First-passage-time and busy-period distributions of discrete-time Markovian queues: \(\text{Geom}(n)/\text{Geom}(n)/1/N\)
The authors consider discrete-time queueing models with finite waiting room. The interarrival- and service-times are described by independent random variables, transitions are dependent on the number of customers in the system. The authors investigate first passage time distributions with respect to the number of customers and related busy time distributions. They give a representation of these distributions in terms of the roots of certain determinants. They demonstrate the usefulness of their results by numerical and graphical results. Extensions are given to continuous- time models.
scientific article; zbMATH DE number 698868