Some methods of investigating regeneration times in queueing networks

The determination of regeneration times and their investigation play an important role in the analysis of the rate of convergence to a steady-state distribution and in the time-uniform estimation of the stability of the processes occurring in queueing systems. To solve the problems, use is made of the methods of innovation events, test functions, splicing, and so on. The transition from investigating specific queueing systems to that of networks requires further development of the methods. The present paper describes a version of the method of test functions. The present method allows us to reduce the investigation of acyclic queueing networks with multiserver systems at their nodes to that of the ordinary G/G/1/• system.