*5.2. Planning for the Two-Resource-Two-Agent-Type*

We also evaluated SC-M\* in more complex environments: two agent types requesting two resources. This experiment considered both Wi-Fi and space capacity (i.e., *A* = {*A*<sup>1</sup> : "*WiFi*", *A*<sup>2</sup> : "*Space*"}). Type I agents use *f*<sup>1</sup> in Figure 2 as the collision CDF for the Wi-Fi resource, and the linear CDF *f*<sup>2</sup> for the space resource, implying that they treat Wi-Fi and space as important and trivial, respectively. On the other hand, Type II agents use *f*<sup>1</sup> for space and *f*<sup>2</sup> for Wi-Fi. Each agent has a 50% chance of being Type I. Both CDFs are adjusted using the same *δ* at each trial, as illustrated in Figure 2.

Figure 6a shows the success rate of the two-resource-two-type SC-M\* with different thresholds *T* = 0 (equivalent to the basic M\*), 0.2, 0.35, and 0.45, and with a fixed offset parameter *δ* = 9.0. Table 2 (left) shows the run time for the experiments. As can be seen from the results, in general, SC-M\* can handle the two-resource-two-type systems and plan for more than 80 agents. Because more resources contribute more factors to increasing the collision score, a relatively large offset (*δ* = 9.0) is needed to achieve comparable performance to the one-resource-one-type SC-M\*.

**Figure 6.** Impact of the collision threshold *T* (given *δ* = 9.0) and offset parameter *δ* (given *T* = 0.35) on two-resource-two-type SC-M\*.


**Table 2.** Run time of two-resource-two-type SC-M\* under different parameters.

Figure 6b and Table 2 (right) present the impact of the offset parameter *δ* on performance. Different from the first experiment, SC-M\* with the above configurations is less sensitive to *δ*, when compared to Figure 5. The reason is that 50% of the agents are insensitive to one of the resources because of the linear CDF *f*2, thus increasing *δ* does not contribute to a significant reduction in collisions. This property implies that we can control the importance levels of resources efficiently through the design of collision CDFs. This experiment demonstrates that, with the proper parameter settings, SC-M\* can feasibly handle a complex environment with multiple resources and multiple agent types.
