A new algorithm in throughput prediction of ALOHA protocol by using GM(1,1) model

In the grey theorem, the resultant sequence of AGO manipulation can be fitted into an exponential function because the sequence is considered as an equivalent to the solution of a grey differential equation. Therefore, we can obtain an approximate solution by using the grey prediction model whenever the closed solution of an equation is of exponential form. In communication system, ALOHA protocol is a simple and premier communication protocol. As everyone knows that the throughput of an ALOHA system is related to the provided packet traffic. In fact, the relationship between the system throughput and provided packet traffic can be depicted as an exponential function. Therefore, in this paper, we establish a prediction model of the throughput based on the grey prediction model. This is the first achievement. The second achievement is to accomplish a modified GM(1, 1) prediction model to cope with the monotonically decreasing data sequence. This new development opens a virgin soil, so this modified GM(1, 1) prediction model is considered as a milestone for new applications.