5.3.3 Calculation of Transaction Number

To model transactions within the provided context, we adopt the following structured approach (Pan et al. 2022):

• Monthly Active Users (MAU): This metric embodies the number of users actively engaging with the platform during a specific month. Recognizing that not every user of a platform remains active consistently, we establish a proportion that represents the fraction of the total users (Users) active monthly. The model for this is expressed as:

$$MAU(t) = k_{mau} * Users(t) \ \ \ \ \ \ \ \tag{13}$$

Where:

o denotes the active users during month .

o symbolizes the proportion of active users relative to total users, drawn as a random value within the range

o signifies the aggregate number of users in month t.

• Maximum Transaction (TXmax): This metric designates the utmost possible transactions that might transpire on the platform, considering both the active user count and the mean transaction volume for each active user . The model is:

$$TX_{max}(t) = MAU(t) * TX_{MAU}(t) \ \ \ \ \ \ \ \tag{14}$$

Where:

o defines the pinnacle of potential transactions in month t.

o stands for the average transaction volume for each active user. This is presumed constant across time.

o again, represents the active users during month t.

• Actual Transactions (TX): This quantifies the genuine transaction count transpiring on the platform within a distinct month. It incorporates the transaction profile (), serving as a multiplier that mirrors the adoption trajectory of the technology. The mathematical model for this is

$$T_{actual} (t)=T_{max} (t)×K_{TX} (t)\ \ \ \ \ \ \ \tag{19}$$

Where:

o is the realized transactions during month t.

o indicates the maximum conceivable transactions for month t.

o depicts the transaction profile for month t, as extracted from the preceding transaction profile curve calculations.

By following this methodology, one can accurately estimate transaction numbers based on active user metrics and transaction profiles

Figure 75. Transactions over time

Please note that the model introduced here offers a swift approximation of transactions within the network, drawing primarily from user count and the network's inherent product value. While this approach is particularly valuable for initial estimations, there are more intricate models [(Nsour and Sayama 2020), (Shi et al. 2021), (C. Wang et al. 2023)] available that yield detailed results. While these advanced models furnish nuanced insights, they necessitate more foundational assumptions and extended computations. As a result, for primary estimations, our presented model offers a balance, excelling in terms of user-friendliness and ease of application