M/M/sM/M/s queue with impatient customers and retrials

We consider an M/M/sM/M/s queue with balking, reneging and retrials. The customer who has balked at entering the system or reneged on waiting line can join the virtual pool of customers, called orbit and repeats its request after random amount of time. The probabilities that the balking customers and reneging customers join orbit may depend on the number of customers in service facility. The number of customers in orbit and service facility is described by a Markov chain on two-dimensional lattice space Z+×Z+Z+×Z+, where Z+={0,1,2,…}Z+={0,1,2,…}. An algorithm for the stationary distribution of the Markov chain is derived and some numerical results are presented.