# Analytical Model for Enhancing the Adoptability of Continuous Descent Approach at Airports
## 6 Numerical Results to Illustrate the Model
Using Equation (18) to determine \(T_{des}\), we determined the service rate, \(\mu_{CDA}\) and \(\mu_{SDA}\), under the CDA and SDA conditions in the following manner, using a calculation similar to Equation (19), described earlier:  
\[\mu_{CDA}=k_{CDA}/Tdes_{CDA} \tag{25}\]  
\[\mu_{SDA}=k_{SDA}/Tdes_{SDA} \tag{26}\]  
Because CDA requires greater minimum separation distances between aircrafts than SDA, this reduces the rate at which CDA arrivals can be processed through the stacking space and, thus, results in \(\mu_{CDA}\) being lower than \(\mu_{SDA}\). Figure 7: The number of aircrafts arriving in each time period at BNA airport. Using the above parameters and Equation (22), we calculated the values of the probabilities of blocking, \(P_{kCDA}\) and \(P_{kSDA}\), for CDA and SDA, respectively, and show the results in Figure 9.  
Observe in Figure 9 that the probability of CDA blocking (i.e., CDA requests being denied), \(P_{kCDA}\), is consistently less than the probability of an SDA request requiring the aircraft to enter the holding pattern, \(P_{kSDA}\). By looking at graphs such as Figure 9, the air traffic controller can see those periods of time when the vast majority of aircrafts will be able to use CDA, i.e., when the probability of CDA blocking, \(P_{kCDA}\), is sufficiently low. For example, except for the late afternoon periods between 15:00 to 15:15 and from 15:30 to 16:45, there is less than one percent probability of CDA blocking. Aside from those late afternoon exceptions, the other time periods would be favorable for permitting CDA arrivals for all (or nearly all) arriving aircrafts. Even during the late afternoon time  
Figure 8: Capacity of the TMA’s stacking space \(k\). Figure 9: Probability of blocking of the two descent methods. periods, the probability of CDA blocking is low enough that the air traffic controller may be able to permit many of the aircrafts to land using CDA. Different air traffic controllers will have different probabilities at which they will be comfortable with using CDA. Their thresholds in such decision-making may change over time as they gain experience using the model. Overall, the information should be helpful to the air traffic controllers by focusing their attention on those opportunities to increase the use of CDA and thus lead to more sustainable air transportation operations. After deciding on the periods of time when CDA may be used for all (or nearly all) arriving aircrafts, knowing the bounds on the number of aircrafts that may fit safely in the stacking space, \(k_{CDA}\) and \(k_{SDA}\), as shown in Figure 8, may help the air traffic controller to decide on an aircraft-by-aircraft basis whether to admit a particular aircraft's descent using CDA. For instance, if an aircraft arrives during a period of time when the controller plans on permitting CDA and when the actual number of aircrafts within the stacking space upon a particular aircraft's arrival at the TMA is less than \(k_{CDA}\), then the controller knows it is likely fine to accept that particular aircraft's request to use CDA, and otherwise, it is not.