The Dynamic Analysis and Design of A Communication link with Stationary and Nonstationary Arrivals

Most research in queueing theory is typically based on the steady-state analysis. In today’s dynamically changing traffic environment, the steady-state analysis may not provide enough information to operators regarding Quality of Service (QoS) requirements and dynamic design. In addition, the steady state analysis is not practical for nonstationary arrivals. In this paper, we consider the time-dependent behavior of a communication link depicted by an Erlang loss queue with stationary and nonstationary arrival rates. The time-dependent analysis for stationary arrival rates captures the dynamic nature of the system during its transient phase. The time-dependent analysis for nonstationary arrivals is of great interest since the arrival rate in most communication systems varies over time. In this paper, we review and compare various methods that have been proposed in the literature for the timedependent analysis of the nonstationary Erlang loss system for both stationary arrivals and nonstationary arrivals. We try to classify five practical methods into two categories: (1) closed-form exact solution and closed-form approximation; (2) numerical exact solution and numerical approximation. Our work tries to compare their computation complexity and accuracy. We apply some of these techniques to dimensioning dynamically a single communication system.