Heterogeneity of service is a major aspect of many real multi-server queueing situations such as banks, hospitals, telecommunication networks, manufacturing systems and several busi- ness organisations. In this paper we consider a two-server heterogeneous queueing system with disastrous breakdowns, repair, balking and reneging and customer impatience where customers became impatient when the system is down. The system size probabilities in tran- sient state are obtained in modified Bessel function closed form using generating functions and the identity of the confluent hypergeometric function. Further, the steady-state system size probabilities are derived in closed form using identities and hypergeometric function. Numerical illustrations are also shown to visualize the system effect.
Keywords: Heterogeneous servers - System disaster - Server repair -Customers’ impatience - Hypergeometric - Moments - Steady-state
probabilities.