After failures, a transmitter increases its random retry window by a multiplicative factor, so its access behavior depends on its collision history. This reduces immediate repeated contention, but its stability and delay properties depend on the exact rule and traffic model.
A packet with previous collisions attempts independently in each slot with probability . On failure it advances to stage , and on success it leaves. The Markov chain state records the number of packets at every stage, rather than only the total backlog. This memoryless-window model is related to binary exponential backoff, but its geometric waiting times differ from uniform counters in finite retry windows.
// Target: probability-and-statistics.bigb
For geometric-attempt exponential backoff, assume each attempted transmission fails independently with a fixed probability . The probability of reaching stage is , and its mean waiting time is . The Tonelli theorem gives , finite exactly when . The packet succeeds almost surely for every , so almost-sure success does not guarantee finite mean delay. A fixed independent failure probability is a simplifying assumption, not a theorem about collisions in an interacting network.
// Target: probability-and-statistics.bigb
After collisions a packet chooses an independent counter uniformly from and retries when it expires. The window doubles after a further collision. This is an example of exponential backoff with a nonconstant retry rule, contrasting with constant-probability slotted ALOHA.
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Exponential backoff is a strategy used in network protocols and other systems to manage retries after a failure, particularly in situations where a resource is temporarily unavailable. The basic idea is to wait progressively longer intervals between successive attempts to perform an operation (such as sending a network request) after each failure, up to a predefined maximum time or retry limit.