On the stability of exponential backoff

Abstract

Random access schemes for packet networks featuring distributed control require algorithms and protocols for resolving packet collisions that occur as the uncoordinated terminals contend for the channel. A widely used collision resolution protocol is the exponential backoff (EB). New analytical results for the stability of the (binary) EB are given. Previous studies on the stability of the (binary) EB have produced contradictory results instead of a consensus: some proved instability, others showed stability under certain conditions. In these studies, simplified and/or modified models of the backoff algorithm were used. In this paper, care is taken to use a model that reflects the actual behavior of backoff algorithms. We show that EB is stable under a throughput definition of stability; the throughput of the network converges to a non-zero constant as the offered load N goes to infinity. We also obtain the analytical expressions for the saturation throughput for a given number of nodes, N. The analysis considers the general case of EB with backoff factor r, where BEB is the special case with r = 2. We show that r = 1/(1 − e−1) is the optimum backoff factor that maximizes the throughput. The accuracy of the analysis is checked against simulation results.

Multi-round contention in wireless LANs with multipacket reception

“…Most of what we know about WLAN is based on the conventional collision model, where packet collisions occur when two or more stations transmit at the same time [1], [2]. With advanced PHY-layer signal processing techniques, it is possible for an access point (AP) to detect multiple concurrently transmitted packets through, for example, multiuser detection (MUD) techniques [3], [4].…”

“…A station transmits an RTS packet when its backoff timer reaches zero. Previous work in [1], [2], [5] has shown that the backoff process yields an equivalent transmission probability τ at which a station transmits in a generic (randomly chosen) time slot. When the number of stations, K, is large, it is reasonable to assume that the number of transmissions in a generic time slot follows a Poisson distribution with parameter λ = Kτ [5].…”

Upper Bound on Overall Delay in Wireless Broadband Networks with Non Real-Time Traffic

“…Infinitely-many user model is known to highlight the limiting performance metrics of the algorithm, whereas finitely-many user model provides insight to the practical applicability of the algorithm. Finally, the operation of the BEB algorithm in the saturation conditions, where every network user always has pending data packets, was investigated by means of Markov models in [5] and [6].…”

“…Furthermore as the embedded epoch happens at least by α time earlier as the end of the contention-based transmission opportunities the above delay part is upper bounded by α(K − 1) + (i − 1)τ . Taking this term into account in the scheduling packet delay, expressing the sum of the reservation and the scheduling packet delays by applying Little's formula and using (6) results in the upper bound on overall packet delay in the considered wireless broadband network as:…”

“…The BEB algorithm operation is thoroughly investigated in [22]. According to [5] and [6] the consideration of the entire system could be reduced to the consideration of the tagged SS only. For a contention-based transmission opportunity the conditional collision probability, conditioning on the fact that the SS attempts the transmission (p c ) is introduced as:…”