Abstract
Non-Homogeneous Poisson Processes (NHPPs) are widely used to model event arrivals whose rates vary over time. A central challenge in NHPP modeling is accurately estimating the intensity function, which governs event occurrence dynamics. In applications such as airport passenger arrivals, intensity functions frequently exhibit non-constant and time-dependent behavior that requires flexible modeling tools. This thesis examines NHPP modeling and parameter estimations using a log-linear intensity function, applied to real passenger arrival data from Erbil International Airport (EIA) between January 2021 and September 2024.
The study employs four parameter estimation approaches: classical methods Maximum Likelihood Estimator (MLE) and Method of Moments (MoM) and intelligent optimization techniques Particle Swarm Optimization (PSO) and Firefly Algorithm (FFA). Model validation includes homogeneity testing, Q-Q plots, and k-fold cross-validation to assess model adequacy. Two simulation strategies are implemented to evaluate the behavior of estimators under controlled conditions. Estimator performance is compared using the Root Mean Square Error (RMSE).
Findings show that the log-linear NHPP model effectively captures the time-varying structure of passenger arrivals at EIA. Homogeneity tests conclude that arrival rates are non-constant, supporting the use of NHPP instead of HPP. Among the estimation approaches, PSO achieves superior performance, producing more accurate parameter estimates with lower RMSE and faster convergence compared to MLE, MoM, and FFA. Simulation results further validate the robustness of PSO under varying data conditions.
The log-linear NHPP framework, combined with intelligent optimization methods, provides a reliable tool for modeling time-dependent arrival processes. PSO is identified as the most effective estimation method for the examined dataset. The proposed approach offers practical value for airport planning, scheduling, and resource management. Future work may incorporate advanced machine learning algorithms, including neural networks, to enhance estimation accuracy and predictive performance.
