## 4 Results
### Mixed Life Support System with Partially Autonomous LSS Functions \((0<\eta<1)\)  
Part of the LSS is placed on board the autonomous transport system and part of the life support resources generated by it are generated on the spot and do not require replenishment by delivery by a cargo vehicle. This makes it possible to more fully use  
Figure 3: The function of replenishing life support system resources at different levels of LSS autonomy. (**a**)—for OLSS architecture, (**b**)—for MLSS architecture.  
the releasing volume of the truck to deliver a larger part of the LRSs not generated on the autonomous system itself, which in this case is enough for a longer time (Figure 3b):  
\[\tau_{\eta}=\frac{z_{0}}{\gamma(1-\eta)}\]  
At the same time, the number of flights of a cargo vehicle during the mission will be  
\[u=\frac{T_{m}}{\tau_{\eta}}=\frac{T_{m}\gamma(1-\eta)}{z_{0}}\]  
In this case, the cost of shipping the LSR will be  
\[C_{r}(\Omega,t)=c_{1}u=\frac{c_{1}T_{m}\gamma(1-\eta)}{Z_{0}}\]  
The cost of the LSRs consumed by the crew during the mission will be  
\[C_{m}(\Omega,t)=s_{1}(1-\eta)T_{m}\]  
The greatest difficulty in analyzing the cost of the LSS life cycle in the early stages of its creation is the determination of the cost of its architecture, which is located on an autonomous transport system. In the work [38] based on experimental data, it is shown that the specified cost is well approximated by power functions, which allows for the expression to be used to describe the cost of the LSS architecture:  
\[C_{\eta}(\Omega,t)|_{0<\eta<1}=c_{0}\eta^{b} \tag{8}\]  
where \(b\) is some coefficient, the value of which can be determined experimentally [38]. Dependence (8) is confirmed by the experimental studies given in [38].  
For this LSS architecture under consideration, the cost of its life cycle based on the resulting expressions will be determined as follows:  
\[C(\Omega,t)|_{0<\eta<1}=C_{\eta}(\Omega,t)+C_{r}(\Omega,t)+C_{m}(\Omega,t)=c_{ 0}\eta^{b}+(1-\eta)T_{m}\bigg{(}\frac{c_{1}\gamma}{z_{0}}+s_{1}\bigg{)} \tag{9}\]  
This section delineates an in-depth analysis of various life support system architectures tailored to space stations for a diverse range of missions. This analysis is conducted through the application of Formulas (3), (7) and (9), each modeling the LSS life cycle cost for a particular type of architecture.  
Expression (3) lends itself to the characterization of the life cycle cost for a fully physical-chemical life support system, probing into the nuances of initial cost dependencies and system structures. Expression (7) describes the life cycle cost for a hybrid life support system, offering a comprehensive view of operational costs while encapsulating the interactions between the physical-chemical and bioregenerative components. Lastly, Equation (9) is applied to a fully bioregenerative life support system, amalgamating the concepts addressed in the previous formulas to present a holistic understanding of the life cycle cost in such a system.  
The above-mentioned models give a detailed, quantitative framework for analyzing, comparing, and ultimately designing different architectures of life support systems, each catering to different types of space missions. This framework as a methodological tool enhances the decision-making process in early design stages, providing researchers with key insights to inform their design choices of future space missions.