## 2 Related Work
### Congestion Management  
Current congestion-aware algorithms in emergency evacuation can be divided into congestion-free algorithms and congestion-ease algorithms. Congestion-free algorithms, such as [19], take node and edge capacity into account and assign a time and routes schedule to evacuees with regard to capacity constraints. This approach can efficiently avoid congestion, but it is not very realistic, because some civilians may have to wait for a certain time before evacuating. Congestion-ease algorithms employ mathematical models to estimate the time delay on a path and to redirect evacuees accordingly. For example, [33] proposes a distributed navigation protocol based on the artificial potential field model to guide evacuees to exits with minimal congestion. Each sensor holds a potential, which is determined by flow velocity, distances to all exits and the weights of exit capacity. Exits are assigned with the maximal value, and paths are constructed from lower potential values to higher potential values. However, the spread of hazards is not considered, and therefore, evacuees can actually be directed to a hazardous area. An egress dynamic feedback control model is proposed in [34] to balance the crowd among exits.  
Actuators at each egress build a graph, which is classified as safe, alert and danger regions. If an egress evolves in a danger region, a control algorithm will be performed to reduce the number of evacuees that choose the related exit to regress the state to the safe/alert region. However, some parameters to delimitate the graph are difficult to know in reality, such as the maximum available time for a safe evacuation. Furthermore, this approach only considers the congestion around the exits, but does not take the jamming on the path into account. Reference [35] establishes a macroscopic probabilistic model to mimic the chaotic collective motion with respect to fire status, passage capacity, psychological factors and crowd flow rates. Simulations are performed on a traditional network-flow model, which incorporates the above crowd model, and fire propagation is imitated by a cellular automation model. The evacuation planning problem is then translated to a Markov decision problem, which aims to maximise the total number of evacuees and minimise the relevant risks. To solve this optimisation problem, a divide-and-conquer approach is used to divide evacuees into different groups, and multiple groups are coordinated within a Lagrangian relaxation framework. Queueing models can also be used to evaluate congestion in such systems [36, 37]. A M/M/1 queueing model [38] is employed in [1] to analyse the time needed to exit with respect to congestion. Compared with closed queueing network models, this open model-based approach is more computationally efficient and can avoid long time simulations. The \"time to exit\" is over-estimated due to the assumption of the highest arrival rate and deterministic service times. However, this analytical model is useful in emergency procedure design and densely-populated evacuations.  
In summary, regarding the aforementioned literature, most experiments in the previous work employ simulated evacuees with identical physical attributes. Hence, the analysis based on those experiments may not reflect the real situation, where evacuees actually have different velocities and health conditions. Furthermore, previous emergency navigation algorithms provide routes with the same property (shortest, safest or quickest) to civilians and ignore their specific service requirements. Therefore, evacuees tend to congregate in the main channels and cause a stampede or congestion, due to the limited space and diverse mobility. Moreover, injuries and fatalities are likely to be increased owing to the dissatisfaction of the unique service needs of evacuees. In addition, although jamming has a significant impact on the performance of emergency navigation algorithms, the previous congestion management algorithms or models are either not very realistic or too computational complex.