A Markovian inventory system with retrial and impatient customers

We consider an inventory system in which the customers who arrive during the stock out period join an orbit of infinite size. The customers in the orbit are assumed not only to retry for their demand, may renege from the orbit at random time. This situation is modelled in this work by assuming Poisson arrivals for customers, exponential lead time for orders placed under (s, S) ordering policy, exponential time between successive attempts of retrial of a customer and exponential times for reneging by customers in the orbit. The condition for ergodicity of the system which is modelled as Markov processes is obtained. The joint probability distribution of the number of customers in the system and the inventory level is obtained in steady state case. The measures of system performance in the steady state are derived and the long run total expected cost rate is derived. The results are illustrated with numerical examples.