On variants of state-dependent queueing systems for egress modelling

An M/G/c/c state dependent network is a quantitative model for replicating and analyzing the behavior of occupants travelling through a network. The model, however, assumes that its inter-arrival times are independent and exponentially distributed, which inadequately reflects the dynamic and high-stakes nature in emergency situations. This paper simulates the M/G/c/c model for emergency evacuations using Erlang-k distributions—representing the real-world arrival patterns of evacuees in a more controlled and less random arrivals—and correlated inter-arrival times—common during evacuations as occupants moving in clusters due to panic or structural flow patterns. To achieve this, an M/G/c/c simulation model was first developed using Arena simulation software. The model was used to analyze the impact of various arrival rates on system performance metrics. Consequently, the performance metrics were compared with those obtained by replacing exponential inter-arrival times with Erlang-k distributions and independent arrivals with correlated cluster arrivals. The results show that Erlang-k distributions lead to better performance and smoother flow since the arrival is more controlled, while correlated arrivals increase congestion.