## 4 QoS Metrics
\(K[X]\) is a function that takes the value zero if X is smaller than zero or X if X is larger than or equals zero, respectively. Term \(q_{0}^{i}\) is the current queue length of the node, \(\pi(i)\); \(\bar{\lambda}\) is the average arrival rate of the node, \(\pi(i)\); \(\bar{\mu}\) is the departure rate of the node, \(\pi(i)\); \(T_{\pi(i)}\) is the potential time cost to reach the node, \(\pi(i)\). Energy efficiency-oriented goals will search for the path with minimum energy consumption, because the depletion of power for specific evacuees, such as disabled people in electric-powered wheelchairs, can be fatal. The maximum theoretical range with regard to different models of wheelchairs is approximately 28.98 kilometres, with an average energy consumption of 2.27 ampere-hours [48]. However, due to the unpredictability of disasters and daily driving behaviours [49], electric-powered wheelchairs can hardly be full-charged when an evacuation starts and, therefore, increase the likelihood for a disabled civilian to get stranded. The congestion ease algorithm is embedded in the energy efficiency-oriented goal function, as the acceleration and deceleration process can cause significant energy consumption when a braking event occurs. This function can be applied to electric powered wheelchairs or robots with battery power limitation. \[G_{e}=c_{b}\cdot C_{total}+\sum_{i=1}^{n-1}c_{s}\cdot E^{e}(\pi(i),\pi(i+1))+ \sum_{i=2}^{n-1}c_{t}\cdot\theta(\pi(i-1),\pi(i),\pi(i+1)) \tag{2}\]  
If \(C_{total}\) is the total congestion calculated by Algorithm 1, then \(c_{b}\) is the energy consumption of a wheelchair when a braking event happens, and \(c_{s}\) is the energy consumption per centimetre when moving straight on an edge. \(E^{e}(\pi(i),\pi(i+1))\) is the effective length of the edge between node \(\pi(i)\) and node \(\pi(i+1)\). Term \(c_{t}\) is the energy consumption per degree when a turning event happens, and \(\theta(\pi(i-1),\pi(i),\pi(i+1))\) is the rotation angle between edge \(E(\pi(i-1),\pi(i))\) and \(E(\pi(i),\pi(i+1))\). The safety-oriented goal function discovers the safest path. It can be used for sick people or children, as they are more likely to faint due to the impact of poisonous smoke in a fire. To estimate the hazard intensity of a node, we assume the hazard spread rate is \(a\) (cm/s) and the hazard growth rate at a node is \(b\). \[G_{s}=\sum_{i=1}^{n-1}1[t_{evacuee}^{\pi(i+1)}+t_{current}<t_{hr}^{\pi(i+1)} ]\cdot b\cdot(t_{evacuee}^{\pi(i+1)}+t_{current}-t_{hr}^{\pi(i+1)})+E^{s}( \pi(i),\pi(i+1)) \tag{3}\]  
where \(1[X]\) is a function that takes a value of one or twp if X is false or true, respectively. The term, \(t_{evacuee}^{\pi(i+1)}\), is the time for an evacuee to reach node \(\pi(i+1)\), and \(t_{current}\) is the time elapsed since the hazard occurred. The term, \(t_{hr}^{\pi(i+1)}\), is the time for the hazard to reach node \(\pi(i+1)\); it can be estimated with the hazard spread rate, \(a\). \(E^{s}(\pi(i),\pi(i+1))\) is then the effective safety value between node \(\pi(i)\) and node \(\pi(i+1)\). We employ \(E^{s}(\pi(i),\pi(i+1))\) to ensure that the value of \(G_{s}\) is not nil if the hazard does not reach the path during a civilian's evacuation process. The details of this approach are shown in Algorithm 2.