Closed-form formulae for moment, tail probability, and blocking probability of waiting time in a buffer-sharing deterministic system

Obtaining analytic expressions for characteristics in probabilistic systems with finite buffer capacities such as (higher) moments and tail probabilities of stationary waiting times, and blocking probabilities is by no means trivial. This is also true even for a system with deterministic processing times. By using the max-plus algebraic approach in this study, we introduce closed-form formulae for characteristics of stationary waiting time in a complete buffer-sharing m-node tandem system with constant processing times. Numerical examples are also provided.