This paper analyzed the berth ship-handling system of a congested container terminal using queueing theory and simulation in a complementary manner. In particular, using actual performance data from 1989, it was demonstrated that BCTOC is a heterogeneous multiserver system with an exponential distribution for ship inter-arrival times and different Erlang distributions for service times. Specifically, Berth 52 was found to have an Erlang-6 distribution, while Berths 53, 61, and 62 had Erlang-5 distributions. A queueing model was constructed through the estimation of these distributions, but because it was a complex model with large shape parameters (M/E^(χ)_κ/4), analytical analysis was difficult, so the necessary performance measures were obtained through simulation. According to the simulation results, the average waiting time was 9.83 hours, the average berthing time was 17.13 hours, berth occupancy was 84.125%, and the number of arriving vessels was 1,720, which were similar to the values derived from actual data. The only difference was approximately 1.2 hours in waiting time, which was analyzed as being attributable to shipping companies adjusting their schedules themselves due to congestion at BCTOC. Meanwhile, in 1989, only 36.9% of all vessels began receiving service within one hour of arrival, and 12.9% of vessels waited for more than 24 hours, indicating that the overall service level of the system was very poor, necessitating urgent facility expansion.