A STEADY-STATE BEHAVIOUR OF AN M M 1 QUEUE WITH OPTIONAL DIFFERENTIATED WORKING VACATIONS, SERVER BREAKDOWN, AND CUSTOMER BALKING

This paper analyses the steady-state behaviour of an M M 1 queueing system incorporating optional differentiated working vacations, server breakdowns, and customer balking. Following a busy period, the server might transition into an optional I or II working vacation, leading to a reduction in the service rate. Customers may balk when the server is on vacation or experiencing a breakdown. The model's stable solution is derived using probability-generating functions, enabling the evaluation of key performance metrics. A cost optimization framework is employed to minimize the cost by balancing system parameters. Numerical examples demonstrate the impact of varying arrival and service rates on customer queue length and waiting times.