A POISSON-POISSON MODEL TO ANALYZE CONGESTION DATA

Abstract

Congestion in internet network often worsens the performance of the network. An analysis of congestion data plays a significant role in congestion detection and control. To detect and control congestion, analysis of number of packet arrival, packet inter arrival times, throughput, queuing delay, etc. are some important phenomena. Fitting probability distributions to packet arrival, throughput, inter arrival time, etc. are essential in order to control congestion in future, setting appropriate values of parameters beforehand (buffer size, number of packet arrival, inter arrival time, average queuing delay, etc.). Number of packet arrival within a certain time interval is a count random variable that follows a Poisson distribution. Similarly, throughput/number of packet departure within a certain time interval is also a Poisson random variable but it is correlated with the number of packet arrival. In most of the previous studies, univariate distributions have been used to identify the best fit probability distributions for congestion data. In this study, an attempt is made to use a PoissonPoisson model for packet arrival and departure (throughput) from the network where correlation between the packet arrival and departure is considered. Using simulation, the performance of models in each situation (small/large sample size, low/heavy congestion) is evaluated. This technique is expected to simplify the analysis of big data stemming from the congestion in TCP/IP network.