Abstract
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.
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Efrosinin, D. Queueing model of a hybrid channel with faster link subject to partial and complete failures. Ann Oper Res 202, 75–102 (2013). https://doi.org/10.1007/s10479-011-0939-7
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DOI: https://doi.org/10.1007/s10479-011-0939-7