Analysis of a Heterogeneous Queuing Model with Intermittently Obtainable Servers under a Hybrid Vacation Schedule

Abstract

This paper investigates the concept of a Markovian queueing model with heterogeneous, intermittently available servers with feedback under a hybrid vacation policy. Both the asymmetric transition representation and the hybrid vacation policy are addressed in this article. The necessary and sufficient conditions for system stability are presented. In addition, the steady-state probability distribution of the queueing model was derived by employing the matrix geometric method. Furthermore, a few formulae were constructed to determine the model’s performance indicators. Finally, the influence of system parameters was also investigated using some numerical examples.

Keywords

• heterogeneous server
• feedback
• intermittently obtainable service
• hybrid vacation
• breakdown