Discrete time queueing system with unreliable server

Consideration is given to the discrete time queueing system $\mathrm{Geo}/\mathrm{G}/1/\infty$ with server subject to two types of breakdowns. The server can break down either when it is busy or when it is idle, which happens with different probabilities. Repair time distribution depends on the type of the breakdown. Expressions for the stationary probability distribution and other main stationary characteristics are given. It is shown how the obtained results can be used to find some stationary characteristics of $\vec{\mathrm{Geo}}_2/\vec{\mathrm{G}}_2/1/\infty$ with two types of customers and preemptive priority.