Short Segment Cumulative Modeling Algorithm for Markovian Model on Packet Loss

In this Paper, we worked on the modeling of packet loss using very short segments of time, the model suggested in this paper is based on binary time series, it is represented by investigating the probability of losses occurrence and loss dependency using Markov models. A well known problems of time series modeling is achieving segment's stationarity, this obstacle dictates using long time segments in order to achieve small average variations. we suggested a short segment cumulative modeling algorithm using segments of 15 minutes instead of 2 hours, through making a higher segmentation and give expectation for the models value for a given segment dynamically and cumulatively, this was achieved with error less than 0.001 for single segment. these results were compared with models created using very long segments of 2 hours, the overall error between the two models (short segments and long segments) were less than 0.001. The data set used was real data obtained from EUMED Connect Network (Mediterranean research network connects 6 Arab countries) from the Palestinian side. The research exploited a data set of 72 hours. each country was expressed by a randomly selected 12-hour dataset, each dataset was divided into two-hour segments, each segment was modeled as a binary time series. From the 36 segments, 26 segments were found stationary. For Stationary segments, the research investigated the segment correlation and used it as a modeling reference. 11 segments were modeled using Bernoulli model, 12 segments were modeled using 2-state Markov chain and 5 segments showed k-th order Markov chain tendencies with orders 2, 3, 8, 27, 38. The models were built under 0.05 threshold in average filter condition of stationary and with confidence of 95% for lag dependency selection. the comparison between long term segment modeling and short term segment modeling was carried out showing errors around 0.001 in average between the two modeling approaches. The importance of this research is being able to expect the packet losses for longer time on early stages of losses.