Gapnot Protocol -

(normalized): [ S = N \cdot p \cdot (1-p)^N-1 \cdot e^-\lambda G ] Where λ is the arrival rate and G is the gap factor. The term e^-\lambda G models the reduction in collisions due to enforced gaps.

def send_frame(self, frame): backoff = random.uniform(self.w_min, self.w_max) * (1 + self.rho_est) wait(backoff) if self.can_transmit(current_time(), frame.duration): transmit(frame) self.last_tx_time = current_time() else: self.rho_est = min(0.9, self.rho_est + 0.05) self.send_frame(frame) # retry Scenario: 30 nodes, Poisson traffic (total offered load 0.7), 1 Mbps channel, 500-byte frames. gapnot protocol

Simulation shows GAPNOT achieves with N=20 and G=2.0, compared to 18% for pure ALOHA and 36% for slotted ALOHA without synchronization overhead. 7. Advantages and Trade-offs | Aspect | Advantage | Trade-off | |--------|-----------|------------| | Synchronization | None required | Slightly lower peak utilization than TDMA | | Power | Can sleep between probabilistic checks | May need occasional wake-up to update ρ_est | | Fairness | Enforced non-overlapping prevents starvation | Latency increases with G | | Hidden terminals | Reduced due to randomness | Not eliminated entirely without RTS/CTS | | Scalability | Graceful degradation up to ~50 nodes | Beyond 100 nodes, ρ_est error grows | 8. Implementation Example (Pseudocode) class GAPNOTNode: def __init__(self, w_min=10, w_max=100, gap_factor=2.0): self.w_min = w_min self.w_max = w_max self.G = gap_factor self.rho_est = 0.2 self.last_tx_time = 0 def can_transmit(self, now, frame_duration): # Enforce non-overlapping gap if now - self.last_tx_time < frame_duration * self.G: return False # Probabilistic decision based on estimated load p_tx = 1.0 / (1 + self.rho_est * 5) # heuristic return random.random() < p_tx (normalized): [ S = N \cdot p \cdot

| Preamble (8 bytes) | Header (4 bytes) | Payload (variable) | FCS (2 bytes) | Post-gap (optional) | |--------------------|------------------|--------------------|---------------|---------------------| Simulation shows GAPNOT achieves with N=20 and G=2