A retrial inventory system with an unreliable server (Q2204282)

Summary: In this paper, we analyse an unreliable \((s, S)\) inventory system with infinite capacity orbit. Customers join the retrial orbit if they are interrupted by a server breakdown and repeatedly attempt to access the server at iid intervals until it is found functioning and idle. We provide stability condition and steady state system size probabilities of the underlying stochastic process. Also, we provide several other characteristics of the system like average waiting time of a customer in the orbit, average number of breakdowns of the server, average duration of a failed service, etc. We obtained a total expected cost function which is optimal in both \(s\) and \(S\) and provided some numerical illustration.