MARKOVIAN HETEROGENEOUS ARRIVAL RATES AND SINGLE SERVER WORKING VACATION QUEUE WITH IMPATIENT CUSTOMERS

In this paper, we analyse an M/M/1 queueing system with impatient customer and working vacation.The server begins the working vacation when the server finds no customer in the system and the server serves in a vacation period with slow service rates.If the server come back from a working vacation and find the queue empty, it starts the another working vacation.Otherwise, it switches to a normal busy period.If the server is busy or working vacation When a customer comes to the system, it activates an impatience timer.If the customer's service has not finished before the customer's impatience timer expires and never comes back, the customer leaves the system.The balance equations of the model are all derived using statetransition diagram.Then, we obtain various performance measures such as the mean system sizes.Some numerical results and graphical representation are also represented.