Queueing model of a hybrid channel with faster link subject to partial and complete failures

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.