Minimum transmission energy with Dijkstra routing initiates each node to send an L=2000 bit packet to the gateway during each round utilizing a route through neighboring nodes that minimizes the d2 propagation link cost to the gateway. The first node dead, 10 percent, 50 percent, and 80 percent nodes dead subplots are provided in Figure 40 through Figure 43, respectively, for the single gateway case. The total system energy, energy variance, and number of nodes versus transmission round are shown in Figure 44 through Figure 46, respectively. The first node dead, 10 percent, 50 percent, and 80 percent nodes dead occur at round 11, 77, 199, and 354, respectively. The energy stem plot and node distribution plots demonstrate that nodes closest to the gateway die out first and then fan out as subsequent live nodes closest to the gateway become the hot-nodes.
This quickly eliminates service coverage in those areas as expected but is a negative aspect of MTE routing in WSNs. The energy depletion rate of the network during the linear region of Figure 44 is 0.2140 J/round.
The energy bar and stem plots in Figure 40 through Figure 43 reveal a large variation in energy across all nodes. Nodes that are farthest away from the gateway are not used by their peers as frequently for routing, thus their energy is preserved. This creates a large energy variance and the quickest die out for all results collected in this thesis. The first node dies out quickest using this algorithm in part because there is no data aggregation strategy in place. This increases the transmission energy required of the hot-node at each round, thus fully depleting its battery power quickly. Since the first node dies out quickly, the timeframe for a linear energy depletion rate is also low (Figure 44). Also, since nodes farthest from the gateway are not utilized compared to nodes closer to the gateway, they remain in service the longest (Figure 46).
Figure 40. MTE routing in a single gateway WSN illustrating first node dead die out topology versus transmission roundand energy distribution.
Figure 41. MTE routing in a single gateway WSN illustrating 10 percent nodes dead die out topology versus transmission roundand energy distribution.
Figure 42. MTE routing in a single gateway WSN illustrating 50 percent nodes dead die out topology versus transmission round and energy distribution.
Figure 43. MTE routing in a single gateway WSN illustrating 80 percent nodes dead die out topology versus transmission round and energy distribution.
Figure 44. MTE routing in a single gateway WSN. The total WSN energy versus transmission round is illustrated.
Figure 45. MTE routing in a single gateway WSN. The WSN energy variance versus transmission round is illustrated.
Figure 46. MTE routing in a single gateway WSN. The number of nodes alive versus transmission round is illustrated.
2. Multi-gateway
Minimum transmission energy with Dijkstra routing initiates each node to send an L=2000 bit packet to the gateway during each round utilizing a route through neighboring nodes that minimizes the d2 propagation link cost to the closer gateway. The gateway with the lower total link cost route metric is used. The first node dead, 10 percent, 50 percent, and 80 percent nodes dead subplots are provided in Figure 47 through Figure 50, respectively, for the multi-gateway case. The total system energy, energy variance, and number of nodes versus transmission round are shown in Figure 51 through Figure 53, respectively. The first node dead, 10 percent, 50 percent, and 80 percent nodes dead occur at round 17, 100, 293, and 453, respectively, corresponding to a percent increase of 55 percent, 30 percent, 47 percent, and 28 percent, respectively, when compared to single gateway die out statistics for the same algorithm. The energy stem plot and node distribution plots demonstrate nodes closest to each gateway die first quickly, eliminating service coverage in those areas. The energy depletion rate of the network during the linear region of Figure 51 is 0.1418 J/round, which corresponds to a 34 percent reduction in network energy depletion rate compared to the single gateway case.
The previous single gateway case depleted nodes farthest from the gateway slowly. In the multi-gateway scenario, nodes in the middle of the sensor field are preserved longest since they are not used for routing as much as hot-nodes that are closest to the gateway. There is an opposite node die out reaction when using Dijkstra’s algorithm in MTE routing compared to the direct routing simulation. Specifically, the direct packet transmission algorithm depleted nodes farthest from the gateway, while MTE transmission depleted areas needed for packet routing first.
Our comments regarding energy variance are similar in the single gateway and multi-gateway MTE scenarios except the multi-gateway yields a smaller energy variance during each round. The addition of the second gateway lowers the total number of transmissions during each round, which is an improvement and, subsequently, lowers the energy variance as compared to the single gateway case. However, the lack of data aggregation and the fact that nodes use their neighbors excessively for routing causes a large energy variance and, therefore, nodes die out quickly.
Figure 47. MTE routing in a multi-gateway WSN illustrating first node dead die out topology versus transmission round and energy distribution.
Figure 48. MTE routing in a multi-gateway WSN illustrating 10 percent nodes dead die out topology versus transmission round and energy distribution.
Figure 49. MTE routing in a multi-gateway WSN illustrating 50 percent nodes dead die out topology versus transmission round and energy distribution.
Figure 50. MTE routing in a multi-gateway WSN illustrating 80 percent nodes dead die out topology versus transmission round and energy distribution.
Figure 51. MTE routing in a multi-gateway WSN. The total WSN energy versus transmission round is illustrated.
Figure 52. MTE routing in a multi-gateway WSN. The WSN energy variance versus transmission round is illustrated.
Figure 53. MTE routing in a multi-gateway WSN. The number of nodes alive versus transmission round is illustrated.