Analysis of two-server queueing system with impatient customers and a synchronous vacation policy

In this paper, we carry out an analysis for a queueing system with impatient customers and a synchronous vacation policy. Customers arrive according to a Poisson process, and two parallel servers provide heterogeneous exponential service to customers on a first-come first-served basis. It is assumed that arriving customers balk with a probability and renege according to an exponential distribution when both servers are unavailable. At a service completion instant if there are no customers in the system, the two servers take a vacation together. For this system, we first develop the equations of the steady-state probabilities. Then, we derive a matrix form solution for the steady-state probabilities. Finally, we give some performance measures of the system such as the expected number of waiting customers, the expected number of the customers in the system, and the average rate of customer loss due to impatience.