Abstract

Modeling and predicting extreme observations in network latency data is an important task for monitoring the performance and reliability of communication systems. In this paper, we develop a comprehensive inferential and predictive framework for network latency times using upper and lower current record values from the two-parameter exponential distribution. First, explicit expressions for the probability density functions and cumulative distribution functions of the lower and upper current records are derived. Closed-form expressions for the r-th moments of these records are also obtained. Parameter estimation for the location and scale parameters is then investigated using both maximum likelihood estimation and Bayesian estimation. Because the Bayesian estimators do not admit closed-form solutions, a Markov Chain Monte Carlo approach based on the Metropolis–Hastings algorithm is employed to compute the posterior summaries. To forecast future latency behavior, classical predictive intervals and Bayesian predictive procedures are developed for future upper and lower current records as well as for future record ranges. The Bayesian framework additionally provides Bayesian predictive values and Bayesian predictive intervals that incorporate parameter uncertainty. The performance of the proposed procedures is evaluated through a simulation study. Finally, the methodology is applied to real network latency time data from Saudi Arabia. The results demonstrate that record-based inference combined with Bayesian prediction provides effective tools for modeling and forecasting extreme latency observations in modern communication networks.

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