Strong Stability and Uniform Ergodicity Estimates for the Waiting Proce ss in Queueing Models with Impatient Customers

#### D. Aissani, Z. Mouhoubi

2019, v.25, Issue 2, 329-358

ABSTRACT

We provide sufficient conditions for the strong stability and the uniform ergodicity for the discrete-time waiting
process describing the $GI/GI/1$ single-server queue with general
patience time distribution. The rate of convergence to
the stationarity and the potential of the chain are derived also.
In addition, we obtain upper bounds of the deviation of the stationary
and transition characteristics under perturbation of patience time distribution. The perturbation of the structure of the $GI / GI / 1$ queueing system with ordinary customers which leads to
the $GI / GI /$ 1 system with impatient customers is also considered.

Keywords: strong stability; uniform ergodicity; structural perturbation; renewal equation; potential of the chain; impatient queues