s Aloha performance with multiple transmit nodes

### Network setup#

We consider three scenarios as shown in the figure below, with 2, 3 and 4 transmitting nodes.

Figure 4 5: Simulation scenarios with 2 transmitting nodes in (A), 3 transmitting nodes in (B) and 4 transmitting nodes in (C). In all cases there is a single receiver.

### Properties#

Then we set the UWAN device properties as shown below

Device Properties
Device > Interface (ACOUSTIC) > Datalink Layer
Retry Limit 0,4,6
Slot Length(µs) 731256.4
Device> Interface (ACOUSTIC) > Physical Layer
Source Level (dB//1μPa) 190.8
Modulation QPSK
Data Rate (kbps) 20

Table 4 8: UWAN Device Properties

• Here, we set the Slot Time as 741256.4 $\mu s$, which is the ideal value of 731256.4 $\mu s$ plus a guard interval of 10,000 $\mu s$
• Create a CBR Application from the source nodes (2, 3, 4 and 5 per the cases) to the destination (Node 1) with a packet size of 14 bytes and Inter arrival time as 560000$\mu s$.
• Run the Simulation for 10000sec.

### Results#

We observe throughputs from network metrics and packets transmitted and packets collided from the Link Metrics. We collision probability as $P_{c} = \frac{Collision\ Count}{Packet\ Transmitted}$ and tabulate the results in the different cases.

Case #1: Two transmitting nodes

Retry Limit Throughput N1 (bps) Throughput N2 (bps) Aggregate Throughput(bps) Collision Count Packet Transmitted $P_c$
0 0 0 0 26980 26980 1
4 55 51 106 7104 16624 0.427
6 71 65 136 2548 14647 0.173

Table 4 9: Simulation Results with 2 transmitting nodes

Case #2: Three transmitting nodes

Retry Limit Throughput N1 (bps) Throughput N2 (bps) Throughput N3 (bps) Aggregate Throughput (bps) Collision Count Packet Transmitted $P_c$
0 0 0 0 0 40470 40470 1
4 26 26 27 79 12234 19348 0.632
6 43 41 37 121 4969 15726 0.316

Table 4 10: Simulation Results with 3 transmitting nodes

Case #3: Four transmitting nodes

Retry Limit Throughput N1 (bps) Throughput N2 (bps) Throughput N3 (bps) Throughput N4 (bps) Aggregate Throughput (bps) Collision Count Packet Transmitted $P_c$
0 0 0 0 0 0 53998 53998 1
4 0 0 0 25 25 23361 25560 0.914
6 0 0 0 83 83 9966 17391 0.573

Table 4 11: Simulation Results with 4 transmitting nodes

We carry out simulations with different settings of Retry Count. The final results are plotted below. When Retry count is set to zero, all packets collide even when just two nodes are transmitting.

With retry count set to 0, the node attempts a packet transmission. If it fails, there is no retry and the packet is dropped. Recall, that in s-Aloha the transmitter does not back off before the first transmission attempt for a packet. With backlogged queues, the two transmitting nodes keep attempting at each slot. This leads to continuous collisions.

When the retry count is set to 4 (or 6) a transmitting node back off per the exponential backoff algorithm, before every retransmission. The back off algorithm is explained in section 3.2.1. Hence there is an element of randomness in packet transmissions at each slot. Nodes may or may not transmit. The probability of transmission at a particular slot reduces as the Retry Count is increased. Hence, we see lower collision probabilities for Retry count of 6.

Advanced: s-Aloha works as expected only if the slot time is greater than transmission time plus the propagation delay. What happens when slot length is lower than this limit? Under this condition a new slot is available for transmission even before completion of an existing packet transmission. Thus, if an idle node completes its back off before the transmission (where transmission time equals $T_{tx} + \Delta)$ of one another node is complete, it will attempt to transmit at the start of a new slot. The two packets collide and are lost. One would therefore expect higher collision probabilities with smaller slot lengths. NetSim simulation results for 2-node transmitting case with slot time, 250$\ \mu s$ is given below

Retry Limit Throughput N1 (bps) Throughput N2(bps) Aggregate Throughput (bps) Collision Count Packet Transmitted $P_c$ $P_c$ (Ideal slot time)
0 0 0 0 26666 26666 1 1
4 20 20 40 14102 17696 0.797 0.427
6 45 46 91 6987 15109 0.462 0.153

Observe the significant increase in collision probability when the slot time is set lower than the ideal slot time. Next, we fix the retry count at 6 and vary the slot time from 50 ms to 750 ms in steps of 50 ms. In the plot below showing collision probability vs. slot time, we again observe how low slot times lead to higher collision probabilities.