## 4 Simulation Setup  
We evaluate the proposed aggregate Throughput Optimal Flow Rate Allocation scheme (TOFRA) using network simulator NS-2, version 2.34 [25]. Concerning medium access control, a slotted aloha-based MAC layer is implemented. Transmission of data, routing protocol control, and ARP packets are performed at the beginning of each slot without performing carrier sensing before transmitting. Acknowledgements for data packets are sent immediately after successful packet reception, while failed packets are re-transmitted. The slot length, \(T_{slot}\), is expressed through: \(T_{slot}=T_{data}+T_{ACK}+2D_{prop}\), where \(T_{data}\) and \(T_{ACK}\) denote the transmission times for data packets and acknowledgements (ACKs), while \(D_{prop}\) denotes the propagation delay. It should be noted that all the packets have the same size. Packet size along with other simulation parameters are introduced in Table 2. All network nodes, apart from sources of traffic, select a random number of slots before transmitting, drawn uniformly from \([0,CW]\). The contention window (CW) is fixed for the whole duration of the simulation and is equal to 5. As far as the physical layer is concerned, the success probability for a link is estimated as follows: in the case where a flow allocation scheme variant is simulated assuming that receivers perform successive interference cancelation (SIC), then the probability that a packet transmitted along link \((j,i)\) is successfully received given that nodes in \(\mathcal{M}\) are also active, is estimated similarly with (9). If instead, interference is treated as noise, success probability for this case is derived by employing (5). Transmitters during each slot that are considered to cause interference are those transmitting data packets or routing protocol control packets. All nodes use the same SINR threshold. Transmission power and noise is 0.1 and \(7\times 10^{-11}\) Watts, respectively, while the path loss exponent is assumed equal to 3.0. As far as routing is concerned, static predefined routes to the destination are employed. Hello and Topology Control (TC) messages are propagated throughout the network every one and five seconds, respectively. Each topology control message may carry the following information: (a) transmission probability, (b) position, and (c) an indication of whether \begin{table}
\begin{tabular}{l l} \hline \hline
**Parameter** & **Value** \\ \hline Max Retransmit Threshold & 3 \\ Contention Window & 5 \\ Path Loss Exponent & 3.0 \\ Packet size & 1500 bytes \\ Simulation duration & 20,000 slots \\ Transmission power & 0.1 W \\ Noise power & \(7\times 10^{-11}\) W \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters used in the simulations. it is a flow originator or not. As also discussed in Section 2, transmission probabilities are assumed to be fixed for relay nodes, since contention window (CW) remains fixed for the whole simulation period. Using this information from the TC messages, each node can infer both the network topology and the success probability for each link based on either (5), or (9), since all link distances are known. Upon each TC message reception, each flow source can solve the topology-specific instance of the flow allocation optimization problem presented in Section 3, using the simulated annealing method. In this way, the flow rates (packets per slot) that should be assigned on each path to achieve maximum average aggregate throughput are estimated along with the average aggregate throughput for all flows. According to this process, flow rates are estimated in a distributed manner for all flow originators. In each simulation scenario flows carry constant bit rate UDP traffic, while the simulation period is 20,000 slots. Queues for flow originators are kept backlogged for the whole simulation period. It should also be noted, that the values for specific network parameters that are summarized in Table 2 are indicative.