# An Adaptive Back-Off Mechanism for Wireless Sensor Networks
## 2 Review of Related Work
### Modified Back-Off Mechanisms  
Back-off mechanisms are at the core of carrier sense procedure. In the S-MAC protocol, after detecting the medium free for a distributed inter-frame spacing (DIFS) period, the node should then calculate a random back-off time for another deferral time and start a timer that gradually declines. If the medium is still free when the timer declines to 0, the node starts transmitting. Contrarily, if the node detects that the medium is becoming busy before the time is up, it cancels the timer and goes to sleep and then starts another carrier sense after waking up. The back-off time of S-MAC can be generated as shown in Equation (1):  
\[Backoff\_Time=Random(0,CW)\times SlotTime \tag{1}\]  
where \(Random(0,CW)\) is a function that draws a pseudorandom integer from a uniform distribution over the interval \([0,CW]\). \(CW\) is the contention window size, which is a constant in S-MAC. \(SlotTime\) is the basic delay unit set by the system. As mentioned above, the back-off mechanism of S-MAC adopts a fixed contention window size to calculate the back-off time in order to avoid the data collision. However, in real wireless sensor networks, traffic status is usually constantly changing. When the traffic load is light, a relatively big contention window may cause a large delay. On the other hand, when the traffic is heavy, a smaller one may lead to a serious data collision and a low delivery rate. In addition, when the medium is observed busy, after each back-off process, the same contention window size is adopted and the back-off time will be recalculated again. To sum up, S-MAC's back-off mechanism is insensitive to the traffic load's variation and relatively inefficient because of the repetitive calculation of back-off time, which adopts a fixed-size contention window. For the reasons given above, S-MAC cannot adapt to dynamic network traffic, especially a heavy one, and may lead to an insufferably low throughput and energy efficiency. Binary exponential back-off (BEB) mechanism is a classical contention window adjustment algorithm. The back-off timer is calculated using Equation (1). However, what is distinct from S-MAC is that the contention window (\(CW\)) size is unfixed and the window size can varywith whether the transmission is successful or not. Specifically, the initial \(CW\) is set to be a minimum value, which is denoted as \(CW_{\min}\), and it is doubled for the next transmission attempt every time the packet is involved in a collision until it reaches the max contention window size \(CW_{\max}\). Moreover, \(CW\) is reset to the initial value after every successful transmission. The BEB algorithm is given in Figure 2.  
Compared with S-MAC, though the BEB mechanism takes transmission status into consideration and adjusts the contention window size, it still cannot efficiently adapt to the variation of the traffic load. Especially in the heavy load network, the contention window's sudden decrease causes a capture effect that permits a node to seize the channel for a long time, which reduces the medium access' fairness and the overall network throughput [16]. In order to improve the fairness in the network, some adaptive back-off mechanisms based on BEB have been proposed [17; 18; 19; 20; 21]. In these papers, the contention window sizes of different nodes are balanced to prevent certain nodes from occupying wireless channel for too long on condition of an efficient medium access. In [17; 18], collision probability was chosen as a parameter to adjust the contention window size. The node with a higher collision probability was allocated with a larger window. In [19; 20], distributed and shadow-price-theory-based proportional fairness back-off schemes were designed to overcome the funneling effect in multi-hop WSN. The node with more data to be sent had a higher transmission priority. In [21], after a successful transmission, the back-off value was set between current \(CW\) and the minimum value, which was different from the BEB mechanism and improved fairness.