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ALGORITHM 4. Calculate the Set of Maximal Independent Sets M Require: is a n n matrix where n = number of nodes. [i][j] = 1 if i can hear node j. Else [i][j] = 0. Require: N is an array of all the nodes. {// L denotes the number of iterations we attempt to compute unique independent sets.} {// M is the set if all MICS} Initialize M to empty set for i = 1 to L do Randomize the ordering of N S = {N[1]} {// S denotes a maximal independent set being computed} for i = 2 to N.size() do src N[i] for j = 1 to S.size() do if [src][S[j]] == 1 then Break the for loop i end if end for Add src to to independent set S end for {// At this point, S will be one of the maximal independent sets} if S is not present in M then Add the maximal independent set S to M end if end for return M
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The computation of maximal independent sets plays an important role in the analysis of CSMA protocols [31, 57 59], as well as routing protocols [49]. The problem is NP-hard, and approximation techniques are often used for practical purposes. A simple way of approximating the maximal independent sets of nodes that can concurrently transmit under the Protocol Model of interference is given in Algorithm 4. The model is validated by observing the interactions in a simulated environment. The results show that the model captures a vast majority of the interactions. Two or more links initiating at the same instant of time without the knowledge of each other accounts for a miniature fraction of the packet losses, which is not captured by the model in reference 31. In the IEEE 802.11 [19] MAC protocol, a packet loss is observed when the sender does not receive a CTS for the RTS (which is called as RTS timeout), or if the ACK packet is not received for the DATA (an ACK timeout). In Figure 7.6a, the formulation is validated against simulation results to see if the model captures such losses. It was seen that less than 3% of the packet losses occurred between different MICS and thus were not captured by the model. Accordingly, truly concurrent transmissions are rare, and most collisions occur due to the failure of the MAC protocol to prevent interfering sources from concurrent transmissions. This result supports the use of the
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EFFECT OF INTERFERENCE ON ROUTING IN MULTIHOP WIRELESS NETWORKS
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Ratio of Throughput Improvement
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4 2.5 x 10
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Timeouts detected by formulation Timeouts not detected by formulation
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4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 50 60 70 80 90 100 110 120 130 140 150
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4 conns IA Routes 4 conns SIA Routes 6 conns IA Routes 6 conns SIA Routes
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Figure 7.6. Accuracy of the model to capture interactions. This graph shows the observed number of packet drops and the accuracy of the model in predicting these drops. (b) Effectiveness of scheduling formulation. This graph compares the throughput observed in simulation by (i) most stable routes predicted by DSR (ii) routes obtained from interference-aware formulation, and (iii) routes obtained from an interference- and scheduling-aware formulation. (Figure 7.6 represents the results presented in reference 31.)
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MICS-based formulation to estimate the effect of the low-level interactions of the MAC protocol. The study also estimates the fraction of packet drops that occurs at each link due to ineffective handshake of the MAC protocol. Such a metric is similar to the ETX metric which captures the amount of packet losses. The integration of such MAC modeling with routing formulations provides a more accurate globally aware routing model and is a challenging and important research goal. Kolar and Abu-Ghazaleh [31] also performed a global scheduling and interference-aware (SIA) routing and measured the performance gains. SIA was implemented by rst getting the best route from the Interference-aware formulation (IA Routes) from the basic MCF linear program model [52]. Then, the packet losses at different links were estimated using the scheduling model discussed above. The links that had the highest con icts were mutually excluded by adding further constraints into the LP formulation; the extended model is then re-executed. These steps were repeated until the solution converged or the number of runs exceeded a predetermined threshold, at which time the best routes found are used. Figure 7.6b compares general IA routes proposed in reference 52 with SIA routes. The IA routes work on the Protocol model of interference which assumes a constant interference range. The performance is reported normalized to the performance of the traditional routes obtained using the best DSR routes. It can be seen that the SIA routes perform better than the IA routes. The effectiveness of the scheduling formulations can be seen in high contention areas; as described above in Figure 7.1 in Section 7.4.1, it is in that area that scheduling plays a higher role in determining link capacity. It can be seen in Figure 7.6b that SIA advantages are more pronounced under higher
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