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In this paper we find stability conditions of a two-class retrial system with unreliable server, in which the new customer joins a class-dependent orbit queue regardless of the state of the server. The interrupted customer joins the top of the corresponding orbit and tries to occupy the server after a class-dependent exponential retrial time. To find stability conditions, we apply two different approaches, regenerative approach and the stability analysis of a Markov chain (the MC approach) which has been developed in Fayolle et al. (Topics in the constructive theory of countable Markov chains, Cambridge University Press, Cambridge, 1995). The former approach allows to obtain a transparent and intuitive necessary stability condition. Then we apply the MC approach to obtain the stability criterion of the embedded two-dimensional Markov chain describing the state of orbits at the instances when the server becomes free. We use a necessary stability condition obtained by the regenerative method to present the stability criterion in a compact form. Moreover we discuss a modified controllable system and compare stability zones of these two systems. Some numerical examples based on simulation results are included as well which illustrate the theoretical issues. [ABSTRACT FROM AUTHOR]

This paper presents a Markovian queueing model for a hybrid channel consisting of two links with different throughputs. The busy faster link is assumed to be unreliable, with possible partial and complete failures. Partial failures lead to a reduction in the service rate, while complete failure stops the service. Repairs return the faster server to a non-failed state. The problem of the optimal allocation of customers between the servers is considered. The optimality of a threshold-based policy that depends on the failure state of the faster server is proved. The dynamic behaviour of the system for the given threshold policy is described by a four-dimensional Markov process that can be treated as a QBD process with a large number of boundary states. Stationary analysis of the system is performed by means of a matrix-geometric approach, and the main performance measures are derived. [ABSTRACT FROM AUTHOR]