Imprecise Markov Models for Scalable and Robust Performance Evaluation of Flexi-Grid Spectrum Allocation Policies

TL;DR

This paper develops scalable imprecise Markov models to evaluate the performance of flexible spectrum allocation policies in optical networks, providing guaranteed bounds on blocking probabilities.

Contribution

It introduces reduced-state imprecise Markov chain models that offer guaranteed bounds on performance metrics, addressing scalability and accuracy issues in existing models.

Findings

Exact Markov models enable precise performance computation for small systems.

Reduced-state models approximate blocking probabilities efficiently but lack guaranteed accuracy.

Imprecise Markov models provide bounds on blocking probabilities, ensuring reliable performance evaluation.

Abstract

The possibility of flexibly assigning spectrum resources with channels of different sizes greatly improves the spectral efficiency of optical networks, but can also lead to unwanted spectrum fragmentation.We study this problem in a scenario where traffic demands are categorised in two types (low or high bit-rate) by assessing the performance of three allocation policies. Our first contribution consists of exact Markov chain models for these allocation policies, which allow us to numerically compute the relevant performance measures. However, these exact models do not scale to large systems, in the sense that the computations required to determine the blocking probabilities---which measure the performance of the allocation policies---become intractable. In order to address this, we first extend an approximate reduced-state Markov chain model that is available in the literature to the three considered allocation policies. These reduced-state Markov chain models allow us to tractably compute approximations of the blocking probabilities, but the accuracy of these approximations cannot be easily verified. Our main contribution then is the introduction of reduced-state imprecise Markov chain models that allow us to derive guaranteed lower and upper bounds on blocking probabilities, for the three allocation policies separately or for all possible allocation policies simultaneously.