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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]

This paper deals with heterogeneous queues where servers differ not only in service rates but also in operating costs. The classical optimisation problem in queueing systems with heterogeneous servers consists in the optimal allocation of customers between the servers with the aim to minimise the long-run average costs of the system per unit of time. As it is known, under some assumptions the optimal allocation policy for this system is of threshold type, i.e., the policy depends on the queue length and the state of faster servers. The optimal thresholds can be calculated using a Markov decision process by implementing the policy-iteration algorithm. This algorithm may have certain limitations on obtaining a result for the entire range of system parameter values. However, the available data sets for evaluated optimal threshold levels and values of system parameters can be used to provide estimations for optimal thresholds through artificial neural networks. The obtained results are accompanied by a simple heuristic solution. Numerical examples illustrate the quality of estimations. [ABSTRACT FROM AUTHOR]

The paper studies a controllable multi-server heterogeneous queueing system where servers operate at different service rates without preemption, i.e., the service times are uninterrupted. The optimal control policy allocates the customers between the servers in such a way that the mean number of customers in the system reaches its minimal value. The Markov decision model and the policy-iteration algorithm are used to calculate the optimal allocation policy and corresponding mean performance characteristics. The optimal policy, when neglecting the weak influence of slow servers, is of threshold type defined as a sequence of threshold levels which specifies the queue lengths for the usage of any slower server. To avoid time-consuming calculations for systems with a large number of servers, we focus here on a heuristic evaluation of the optimal thresholds and compare this solution with the real values. We develop also the simple lower and upper bound methods based on approximation by an equivalent heterogeneous queueing system with a preemption to measure the mean number of customers in the system operating under the optimal policy. Finally, the simulation technique is used to provide sensitivity analysis of the heuristic solution to changes in the form of inter-arrival and service time distributions. [ABSTRACT FROM AUTHOR]