Strong stability in retrial queues. (English) Zbl 1050.60073

Berdjoudj, Louisa; Aissani, Djamil

Teor. Jmovirn. Mat. Stat. 68, 11-17 (2003); and Theory Probab. Math. Stat. 68, 11-18 (2004).

The authors study the strong stability in retrial queues after perturbation of retrial parameters. Queueing systems, in which customers who find all servers and waiting positions (if any) occupied may retry for service after a period of time, are called retrial queues. It is supposed that perturbations of the transition kernel of the imbedded Markov chain are small with respect to some norms in the operator space. The authors describe the model of the M/G/1/1 retrial queue and study the strong stability of the stationary distribution of the imbedded Markov chain in the M/G/1 queueing system with infinite retrials, after perturbation of retrial parameters. The stability inequalities with exact computation of constants are derived.

Reviewer: A. D. Borisenko (Kyïv)

MSC:

60J25	Continuous-time Markov processes on general state spaces
60K25	Queueing theory (aspects of probability theory)

Keywords:

strong stability; retrial queues; perturbation; approximation