## 5 Discussion  
In the context of the provided Figure 2, the boundary values of the duration of missions \(T_{1}\) and \(T_{3}\) are critical in determining the most effective life support system architecture choice. \(T_{1}\) represents the mission duration below which the Open LSS architecture is deemed to be the most effective option. This boundary value is determined based on factors such as the cost and logistical feasibility of resupply missions. When the mission duration is relatively short, it may be more cost-effective and practical to rely on external resource delivery through resupply missions, rather than investing in complex onboard resource generation and recycling systems. Below \(T_{1}\), OLSS offers advantages in terms of lower initial development costs and reduced system complexity. The boundary value of \(T_{1}\) can be defined by equating expression (8) to expression (9):  
\[T_{1}=\frac{c_{0}\eta^{b-1}z_{0}}{c_{1}\gamma+s_{1}z_{0}}\]  
In this case, with the duration of the mission \(T_{m}<T_{1}\) from a cost-effective point of view, it is advantageous not to use a mixed LSS architecture. \(T_{3}\) represents the mission duration beyond which the Closed LSS architecture becomes the most effective choice. This boundary value is determined by considering factors such as the increased cost efficiency and self-sufficiency of CLSS over extended durations. CLSS, with its fully autonomous resource generation and recycling capabilities, is well-suited for long-duration missions wherein dependence on external resupply missions may become impractical or costly. Beyond \(T_{3}\), CLSS offers advantages in terms of greater self-sufficiency, reduced reliance on external resources, and minimized environmental impact from reduced resupply missions. The boundary value of \(T_{3}\) can be defined by equating expression (3) to expression (9):  
\[T_{3}=\frac{c_{0}z_{0}\Big{(}1-\eta^{b}\Big{)}}{(1-\eta)(c_{1}\gamma+s_{1}z_{0 })}\]  
In this case, with the duration of the mission \(T_{m}>T_{3}\) from a cost-effective point of view, it is advantageous to use a fully autonomous LSS, which ensures the production of all LSRs on board. The range between \(T_{1}\) and \(T_{3}\) represents the domain wherein the Mixed LSS architecture becomes the most effective option. MLSS combines aspects of both OLSS and CLSS, offering a balance between cost-effectiveness and self-sufficiency. Within this range, the mission duration allows for a mix of external resource delivery and onboard resource generation, striking a balance based on factors such as cost, logistical feasibility, and desired level of autonomy. Of real practical interest is the determination of the boundary value of \(T_{3}\), because at present, as it was shown in the first sections of this article, various LSS configurations are actively used in practice, and it is interesting to compare them with architectures that provide fully autonomous generation of LSRs directly on autonomous transport systems. The focus of this paper is on developing a conceptual cost model for life support systems in autonomous space systems at an early design stage. The goal is to propose a methodology that allows for a high-level understanding of the trade-offs between different life support system architectures, taking into account a range of factors such as mission duration and system autonomy. However, it is important to note the inherent complexity and uncertainty involved in these models, especially at the early design stages:  
* Simulating the effectiveness of the proposed model requires access to detailed data and parameters, many of which are not publicly available due to the sensitive nature of space exploration activities. Also, it is worth noting that the effectiveness of differentlife support systems will heavily depend on specific mission parameters, technological advancements, and even unpredictable factors like crew behavior, which can be challenging to simulate accurately.