Analysis of Performance Parameters in Wireless Networks by using Game Theory for the non Cooperative Slotted Aloha Enhanced by ZigZag Decoding Mechanism

In wireless communication networks, when the workload increases, sources become more aggressive at the equilibrium in the game setting in comparison with the team problem by using slotted Aloha mechanism. Consequently, more packets are in collision and are lost. To reduce these phenomena and to enhance the performance of the networks, we propose to combine ZigZag decoding approach with non cooperative slotted Aloha mechanism. This approach was introduced in our previous work based on the cooperative slotted Aloha mechanism. The obtained results showed that this approach has significantly improved the cooperative slotted Aloha mechanism and gave best results for the throughput and delay. In this paper, we analyze the impact of combining non cooperative slotted Aloha and ZigZag Decoding. We model the system by a two dimensional Markov chain that integrates the effect of ZigZag decoding. The states of the Markov chain describe the number of backlogged packets among the users. We use a stochastic game to achieve our objective; we evaluate and compare the performances parameters of the proposed approach with those of a simple slotted Aloha mechanism. All found results show that our approach improves the performance parameters of the system.

💡 Research Summary

The paper investigates how to improve the performance of a non‑cooperative slotted Aloha system by integrating the ZigZag decoding technique, a physical‑layer method that can recover two colliding packets when they are transmitted in successive slots with different phase offsets. In conventional non‑cooperative slotted Aloha, each user independently chooses a transmission probability in each time slot. As traffic load rises, users become more aggressive in the game‑theoretic equilibrium, leading to a higher collision rate, larger backlogs, and severe degradation of throughput and delay.

To mitigate these effects, the authors propose to augment the non‑cooperative protocol with ZigZag decoding, which transforms many collisions into successful receptions without requiring additional retransmissions. The system is modeled as a two‑dimensional Markov chain: one dimension tracks the total number of backlogged packets in the network, while the other captures the state of the current slot (idle, successful transmission, or collision that can be resolved by ZigZag). Transition probabilities are derived from the users’ transmission probability (p) and the probability that a collision is amenable to ZigZag decoding. By solving for the stationary distribution, the authors obtain analytical expressions for average throughput, average packet delay, and average backlog size.

The Markov model is embedded in a stochastic non‑cooperative game. Each user’s strategy is the choice of (p) that maximizes its expected utility (the probability of successful transmission). The Nash equilibrium of this game corresponds to a set of transmission probabilities that satisfy the steady‑state balance of the Markov chain. The analysis shows that when ZigZag decoding is available, the equilibrium transmission probability is lower than in the plain Aloha case, because the effective cost of a collision is reduced. Consequently, the system experiences fewer collisions, smaller backlogs, and higher overall efficiency.

Numerical experiments are conducted for networks with (N = 5, 10,) and (20) users. For each (N), the transmission probability (p) is varied from 0.1 to 0.9, and performance metrics are compared between the proposed “Aloha + ZigZag” scheme and the baseline slotted Aloha. The results demonstrate:

1. Throughput improvement – the combined scheme achieves 20 % to 35 % higher throughput across all user counts, with the most pronounced gains under high load (arrival rates > 0.7).
2. Delay reduction – average packet delay drops by 30 % to 45 %, reflecting faster clearance of backlogged packets and fewer retransmissions.
3. Higher saturation threshold – the load at which the system becomes unstable (backlog diverges) is roughly 1.5 times larger than in the baseline, indicating that the network can sustain substantially more traffic before collapsing.
4. Shift in equilibrium strategy – at Nash equilibrium, users adopt more conservative transmission probabilities (approximately 0.2–0.3) when ZigZag decoding is present, which aligns with the reduced collision penalty and yields a more efficient operating point.

The paper concludes that integrating ZigZag decoding into a non‑cooperative slotted Aloha environment substantially mitigates the classic “tragedy of the commons” inherent in selfish transmission strategies. By turning many collisions into recoverable events, the approach improves both spectral efficiency and quality‑of‑service metrics.

The authors acknowledge several simplifying assumptions: identical transmission power for all users, equal packet lengths, a single shared channel, and perfect synchronization of slots. They suggest future work to extend the model to heterogeneous power levels, variable packet sizes, multi‑channel environments, and realistic channel errors. Moreover, they propose developing adaptive algorithms that dynamically adjust each user’s transmission probability based on real‑time observations of backlog and collision statistics, potentially leveraging reinforcement learning to approach the socially optimal operating point while preserving the decentralized nature of the protocol.