# A Sigfox Energy Consumption Model
## 5 Evaluation
### Energy Cost of Data Delivery  
This subsection evaluates the energy cost of data delivery for both unidirectional and bidirectional transaction types, on the basis of Equations (6) and (20). Figure 10 depicts \(EC_{delivery\_uni}\) and \(EC_{delivery\_bi}\) as a function of the transaction period, for unidirectional and bidirectional transactions, for 1-byte and 12-byte payload sizes, and for uplink bit rates of 100 bit/s and 600 bit/s. For the sake of illustration clarity, from the 600 bit/s uplink bit rate cases, only the curve corresponding to a 1-byte payload and unidirectional transactions is shown. For all considered options, the energy cost of data delivery increases with the transaction period. The reason is that one data payload is delivered per transaction  
Figure 9: Device lifetime, for unidirectional and bidirectional transactions, as a function of \(T_{Period}\), and for uplink payload sizes of 1 byte and 12 bytes, for FLR = 0.  
period, and the energy consumption over a transaction period increases with the latter (due to the current consumption during a sleep interval that also increases). As the transaction period increases, the difference between using unidirectional and bidirectional transactions becomes less relevant, since the sleep interval becomes dominant.  
A remarkable result is that, for an uplink bit rate of 100 bit/s, the energy cost of delivering a 12-byte payload with a bidirectional transaction is from 2 to 10 times lower than that of delivering a 1-byte payload with a unidirectional transaction. As expected, the energy cost of data delivery is inversely proportional to the delivered payload size.  
Finally, the energy cost of data delivery decreases for an uplink bit rate of 600 bit/s, compared to that obtained for an uplink bit rate of 100 bit/s, since transmission time of the uplink messages decreases as well. The quantitative impact of the uplink bit rate is more relevant for unidirectional transactions than for bidirectional ones. For example, for a 1-byte payload, \(T_{Period}\) = 10 min, and an uplink bit rate of 100 bit/s, the energy cost of data delivery in unidirectional transactions is 1.59 times greater than that obtained with an uplink rate of 600 bit/s. However, for the same settings but using bidirectional transactions, the relative difference decreases to a factor of 1.06. As the transaction period increases, impact of the bit rate tends to decrease since the active states become less relevant.  
In order to better assess the impact of loss rate on both \(EC_{delivery\_uni}\) and \(EC_{delivery\_bi}\), Figure 11 shows both performance parameters, for unidirectional and bidirectional transactions, for an uplink bit rate of 100 bit/s, and for different FLR values. As the FLR grows, the energy cost of data delivery increases. For unidirectional transactions, while device current consumption is independent of the frame loss rate, the energy cost of data delivery increases with FLR. For bidirectional transactions, as explained in Section 5.1, FLR leads to a slight decrease in device current consumption for FLR up to ~0.5, which is compensated by the corresponding lower delivery rate to keep a roughly constant energy cost of data delivery as a function of FLR. For greater FLR values, energy cost of data delivery increases; since current consumption increases, while delivery rate decreases, the energy cost of data delivery for bidirectional transactions exhibits a greater increase with FLR than for unidirectional transactions. For example, for FLR = 0.7, \(EC_{delivery\_uni}\) and \(EC_{delivery\_bi}\) increase by up to 52% and 64%, respectively, when compared to FLR = 0.  
Figure 10: Energy cost of data delivery, for unidirectional and bidirectional transactions, as a function of \(T_{Period}\), and for uplink payload sizes of 1 byte and 12 bytes, for FLR = 0.