# Identification of Bottlenecks in Passenger Handling Processes Using Data-Driven Tools
## 3 Development and Excel-Based Implementation of the Simulation Model
### Simulation of Passenger Arrival at the Airport  
The structure of passenger arrivals at the airport is considered a critical factor in planning handling processes at airport terminals. This includes the number of service personnel, the number of check-in desks, the operational time of handling processes, queue lengths, and other parameters. The structure and pace of passenger arrivals are influenced by several factors, such as departure time, passenger type (business/leisure), and flight destination. Source [20] states that passengers with early morning flights tend to arrive later than the statistical average. Airport check-in rules also significantly affect passenger arrival patterns. Most airports with international operations observe some common passenger behavior patterns [26], as follows:  
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* Ninety percent of passengers arrive at the airport at least 60 min before departure;Business passengers tend to arrive later than leisure passengers;
* Peak system load occurs between 100 and 120 min before departure;
* Morning peaks are shorter but more intense than evening peaks [26]. Passenger arrival at the airport is a stochastic characteristic, meaning that it cannot be determined precisely but can only be estimated based on probability. Therefore, this process is best described using statistical distributions. Given the empirical findings, a normal distribution defined by a mean (average) value and standard deviation proves to be the most suitable choice for modeling passenger arrival times. Graphically, this distribution forms a bell-shaped curve, peaking around the mean, reflecting the tendency of most passengers to arrive around a typical time before departure, as well as natural variability, such as the earlier arrivals of leisure travelers or compressed peaks during morning departures. In this context, the mean value represents the average arrival time in minutes before departure. For example, leisure passengers tend to arrive earlier (often well in advance) due to baggage handling requirements and a desire for greater time buffers, whereas business passengers typically arrive closer to the scheduled departure time. The standard deviation reflects the variability in arrival times and captures individual behavioral differences. A lower standard deviation indicates more consistent behavior, as seen when only one passenger type dominates. In contrast, a higher standard deviation reflects more heterogeneous arrival behavior, typical of mixed passenger populations. Given the assumptions of queuing theory applied in this model, and considering the structural and computational capabilities of Microsoft Excel, the simulation is designed to generate passenger arrivals for a single flight only. This approach allows the model to maintain clarity, ensure the traceability of individual entities, and manage the complexity of interactions within Excel's formula-based framework. While it limits the scope of simulation in terms of multi-flight operations or shared resources, it remains fully adequate for observing dynamic behaviors, testing queue loads, and analyzing service performance under varying input parameters for a representative flight scenario. To generate passenger arrivals at the airport, it is necessary to define the number of passengers on the flight, the scheduled departure time, the average time of arrival before departure (mean), and the corresponding standard deviation. In Excel, the following function is used to generate passenger arrival times using a normal distribution:  
\[\text{t\_a}_{\text{n}}=\text{t\_d}-\text{NORM.INV(RAND(), \mu, \sigma)}, \tag{1}\]  
where:  
* t_a\({}_{\text{n}}\) is the generated arrival time of the n-th passenger;
* t_d is the scheduled departure time of the selected flight;
* \(\mu\) is mean arrival time before departure (in hours before scheduled departure);
* \(\sigma\) is the standard deviation (in hours), representing variability around the mean.