## 4 Proposed Scheme
### Discussions  
Recently distributed scheduling algorithms for wireless networks with contention based medium access has gained much interest. A series of work [14; 15; 16; 17; 18; 19; 20; 21] has been proposed on assigning channel access priorities to nodes based on the individual loads, e.g., queue lengths. Note however, these studies have been carried out under different context: the emphasis has been on achieving a fraction of the _capacity region_ of the network using only local information, e.g., queue lengths of contending neighbors. The capacity region is defined to be the union of the set of all input rates which can be supported by the network, _i.e._, input loads under which the system can be stabilized.  
Among these studies, [17] and [16] use timers with exponentially distributed timeouts as a means to assign priorities in channel access. If a node has data to transmit, it first sets a timer whose timeout is exponentially distributed independently of other nodes. The node waits until the timer expires, and begins transmission unless the channel is sensed to be busy. The rates of such exponential distribution are set according to certain function of the backlog of the nodes. Thus multiple neighboring nodes independently compete with exponentially distributed timers, and the one whose timer expires first wins the channel. Thus by controlling the rate of timer expiry, the priorities of channel access are implicitly assigned to nodes based on their individual loads.  
A similar idea has been used for policy \(V\)[18] and Q-SCHED algorithm [20]. They also consider a two-phase contention model in which a node picks a minislot to transmit during contention phase. Nodes wait for a random number of minislots before transmission. The distribution of waiting time is a truncated version of geometric distribution which can be regarded as a discrete analogue of (truncated) exponential distribution. However in these schemes there is nonzero probability that a node does not attempt transmission [18; 20]. In such schemes, since the nodes do not always participate in channel contention, the probability of collision will be relatively low. However one should be more aggressive in attempting transmissions in our problem, particularly for nodes with high scores. The reason is that, in the proposed scheme, selective forwarding and overhearing are used in addition to priority based channel access. This in turn increases the probability that high score nodes will be scheduled in the subsequent frames, _i.e._, the effect is disseminated throughout the network. Once a transmission of high score packet is successful, it can suppress unnecessary traffic generated from the neighboring nodes. Also the system parameters \(\gamma\) and \(\beta\) should be set in an aggressive way. Indeed we have heuristically found that setting \(\gamma=3\) and \(\beta=1\) leads to better performance. Note when \(\gamma>1\) and as \(\beta\) gets smaller, the sensors are more aggressive in transmission attempts. In summary, the synergistic effect among the components of the proposed scheme enables us to be more aggressive towards minimizing the latency.  
Furthermore these works focus on achieving a long-term throughput that is sustainable by the network. However our problem pertains to retrieving information in a short period of time. The traffic is bursty in time and space, thus the regime of interest is quite different from such setup. Indeed we will demonstrate using simulation that those scheme may not be effective in reducing the latency of retrieving extreme statistics.