Abstract
We present a novel technique to solve multiserver retrial systems with impatience. Unfortunately these systems do not present an exact analytic solution, so it is mandatory to resort to approximate techniques. This novel technique does not rely on the numerical solution of the steady‐state Kolmogorov equations of the Continuous Time Markov Chain as it is common for this kind of systems but it considers the system in its Markov Decision Process setting. This technique, known as value extrapolation, truncates the infinite state space using a polynomial extrapolation method to approach the states outside the truncated state space. A numerical evaluation is carried out to evaluate this technique and to compare its performance with previous techniques. The obtained results show that value extrapolation greatly outperforms the previous approaches appeared in the literature not only in terms of accuracy but also in terms of computational cost.
Highlights
A common assumption when evaluating the performance of communication systems is that users that do not obtain an immediate service leave the system without retrying
We present a novel technique to solve multiserver retrial systems with impatience
In this paper we address the application of the value extrapolation technique to an important class of queuing systems, for example, retrial queues, which are essentially different of the type of queues to which this technique has been applied
Summary
A common assumption when evaluating the performance of communication systems is that users that do not obtain an immediate service leave the system without retrying. In 8 , a generalization of the approximate technique in 7 was proposed, showing a substantial improvement in the accuracy at the expense of a marginal increase of the computational cost Those approximations are based on the reduction of an infinite state space to a finite one by aggregating states. Other solutions maintain the infinite state space but homogenize it beyond a given level in order to solve the system These later models are known as generalized truncated models 6 and usually present the advantage of providing a much better accuracy than the finite methodologies 9. In this paper we develop the value extrapolation technique to solve a multiserver retrial system, addressing the drawback of computing only a single performance parameter every time the technique is used.
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