# 6G Goal-Oriented Communications: How to Coexist with Legacy Systems?
## 5 Numerical Evaluation
From Figure 10, it is then possible to appreciate the adaptation capabilities of the proposed method with respect to online requirement modifications. In particular, the method is able to autonomously detect this change through the virtual queue and take corresponding actions to stabilize the system towards desired performance. We have shown how the method behaves in the presence of requirement changes, but how does it react to a non-stationary environment? Moreover, what is the effect of computation resource availability (i.e., computing delay) in the proposed scenario under investigation? To answer these questions, we consider a system in which, after 10,000 iterations, due to an exogenous event, the computing time experiences an offset of \(+5\) ms, i.e., it is systematically increased by 5 ms. Similarly, after 30,000 iterations, it is systematically increased by an additional 2 ms (i.e., 7 ms with respect to the starting point). The E2E delay constraint is set to \(D_{\text{max}}=50\) ms. The results in terms of goal effectiveness and goal cost are shown in Figure 11a,b, respectively, with the same approach of Figure 10 (moving averages). From a goal-effectiveness perspective, we can notice how the method is able to attain the desired performance (\(\mathcal{E}_{g}=80\%\)), despite a transient period after the non-stationarity appears in the system, highlighted by the dashed ellipses in the plot. At the same time, adapting to the new system conditions (higher computing time) increases the cost, as a lower communication delay is required to guarantee the delay constraint (we always assume that the inference input/ image upload rate is such that no classification request buffering at the MEH occurs, even when the delay of GO communication is substantially reduced). Indeed, the only way is to reduce interference, i.e., the DO system data rate. Again, the method is able to autonomously detect this change through the virtual queue and take corresponding actions to stabilize the system towards desired performance. From Figure 11, we can conclude that _the computing resources available to a GO system have a strong impact on the cost of a DO system that coexists and interferes with the former_. This is a clear way of seeing the effect of connect-compute resource availability in goal-oriented communication systems for edge inference. From the numerical results shown in this section, we can draw the following general conclusions:  
* There exists a trade-off between goal effectiveness and goal value, with the latter being related to communication performance of a DO system coexisting with the GO system; our method is able to explore this trade-off, with close to optimal performance in different conditions, depending on the specific requirements (cf. Figure 8a). * Fixing the PER (i.e., adapting communication to maintain an a priori target PER) while adapting the DO user transmit power does not provide much better performance than a strategy with both variables fixed across time (cf. Figure 9). Higher gains are achieved via a fully adaptive system. * Our method is able to dramatically reduce the goal cost, while guaranteeing target goal effectiveness, by adaptively selecting target PER and DO user transmit power, based on measured application performance, even in the cases in which the fixed strategy fails to find a feasible solution (cf. Figure 8(c)). * Changing requirements over time (e.g., because of new application constraints) does not prevent our method from adaptively allocating resources to attain new levels of goal effectiveness and/or goal values (cf. Figure 10). Moreover, the method works in both directions: it increases the cost when a transition to stricter requirements occurs, while it reduces the cost whenever requirements are relaxed. The latter, thanks to properly defined state variables (i.e., virtual queues), is able to capture the behavior of the system in terms of constraint violations.