# Determining the Optimal Configuration of the Multi-Ring Tree for Bluetooth Multi-Hop Networks
## 4 Network Performance
### Network Performance  
The simulation parameters for network performance are defined as follows. For the packet transmission of each node, each packet is generated in accordance with a Poisson arrival pattern. In addition, it was assumed that a single packet is sent in each routing session, and that each data packet has a duration of five time slots. A FIFO (First Input First Output) queue is provided with a length of 80 packets for each node. In each routing session, the source-destination pair was randomly selected, the time division multiplexing (TDD) scheme was adopted for both piconet and scatternet scheduling, and the packets were forwarded using the multi-ring tree topology with the self-routing protocol. For the core network topology, the multi-ring was simulated by \(N=24\) roots with 76 nodes  
Figure 8: Average hop length of min-path algorithm for various \(N\). Figure 7: Computation overhead of min-path algorithm for various \(N\). in the tree subnet. In addition, six combinations for a 24-root example were evaluated, including the single-ring case as the BlueHRT [15] with 24 nodes in a ring, a 2-ring case as the dual-ring tree (DRT) with 12 nodes in a ring [24], a 3-ring case with 8 nodes in a ring, a 4-ring case with 6 nodes in a ring, a 6-ring case with 4 nodes in a ring, and an 8-ring case with 3 nodes in a ring, which were simulated. In order to investigate the scatternet routing performance, three scatternet protocols--BlueHRT, DRT, and optimal multi-ring tree (Optimal MRT)--were compared. The BlueHRT and DRT protocols were chosen for comparison with the Optimal MRT because they both execute architectures similar to the multi-ring tree. To estimate the impact of network congestion in a scatternet, a packet drop probability (PDP) metric was used. When the FIFO buffer overflows in each node, the damaged routing packets--including both the currently received and newly generated routing packets--are dropped. The PDP is defined as the ratio of the total number of dropped packets over the total number of generated packets for all nodes. Figure 9 shows the PDP of the six schemes, where the 4-ring case as the Optimal MRT achieved the lowest PDP compared to both BlueHRT and DRT cases. In addition, all the multi-ring tree simulation cases achieved better PDP performances than the traditional single-ring case in terms of BlueHRT. From the simulation results, it is clear that the roots and all other masters began to drop packets when the FIFO buffers overflowed. To reflect the scatternet capacity of the multi-ring tree, a packet throughput was used to evaluate network performance. The average packet throughput is defined as the ratio of the total number of successful routing packets over the total simulation time in seconds. The simulation results of the packet throughput for the 24-root of the multi-ring tree are shown in Figure 10. According to the simulation results, the 4-ring case as the Optimal MRT achieved the best throughput performance compared to the other five schemes, since the min-path algorithm can determine the optimal configuration with the minimum average path length for the multi-ring subnet. In addition, the routing packet throughput increased continuously as the packet generation rate increased, because the self-routing protocol combined with the multi-ring core network greatly improved the network routing performance compared to the BlueHRT and DRT cases. When the PDP starts as packet generation rate increases in Figure 9, the packet throughput almost reaches constant performance in Figure 10 and the network begins to be congested. As a result, the constant packet throughput can be regarded as the upper bound of network capacity for the multi-ring tree. Figure 9: Packet drop probability of the Optimal MRT, DRT, and BlueHRT. In order to evaluate the multi-hop routing performance, an average packet delay metric was adopted to measure the end-to-end delay of a scatternet.