## 3 Results  
### A Proof-of-Concept Implementation  
The design method of our route planner was verified in the virtual 3D environment, called Ella Software Platform (ESP) [30], to better understand the characteristics and the issues of the planner. The ESP provides the proper tools for the implementation, such as a discrete world, 3D graphics, a physics engine, an MAS module, etc. We performed experiments on a machine with the Intel Core i7 6700 HQ 2.60 GHz processors. ESP can only use one physical thread. The static size of the GSN was 8 \(\times\) 8, and thus there were 64 crossroads see Figure 11.  
Figure 11: The graph structure network (GSN): violet crossroads denote the use of an infinity intention pheromone (IIP); red virtual segments refer to traveling intention ants (IAs). Figure 10: An illustration of keys and values of the intention binary search tree (BST). We evaluated two approaches: (a) with reservations (WRA) and (b) without reservations (NRA). In the approach without reservations (NRA), there are no reservations; however, there are occupations; i.e., the presence of an MRSA at the crossroad. If the next-in-the-list crossroad is occupied, an MRSA stops at the current crossroad and it starts searching for a new route to the destination. However, we needed to implement a simple resolution for a temporal live-lock. The live-lock occurs when two MRSAs try to swap their positions at the neighboring nodes. If an MRSA detects a live-lock, it uses the third found route in its route list (the choice of the second route occasionally led to another live-lock). In this case, the EAs do not test for reservations. In order to increase the throughput of the GSN, they instead check the occupancy of the first crossroad after their deployment. If the crossroad is occupied, the ant reports an unsuccessful execution of the task. For each approach, we used from one to six MRSAs. Each MRSA had to visit ten different destinations (but the destinations were the same for both approaches). Both reserve times (starting and ending) of the reservation intervals were set to 0.3 s. The deployment period was set to 2.0 s. The default number of tickets was set to 10. At the time of writing, there were no measured time characteristics of the MRSs. Table 1 contains the arbitrary durations that were chosen for each itinerary action. The variable velocity of the MRSA was implemented as the function of time. Tables 2 and 3 contain the average and the longest (i.e., the worst) travel time of each D-MAS in the approach with reservations (WRA) and the NRA. The resulting time was influenced by the length of the route and the overall number of agents (1-6) and ants in the environment. The average number of the FAs located in the environment at the same time was 166.1, and the maximum number was 283 per deployment. The average number of FAs per deployment was 1050.1, and the maximum number of the FAs was 1901 per deployment. \begin{table}
\begin{tabular}{c c} \hline \hline
**Action** & **Time [s]** \\ \hline start and stop & 2.0 \\ start and continue & 1.5 \\ continue and continue & 1.0 \\ continue and stop & 1.5 \\ turn right & 1.0 \\ turn left & 1.0 \\ switch direction & 0.0 \\ emergency stop & 2.0 \\ start and stop & 1.5 \\ start and continue & 1.0 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Durations of the itinerary actions. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **FA [s]** & **EA [s]** & **IA [s]** \\ \hline Average time & 0.5553 & 0.2870 & 0.2109 \\ Highest time & 0.7823 & 0.5651 & 0.4998 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: The average and the longest travel times of the ants in the approach with reservations (WRA). \begin{table}
\begin{tabular}{c c c} \hline \hline  & **FA [s]** & **EA [s]** & **IA** \\ \hline Average time & 0.5534 & 0.2652 & N/A \\ Highest time & 0.6998 & 0.4668 & N/A \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The average and the longest traveling times of the ants in the approach without reservations (NRA).