# Improving Bundle Routing in a Space DTN by Approximating the Transmission Time of the Reliable LTP
## 3 System Analysis
### Service Time Estimation  
Because of the planned nature of space DTNs, the system parameters required to solve Equation (8) are known in general at the time of deciding bundle routing with adequate accuracy, except for the service time \(S\), unless the bundle transmissions occur with ideal channel conditions as assumed by the current practice [4]. As discussed in Section 3.2, a positive bit error rate can significantly increase the link service time, impacting the bundle routing optimality.  
A service estimation method is proposed in this section based on Equation (4). To assess the performance benefits of the proposed change, it is sensible to compare it with related methods. The first two methods listed below are commonly used in practice, whereas the third method was inferred from the performance analysis of bundle transmissions in [25]. The fourth method is the proposed one based on Section 3.2:  
* _Method 1_ approximates the service time as given by the one-way propagation delay \(S=D\), which appears adequate when the delays are much greater than the transmission times, as in the case of deep space links. However, it underestimates this value if that condition is not true. This method was used in the initial shortest path computation of the standard contact graph routing (CGR) algorithm (e.g., see the ION-DTN implementation [4]).
* _Method 2_ assumes that the service time is given by the aggregation of the transmission time (also known as the radiation time in the literature) and the one-way propagation delay \(S=S_{0}+D\), where \(S_{0}\) denotes the nominal service time over a lossless channel \(S_{0}=B/r\) (i.e., the ratio of the bundle size and the channel rate), considering that the protocol header's overhead is much smaller than the bundle size so that it can be ignored. This appears to be better suited for situations where the transmission and propagation delays share a similar range of values, but it ignores the impact of retransmissions. This method has also been used in CGR implementation, particularly for the calculation of the remaining link capacity and in the proposed extensions of CGR with earliest transmission opportunity (CGR-ETO) and overbooking [16].
* _Method 3_ considers that the nominal service time is extended by the retransmission efforts and is given by the expression \(S=\frac{S_{0}+D}{1-p}\), where \(p\) is the packet loss probability as before. This geometric approximation results from the assumption that packet losses occur independently [25], which implies an average number of transmission efforts \((1-p)^{-1}\). Again, it is assumed that the impact of the protocol headers is negligible for simplicity. The BER value that yields \(p\) can be determined from the link budget analysis.
* _Method 4_ (proposed method) estimates the service time as given by Equation (4) and as elaborated upon in Section 3.2. To account for possible deviations caused in practice by parameter estimation errors, the expression used to solve Equation (8) (or CGR if the actual space DTN protocols are used) includes a multiplicand \(f\geq 1\), which also serves for performance tuning as Equation (4) is an approximation of the extended service time \(fS_{e}(p)\). An evaluation of the impact of parameter \(f\) can be found in Section 6.  
In the following section, the three reference methods are numerically compared to the proposed method through a reference network scenario.