Figure 13.38 System topology.

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15 C14 14 16 13 10 20 C10 12 C3 C1 1 2 11 3 4 18 C18 6 5 8 17 C5 7 9

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Figure 13.39 Clustering.

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13.5.3 Clustering with prediction 13.5.3.1 (c,t) Cluster framework The objective of the (c,t) cluster framework is to maintain an effective topology that adapts to node mobility so that routing can be more responsive and optimal when mobility rates are low and more ef cient when they are high. This is accomplished by a simple distributed clustering algorithm using a probability model for path availability as the basis for clustering decisions. The algorithm dynamically organizes the nodes of an ad hoc network into clusters where probabilistic bounds can be maintained on the availability of paths to cluster destinations over a speci ed interval of time. The (c,t) cluster framework can also be used as the basis for the development of adaptive schemes for probabilistic QoS guarantees in ad hoc networks. Speci cally, support for QoS in time-varying networks requires addressing: (1) connection-level issues related to path establishment and management to ensure the existence of a connection between the source and the destination; and (2) packet-level performance issues in terms of delay bounds, throughput and acceptable error rates. Ideally, it is desirable to guarantee that the QoS requirements of ongoing connections are preserved for their entire duration. Unfortunately, this is not possible in a time-varying network environment as connections may fail randomly due to user mobility. A more realistic and practical approach is to provide some form of probabilistic QoS guarantees by keeping connection failures below a prespeci ed threshold value and by ensuring with high probability that a minimum level of bandwidth is always available to ongoing connections. The basic idea of the (c,t) cluster strategy is to partition the network into clusters of nodes that are mutually reachable along cluster internal paths that are expected to be available for a period of time t with a probability of at least c. The union of the clusters in a network must cover all the nodes in the network. Assume, without loss of generality, that t is identical at every node in a cluster. If the cluster s topology remains stable over the interval of length t,

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then routing will be deterministic during this interval, and standard assumptions permit the ad hoc network to be modeled as a network of Jackson queues. Assuming that path availability is an ergodic process, c represents the average proportion of time a (c,t) path is available to carry data. Consequently, c places a lower bound on the effective capacity of the path over an interval of length t. Let the link capacity be C b/s and the mean packet length 1/ b. The effective packet service rate eff over the interval t can be determined based upon the path availability according to Equation (13.4). Based on the Jackson model, each node can be treated as an independent M/M/1 queue. Using knowledge of the current aggregate arrival rate and the effective service rate eff , the M/M/1 results can be applied to nd the mean total packet delay T . Since this delay must be less than t, this approach establishes a lower bound on the path availability, as shown in Equation (13.7) eff = cC 1 T = eff 1 t cC 1 + t c tC (13.4) (13.5) (13.6) (13.7)

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An effective adaptive strategy for determining the value of c controls the minimum level of cluster stability required to support the traf c load and QoS requirements of established connections. The choice of the parameter t is a system design decision that determines the maximum cluster size achievable for different rates of mobility when no traf c exists in the network. 13.5.3.2 (c,t) Cluster algorithm There are ve events which drive the (c,t) cluster algorithm, namely, node activation, link activation, link failure, expiration of the timer and node deactivation. Node activation The primary objective of an activating node is to discover an adjacent node and join its cluster. In order to accomplish this, it must be able to obtain topology information for the cluster from its neighbor and execute its routing algorithm to determine the (c,t) availability of all the destination nodes in that cluster. The source node can join a cluster if and only if all the destinations are reachable via (c,t) paths. The rst step upon node activation is the initialization of the source node s CID (cluster ID) to a prede ned value that indicates its unclustered status. The network-interface layer protocol is required to advertise the node s CID as part of the neighbor greeting protocol [79] and in the header of the encapsulation protocol. This enables nodes to easily identify the cluster status and membership of neighboring nodes and of the source of the routing updates a necessary function to control the dissemination of routing information. When its network-interface layer protocol identi es one or more neighboring nodes, the source node performs the following actions. First, the source node identi es the CIDs associated with each neighbor. Next, it evaluates the link

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