Transient analysis of two-phase M/HK/1 queueing system with server start-UP, N-Policy, unreliable server and balking

Queueing models provide the basic frame work for analyzing the practical situations in production processes, Communication networks, transportation systems, and machine repairing. The single server queue with two phases of service with vacations has been extended to various areas. This paper deals with the transient analysis of two-phase service M/Hk/1 queue with vacation, N-policy, server break downs and balking. The paper differs from the existing literature because it investigates the length of the two-phase queueing system with transient behaviour. Explicit expressions are derived for various performance measures. The sensitivity analysis has been carried out to examine the effect of different parameters in the system.