Abstract
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.
Highlights
Many queueing systems are analysed for their dynamic and optimal control related to system access, resource allocation, changing service area characteristics and so on
The paper deals with a known model of a multiserver queueing system with controllable allocation of customers between heterogeneous servers which are differentiated by their service and cost attributes
For the queueing system with two heterogeneous servers it has been shown in [1] by using a dynamic programming approach that to minimise the mean sojourn time of customers in the system, the faster server must be always used and the customer has to be assigned to the slower server if and only if the number of customers in the queue exceeds the certain threshold level
Summary
Many queueing systems are analysed for their dynamic and optimal control related to system access, resource allocation, changing service area characteristics and so on. For the queueing system with two heterogeneous servers it has been shown in [1] by using a dynamic programming approach that to minimise the mean sojourn time of customers in the system, the faster server must be always used and the customer has to be assigned to the slower server if and only if the number of customers in the queue exceeds the certain threshold level This result was obtained independently in more simple form in [2,3]. The policy-iteration algorithm is used in the paper to generate the data sets needed both to verify the quality of the proposed optimal threshold estimation methods and to train the neural networks. We strongly believe that the trained neural network can be successfully used to calculate the optimal thresholds for those system parameters for which alternative numerical methods are difficult or impossible to use, for example, in heavy traffic case, or, in general, to reconstruct the areas of optimality without usage of timeexpensive algorithms and procedures.
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