We analyze an unreliable M/M/1 retrial queue with infinite-capacity orbit and normal queue. Retrial customers do not rejoin the normal queue but repeatedly attempt to access the server at i.i.d. intervals until it is found functioning and idle. We provide stability conditions as well as several stochastic decomposability results.
Operations Research Letters
Sherman, N. P., & Kharoufeh, J. P. (2006). An M/M/1 retrial queue with unreliable server. Operations Research Letters, 34(6), 697–705. https://doi.org/10.1016/j.orl.2005.11.003