the exact capaci- fixed wireless broadband Internet access (or ty of a WMN for any MAC layer implementa- that of a wireless LAN) based on similar tech- tion. nology. Some even claim that the capacity of the network increases with the number of clients. PROBLEM FORMULATION The intuition to support these claims comes from the spatial reuse possible in WMNs: two Before determining the capacity of WMNs, we nodes at opposite ends of the network can trans- will comment on the fairness of multihop net- mit simultaneously without a collision; however, works. We will also define MAC capacity and in a multihop environment, most of the trans- collision domains as essential building blocks for missions are just forwarding traffic, which, as WMN capacity calculation. will be shown, effectively eliminates the gain from spatial reuse. RELAYED TRAFFIC AND FAIRNESS Although there are significant research results The question of the capacity of the network can- on the capacity of wireless ad hoc networks not be properly addressed without discussing the [4–10], these results are focused on the general issue of fairness. Note that a user node in WMNs case where the traffic streams flow between arbi- has to transmit relayed traffic as well as its own. trary pairs of nodes. Moreover, the existing Therefore, besides contention with other nodes results hold in the asymptotic case when the for the same destination node, there is inevitable number of nodes n is very large. It was shown [4] contention between its own and relayed traffic. that for stationary networks, the capacity for This type of contention does not occur in fixed each node decreases as O(1/√n); while for mobile wireless local loops or wireless LANs in infra- networks, if long delays are tolerated, the capaci- structure mode where user nodes are always at ty may remain constant with the number of one-hop distance from the base station or access nodes: O(1) [6]. Another study related to this point. article considers the capacity of regular ad hoc Consider the simple case depicted in Fig. 2a networks [5]. An interesting probabilistic model where two nodes (1 and 2) have the same offered is used in [7] to compute the capacity of a chain load G sent to the gateway (GW). Ideally, as the of wireless nodes. offered load at each of the nodes (G) increases, We will show that the existence of gateways both nodes receive the same share of the MAC in WMNs introduces hot spots in the network layer throughput, B (Fig. 2b). In practice, with- that act as bottlenecks. Due to the presence of out a modified MAC or network layer, as the these bottlenecks, the available capacity for each offered load increases, the node closest to the node is reduced to O(1/n) where n is the number gateway (node 1 in Fig. 2a) gradually but com- of users for one gateway. Most important, in our pletely starves the node further away from the analysis we not only treat the asymptotic case, gateway (as shown in Fig. 2c). The results in Fig. but also compute exactly the minimum and max- 2c are obtained under the assumptions that the imum data rates available for each node in a MAC layer is “fair” and that the traffic to be WMN for a given network topology and link forwarded by node 1 (from node 2 to the gate- layer protocol.
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