# A Lookahead Behavior Model for Multi-Agent Hybrid Simulation
## 5 Case and Experiments
### Experiment Results  
The experiments compare the efficiencies of FS, VS, CR, and LBM-PR. We execute the experiments 100 times with the simulation time of 10,000 s, and count the average numbers of updates, movements, and sensations in the four simulations. The minimum time interval for a time-stepped method (e.g., FS, VS) is limited to 1. The experimental results are shown in Figures 8-10.  
Figures 8-10 show the changes of the average number of updates, movements, and sensations with agent numbers when different time mechanisms are used. \"FS \(\times\) 1\" in the figures represents the FS simulation with a fixed time step of 1. \"FS \(\times\) 2\" represents the FS simulation with a fixed time step of 2. \"Resyn\" represents the asynchronous simulation including the \"CR\" and \"LBM-PR\" methods. Since the average number of movements and the sensation of complete resynchronization and partial resynchronization simulations are the same, the \"Resyn\" curve is used for both of them in Figures 9 and 10.  
Figure 8: The change of average numbers of updates with agent number.  
Figure 7: The process of the moving action when the MovingAgent is attacked.  
The experimental results show that the overall performance of LBM-PR is higher than those of state update mechanisms on the selected samples. Ideally, the number of lookahead occurrences is the same as the number of movements, so that the indicator for movements can reflect that for lookaheads.  
It can be seen from the results that:  
(1) The counted numbers for the FS are not changed with the increasing number of agents, because every agent updates, senses, and moves at every time step, although there might be more interactions when the total number of agents grows larger.  
(2) CR and LBM-PR simulations are superior to the synchronous simulations in efficiency and accuracy for updating the state. Agents in CR and LBM-PR simulations can accurately take their behaviors of \"sense\" and \"move\" when, and only when, required. The number of updates is strictly constrained by the time step in the synchronous simulation. The VS method can capture many more interactions than \"FS \(\times\) 2\", as some interactions may happen between the time step of the \"FS \(\times\) 2\" method. When some interactions occur between the minimum time intervals, even the VR method will miss them. That is why the average number of updates for CR exceeds the numbers for VR and \"FS \(\times\) 1\".  
Figure 10: The change of average numbers of sensations with agent number.  
Figure 9: The change of average numbers of movements with agent number.  
(3) LBM-PR simulation is superior to CR in the average numbers of updates. At every resynchronization time, all agents update their states in CR, while only some involved agents are required to update in LBM-PR.  
(4) The average numbers of movements and sensations for LBM-PR and CR are the same for the same quantities of agents, as the resynchronization only affects the update of the agent but not the motion or sense behavior being performing.  
(5) When the number of agents increases from 10 to 100, the average numbers of sensations for VS, CR, and LBM-PR increase obviously. This is because when the size of virtual space stays the same, there are more agents, and thus more interactions between agents. When the number of agents reaches 100, it can be seen from the VR that detection events happen almost at each step on average. At this point, simulations with a fixed step greater than 1 may lose some interactions that occur between two steps.