The Elevator Group Supervisory Control Systems (EGSCS) are the control systems that systematically manage three or more elevators in order to efficiently transport the passengers in buildings. Double-deck elevators, where two cages are connected with each other, are expected to be the next generation elevator systems. Meanwhile, Destination Floor Guidance Systems (DFGS) are also expected in Double-Deck Elevator Systems (DDES). With these, the passengers could be served at two consecutive floors and could input their destinations at elevator halls instead of conventional systems without DFGS. Such systems become more complex than the traditional systems and require new control methods Genetic Network Programming (GNP), a graph-based evolutionary method, has been applied to EGSCS and its advantages are shown in some previous papers. GNP can obtain the strategy of a new hall call assignment to the optimal elevator because it performs crossover and mutation operations to judgment nodes and processing nodes. In studies so far, the passenger's arrival has been assumed to take Exponential distribution for many years. In this paper, we have applied Erlang distribution and Binomial distribution in order to study how the passenger's arrival distribution affects EGSCS. We have found that the passenger's arrival distribution has great influence on EGSCS. It has been also clarified that GNP makes good performances under different conditions.