Queueing Analysis of a Multi-component Machining System having Unreliable Heterogeneous Servers and Impatient Customers

In this investigation, we deal with performance prediction of machining system with heterogeneous servers working under N-policy. To make multi-component system more reliable and efficient, the facility of cold and warm spares has been provided and the switching failure is taken into consideration. The impatient behaviors i.e. balking and reneging of failed machines are also included to make the investigation more versatile and realistic. The governing Chapman-Kolmogorov’s differential equations are also developed using Conservation Law of Rates. Various performance indices are derived from the state probabilities evaluated by using successive over relaxation (SOR) technique which deals with simultaneous linear equations efficiently and converges more rapidly. Numerical results are also provided to give insight about the problem. To explore the effects of system descriptors, the sensitivity analysis is conducted and results are depicted in tables and graphs. This paper significantly reveals optimal number of failed operating units to initiate service based on cost analysis and prompts worthy parameter of different characteristics of machines and servers.