As TCP is the most widely used reliable protocol in today's network, there exist numerous studies on performance modeling and analysis of this protocol, especially on the congestion behavior over wide-area networks, e.g. the Internet [122,74,84,63,56]. Although we are not adopting TCP as our lightweight reliable layer, their works provide valuable insight on building up our work. In particular, the work in [74] analyzes and models the Fast Retransmit and the Timeout features of the TCP protocol, which happens that our reliable protocol also supports similar features. However, they assume that packet losses are correlated, and if a packet is lost, all subsequent packets from the same congestion window are lost too. This loss assumption simplifies the modeling task, but cannot reflect the real situation under the drop-tail discipline.
Due to the uniqueness of our GBN reliable transmission protocol, a 3-state Markov chain model is used for the loss behavior analysis. This 3-state model can be viewed as an extension of the Gilbert's 2-state error model, which is commonly used for modeling of channel error [61,60] or packet loss [2,74] on the communication network. By delineating the loss process as the likelihood in staying or transiting between states, this provides a method to reflect the temporal correlation between packet loss events. The difference between the 2-state model and our model is that the Gilbert's model characterize the error state directly, while our model characterize the error state indirectly, i.e. each state in our model only represents the occurrence of an event and it is the transition between states that delineates the loss process. Besides, our error structure is built on the interactions between the underlying buffer architecture and the reliable transmission protocol, this gives us a solid ground to reason on our results.
Moreover, there are other approaches to characterize the error or loss dynamic [119,112]. Of particular interest, the work in [119] examines the temporal correlation between packet loss on the Internet connections by collecting real measurements. It found that within 1000ms time-scale, the losses are highly correlated, otherwise, they are independent of each other. By using the same dataset, it also evaluates three loss models of increasing complexity: the Bernoulli (random) model, the 2-state Markov chain model and the k-th order Markov chain model. The results show that the finer the correlation time-scale, the better accuracy we have with more complex model.