## Main Design of DERM
### Track Routing
#### 4.4.1 Determining the Forwarding Direction
Although _DC-Rendezvous_ also exploits the mobility to some extent, it does not utilize the sink location information for routing and thus achieves lower energy efficiency compared with DERM. As expected, the _Rendezvous_ approach has the smallest transmission cost but at the price of tremendous delivery delay since it simply transmits packets to the vicinity of the sink path. As the sink speed increases, the transmission cost per packet of DERM and _DC-Rendezvous_ decreases. The reason is that a higher speed leads to a larger destination region, which provides more room for obtaining an energy-efficient route. Figure 8b shows that _Multihop_ achieves real-time data transmission. DERM and _DC-Rendezvous_ can also meet the delay requirement as their maximum E2E delivery delays are both no greater than 120 s. On the contrary, the maximum E2E delay of _Rendezvous_ is uncontrollable, which all depends on the path length and the sink speed. Figure 8c indicates the results in terms of the E2E delivery delay per packet. _DC-Rendezvous_ yields a larger E2E delay per packet than DERM. It can be explained by the fact that, in _DC-Rendezvous_, many packets wait for \(D_{s}\) seconds and finally find that the sink has not arrived. The maximum E2E delay and E2E delay per packet of _Rendezvous_ decrease significantly when the speed is increased from 1 to 4 m/s because the sink can reach a rendezvous node in less time with a higher speed. Regarding DERM and _DC-Rendezvous_, the maximum E2E delay almost stays unchanged and the E2E delay per packet decreases at a slow rate with increasing of the speed, due to the delay-aware operation. #### 5.3.2 Impact of the Delay Constraint

In Figure 9, we study the impact of the delay constraint on the performance of different routing schemes. Figure 9a shows that the transmission cost per packet of DERM and _DC-Rendezvous_ decreases by 25% and 11%, respectively, when the delay constraint is increased from 60 to 180 s. This is because, like increasing the speed, relaxing the delay constraint will also enlarge the destination region. Figure 9b illustrates that DERM as well as _DC-Rendezvous_ can always meet the corresponding delay requirement when the constraint is changed. Not surprisingly, the performance of _Multihop_ and _Rendezvous_ is little affected by the delay constraint, as shown in Figure 9a-c.

Figure 8: Performance overview under different sink speeds in ideal movement scenarios (\(D_{s}\) = 120 s). (**a**) transmission cost per packet; (**b**) maximum end-to-end delivery delay; (**c**) end-to-end delivery delay per packet. ### Performance Evaluation in Realistic Movement Scenarios

In realistic scenarios, the real sink locations may deviate from the values estimated by the mobility pattern. To test the effectiveness of DERM in such movement scenarios, we assume that the mobile sink pauses at the midpoint of the path for a period of time. The pause time is set to 30 s by default. #### 5.4.1 Performance Overview in Realistic Movement Scenarios

Figure 10 reports the evaluation results under different sink speeds in realistic movement scenarios. From Figure 10a,b, we can observe that the four schemes achieve very close transmission cost per packet and maximum E2E delays to those shown in Figure 8a,b, respectively. There are only some increases in the maximum E2E delay of _Rendezvous_ (e.g., from 1979 to 2008 s when the speed is 1 m/s) due to the pause. This means that the location calibration method performs well in tackling the location deviations for _Multihop_ and DERM. As for _Rendezvous_ and _DC-Rendezvous_, the location information is not used. The transmission cost of DERM decreases by 13%-43% and 24%-38% compared to _Multihop_ and _DC-Rendezvous_, respectively. Furthermore, the location estimation errors inevitably exist in realistic movement scenarios, but the maximum E2E delay of DERM can still meet the delay constraint, which demonstrates the efficiency of the track routing for ensuring on-time delivery. Figure 10c shows the control overhead of the sink location calibration.