Asymptotic optimality of the queue service probability for the radial basis function network-based queue selection rule

•A RBFN-based QSR is used to derive the QSP and waiting time of a multi-queue model.•A multi-queue system with finite capacity in an overload condition is considered.•The machine learning feature of the RBFN is applied in deriving the optimal QSP.•The asymptotic tendency of the QSP is investigated.

A queueing model is generally designed with sufficient capacity or resources to ensure that the system is stable, while preserving quality of service. However, the multi-queue system with finite capacity and timing constraints in an overload condition are more often encountered and discussed in a variety of real-life problems. In such a situation, waiting time is usually an important performance metric quantifying the effectiveness and efficiency of the system. The concerned issue is still an open research topic and is not fully addressed and investigated. Since an exact analysis is practically infeasible owing to the complexity of such systems, emphasis has been concentrated on the approximate analysis. This paper is thus intended to estimate the upper bound of waiting times of a multi-queue system with a specialized scheduling paradigm, extending from a series of our research on message scheduling. Without resorting to complex statistical approaches, the study provides a machine learning methodology to resolve this subject. With the learning capability of the radial basis function network (RBFN) as the queue selection rule, this paper particularly focuses on deriving the asymptotic optimality of the queue service probability, under the conditions of multi-queue, finite capacity, and timing constraints in the overload situation. In fact, the RBFN is incorporated with two novel types of learning which lead to develop the support theorem and to obtain the closed-form of queue service probability as well as waiting time. Importantly, the learning feature is definitely essential in providing optimal queue service probability with dynamical scheduling scheme. Several existing queue selection rules are also evaluated and compared with the RBFN-based queue selection rule. Simulation results illustrate the feasibility and accuracy of the proposed strategy.