Conditions for stability and instability of retrial queueing systems with general retrial times

Tewfik Kernane (1)

1 USTHB - Labo de probabilité et statistique

We study the stability of single server retrial queues under general distribution for retrial times and stationary ergodic service times, for three main retrial policies studied in the literature: classical linear, constant and control policies. The approach used is the renovating events approach to obtain sufficient stability conditions by strong coupling convergence of the process modeling the dynamics of the system to a unique stationary ergodic regime. We also obtain instability conditions by convergence in distribution to improper limiting sequences.

Mots clés: Linear retrial policy; Constant retrial policy; Control retrial policy; Strong coupling convergence; Retrial queues; Stability; instability; Stochastic recursive sequence; Renovation events theory

Domaines: Probabilités [math.PR]

Tewfik Kernane. Conditions for stability and instability of retrial queueing systems with general retrial times. Statistics and Probability Letters, 2008, pp.STAPRO: 5118. ⟨10.1016/j.spl.2008.06.019⟩. ⟨hal-00243143⟩