## 5 Alleviation of Oscillations  
Path oscillations will occur when a sensitive metric [10] is used or the process of updating sensor readings, and the arrival of ACKs are asynchronous when the hazard spreads quickly. This phenomenon does not affect evacuees with portable devices, as they will receive a whole path, but it confuses civilians using visual indicators, because the guiding direction oscillates. In [41], several ways to mitigate oscillations in packet networks are discussed, such as using a path switch probability or a minimum QoS gain threshold to switch routes or ensuring the usage of a path by a minimum number of packets before a path switch can occur, though this last choice would not make sense if \"packets\" are human beings and the path switch is being caused by a deterioration of the safety of certain paths. In our system, we set a path switch probability to ease the direction oscillation on the visual indicators. Moreover, because CPN is a source routed algorithm, each evacuee with a portable device will obtain a route to exits when they begin to evacuate. However, some evacuees cannot stick to the original route as the path condition varies (hazard, congestion, _etc._). A simple method for the evacuees to use the up-to-date suggestion is to adopt the top ranked route at each hop. However, this may cause oscillations when successive decisions vary frequently. Hence, we use \"movement depth\" to ensure that evacuees only accept a new path choice suggestion after traversing a certain number of nodes. To prevent movement depth from hindering the flexibility of the evacuation routing and from directing civilians to hazards, the sequential decisions will be checked periodically to verify if the hazard has reached a particular node. Ifthe hazard has reached any hop or edge related to these decisions, they will be discarded immediately, and an alternate path will be used. However, this approach can also be very dangerous, since evacuees may get close to a hazard and then have no remaining time or possibility to change to a safe path. Thus, such approaches need to be evaluated in the context of varying degrees of risk, which include random rates of movement of the hazard (fire, smoke, gases, _etc._) itself. Ten randomized iterations have been conducted for movement depth from one to 10 in a scenario with a normal fire spreading rate and 120 evacuees. We use this scenario, because the effect of oscillation is more obvious in high density environments due to the larger variation of congestion. As QoS metrics can be divided into sensitive metrics and insensitive metrics [10], we employ the time metric and the distance metric as a representative of the sensitive metric and insensitive metric, respectively, to examine the influence of movement depth. Figure 1 shows that the performance of the time metric-based system reaches the peak mean value when the movement depth is three and then decreases gradually with the increase of the movement depth. This is because when movement depth is small (one or two), though it uses the up-to-date suggestion, some evacuees may be temporarily trapped by the puzzled suggestion. Meanwhile, CPN evaluates the QoS metric of a whole path other than a single edge. In other words, the evacuees should finish the whole path to satisfy their QoS needs if the condition does not change. If they continuously change paths, they will not follow the optimal path, but a collection of the first edge of optimal paths. If the movement depth is too large, evacuees will use the outdated decisions and, therefore, increase the possibility of guiding evacuees near the hazard and backtracking. Figure 2 presents the influence of movement depth in the distance metric-based system. Comparing with the time metric, the distance metric is less sensitive to the variation of movement depth and takes on a fluctuant state when the movement depth is smaller than or equals six. However, the system performance decreases evidently when the movement depth is larger than six.