## 3 The Bike-Share Case
### Evaluation--Formulation of Simulation and ML Models
#### 3.4.3 Stocks and Flows Modelling  
A common way to summarise systems thinking is by stating that a system's behaviour stems from its structure. When we unpack \"structure\", it consists of stocks, flows and feedback. However, in our causal mapping of problematic behaviour in the bike-share case and potential interventions, we did not explicitly distinguish between stocks and flows; instead, we focused on the interconnected feedback loops to offer plausible explanations. While identifying key variables and their relationships suffices to hypothesise behaviour patterns, precise quantification for simulation requires clearly distinguishing between stocks and flows. Figure 7: Causal impact analysis showing the effect of incentives on rental demand for one test day, illustrating key results. The stocks and flows schematic in Figure 8 illustrates the kind of causal map elaboration needed to advance in the simulation process. It highlights the decision-making role of feedback structures and emphasises the importance of stock and flow variables. The feedback or decision structures process cues from stock variables across different system sectors to make decisions that alter flow rates, which, in turn, feed back into the stocks. For example, the inflow rate (I1) into stock S1 depends on S1 and stock S4. Endogenous variables (V[1; 2; 3]), exogenous variables (U1), constants (C1) and time constants (T[1; 2; 3]) simplify the specification and maintenance of algebraic equations in simulation tools like Vensim. Essentially, net inflows are functions of stocks (with constants acting as slow-changing stocks) and exogenous variables; the intermediaries help break complex formulations into manageable parts. This formulation provides the precision to quantify the interrelationships and determine the differential equations for net inflows. Once defined, the system's behaviour over time is simulated by numerically integrating these equations to evolve the stocks. In the bike-share model, focusing on a single station, the bike stock represents the physical inventory that generates information cues for decision-making, influencing future flows. This stock reflects the real-world availability of bikes. A parallel structure also projects the future stock based on machine learning-predicted return and rental flows. The inventory management policy synthesises these two streams to assess outage risks, accounting for reporting and information delays. A set of rules translates this perception into decisions to incentivise returns or rentals. A further algorithmic component that plays a crucial role in the feedback is the expected impact of incentives. During scenario simulations where various plausible rental and return flows operate on the real-world stock (our focus in the last two steps of the evaluation phase), the quality of predictions about incentive effectiveness influences our assessment of the effectiveness of policy variables. For example, if the accuracy of the causal impact of crowdsourcing inventory balancing through incentives is poor, the simulated real-world stocks will deviate from reality, skewing our assessment. If we remove the single-station constraint, additional complexity arises from coordinating incentive actions by leveraging the complementarity between stations or clusters. Specifically, the inventory status of a partner station or cluster with asymmetric demands informs whether to apply incentives. The future-state inventory policy also incorporates a target range for bike availability or station utilisation. The distance between current perceived availability and the upper or lower threshold determines perceived risk, guiding stock levels within these limits. We now review the two main components (in the corresponding stocks and flows formulation), synthesising information cues about the current and anticipated system states. For clarity, in Figure 9, we focus on the returns flow, noting that the dynamics are similar for rental flows.