Performance analysis of time-dependent queueing systems: Survey and classification

• We provide an overview of approaches for the performance evaluation of time-dependent queueing systems.
• We develop a classification scheme that groups approximation approaches according to their underlying key ideas.
• We discuss and establish links between the different approaches.
• We review and classify areas of applications for time-dependent queueing systems.

Many queueing systems are subject to time-dependent changes in system parameters, such as the arrival rate or number of servers. Examples include time-dependent call volumes and agents at inbound call centers, time-varying air traffic at airports, time-dependent truck arrival rates at seaports, and cyclic message volumes in computer systems.There are several approaches for the performance analysis of queueing systems with deterministic parameter changes over time. In this survey, we develop a classification scheme that groups these approaches according to their underlying key ideas into (i) numerical and analytical solutions, (ii) approaches based on models with piecewise constant parameters, and (iii) approaches based on modified system characteristics. Additionally, we identify links between the different approaches and provide a survey of applications that are categorized into service, road and air traffic, and IT systems.