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(2) Bandwidth variation Bi (t) keeps the estimated maximum change of Bi (t) before the next update. The actual maximum bandwidth from i to t is expected to be between Bi (t) Bi (t) and Bi (t) + Bi (t) in the next period. (3) The cost metric Ci (t) is used for optimization, in contrast to the delay and bandwidth metrics used in QoS constraints. Consider an arbitrary update of Di (t) and Di (t). Let Di (t) and Di (t) be the values of Di (t) before and after the update, respectively. Similarly, let Di (t) and Di (t) be the values of Di (t) before and after the update, respectively. Di (t) is provided by a distance-vector protocol. Di (t) is calculated as follows: Di (t) = Di (t) + (1 ) Di (t) Di (t) (13.15)
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The factor (<1) determines how fast the history information Di (t) is forgotten, and 1 determines how fast Di (t) converges to |Di (t) Di (t)|. By the previous formula, it is still possible for the actual delay to be out of the range [Di (t) Di (t), Di (t) + Di (t)]. One way to make such probability suf ciently small is to enlarge Di (t). Hence, we shall modify the formula and introduce another factor (>1): Di (t) = Di (t) + (1 ) Di (t) Di (t) Di (t)converges to Di (t) Di (t) at a speed determined by 1 . 13.7.4 Token-based routing There are numerous paths from s to t. We shall not randomly pick several paths to search. Instead, we want to make an intelligent hop-by-hop path selection to guide the search along the best candidate paths. This is what, for example, the Viterbi algorithm would be doing in trying to avoid search through all possible trajectories of a trellis (ML approach) in a signal demodulation/decoding process. The basic idea of token-based probing is outlined below. A token is the permission to search one path. The source node issues a number of tokens based on the available state information. One guideline is that more tokens are issued for the connections with tighter requirements. Probes (routing messages) are sent from the source toward the destination to search for a low-cost path that satis es the QoS requirement. Each probe is required to carry at least one token. At an intermediate node, a probe with more than one token is allowed to be split into multiple ones, each searching a different downstream subpath. The maximum number of probes at any time is bounded by the total number of tokens. Since each probe searches a path, the maximum number of paths searched is also bounded by the number of tokens. See Figure 13.46 for an example. Upon receipt of a probe, an intermediate node decides, based on its state: (1) whether the received probe should be split; and (2) to which neighbor nodes the probe(s) should be forwarded. The goal is to collectively utilize the state information at the intermediate nodes to guide the limited tickets (the probes carrying them) along the best paths to the destination, so that the probability of nding a low-cost feasible path is maximized. (13.16)
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Figure 13.46 Generation of probes p (number of tokens). 13.7.5 Delay-constrained routing When a connection request arrives at the source node, a certain number N0 of tokens are generated, and probes are sent toward the destination t. Each probe carries one or more tokens. Since no new tokens are allowed to be created by the intermediate nodes, the total number of tokens is always N0 , and the number of probes is at most N0 at any time. When a node receives a probe p with N ( p) tokens, it makes at most N ( p) copies of p, distributes the received tickets among the new probes, and then forwards them along to selected outgoing links toward t. Each probe accumulates the delay of the path it has traversed so far. A probe can proceed only when the accumulated delay does not violate the delay requirement. Hence, any probe arriving at the destination detects a feasible path, which is the one it has traversed. There are two basic guidelines for how to determine N0 and how to distribute the tokens in a received probe among the new probes: (1) Different numbers of tokens are assigned to different connections based on their needs . For a connection whose delay requirement is large and can be easily satis ed, one token is issued to search a single path; for a connection whose delay requirement is smaller, more tokens are issued to increase the chance of nding a feasible path; for a connection whose delay requirement is too small to be satis ed, no tokens are issued, and the connection is immediately rejected. (2) When a node i forwards the received tokens to its neighbors, the tokens are distributed unevenly among the neighbors, depending on their chances of leading to reliable low-cost feasible paths. A neighbor having a smaller end-to-end delay to the destination should receive more tickets than a neighbor having a larger delay; a neighbor
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