Queue-Size Distribution in a Discrete-Time Finite-Capacity Model with a Single Vacation Mechanism

In the paper a finite-capacity discrete-time queueing system with geometric interarrival times and generally distributed processing is studied. Every time when service station becomes idle it goes for vacation of random duration that can be treated as power-saving mechanism. Application single policy one way to achieve symmetry in terms operating costs. A differential equations transient conditional queue-size distribution established. The solution corresponding written double probability generating functions found using analytical method based on linear algebraic approach. Moreover, representation probability-generating function stationary obtained. Numerical study illustrating theoretical results attached well.