Efficient Method to Approximately Solve Retrial Systems with Impatience.

Journal of Applied Mathematics (Impact Factor: 0.72). 01/2012; 2012. DOI: 10.1155/2012/186761
Source: DBLP


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.

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Available from: Vicente Casares-Giner, Oct 05, 2015
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    ABSTRACT: We present a new approximation method called value ex- trapolation for Markov processes with large or inflnite state spaces. The method can be applied for calculating any per- formance measure that can be expressed as the expected value of a function of the system state. Traditionally, the state distribution of a system is solved in a truncated state space and then an appropriate function is summed over the states to obtain the performance measure. In our approach, the measure is obtained directly, along with the relative val- ues of the states, by solving the Howard equations in the MDP setting. Instead of a simple state space truncation, the relative values outside the truncated state space are extrap- olated using a polynomial function. The Howard equations remain linear, hence there is no signiflcant computational penalty. The accuracy of value extrapolation, even with a heavily truncated state space, is demonstrated using proces- sor sharing systems and data networks as examples.
    Proceedings of the 1st International Conference on Performance Evaluation Methodolgies and Tools, VALUETOOLS 2006, Pisa, Italy, October 11-13, 2006; 01/2006
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    ABSTRACT: We evaluated the impact that new session retrials have on the performance of a mobile cellular network which deploys a fractional number of guard channels, a queue for handover sessions and an exponential deadline for serving those requests, modeling in this way the overlapping area between cells. To solve the Markov model we introduced an approximate methodology which is substantially more accurate than pre-vious ones, while increasing the computation cost only marginally. Results show that deploying a handover queue and a fractional number of guard channels help to improve system capacity while guaranteeing a given QoS objective. Finally, we evaluated the magnitude of the over-dimensioning that takes place when retrials are perceived as an increment in the arrival rate of new sessions, showing that it can be severe when the terminals retry persistently as occurs when equipped with automatic redialing. Keywords— Cellular networks, fractional guard channel, retrials, quasi–birth–and–death process.
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