On Truncation of the Matrix-Geometric Stationary Distributions

Naumov, Valeriy; Gaidamaka, Yuliya; Samouylov, Konstantin

doi:10.3390/math7090798

Cited by 1 publication

(1 citation statement)

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“…We note that whileÃ is block-tridiagonal, adding H may disrupt this structure, since the positions of non-zero entries in H depend on the ratios among a s , G s and w s (n s ). This makes it difficult to apply special block-matrix methods for solving the global balance equations, such as in References [38,44]. However, A is sparse, which allows for the use of sparse linear systems' routines such as UMFPACK.…”

Section: Stationary State Distributionmentioning

confidence: 99%

An Analytical Model for 5G Network Resource Sharing with Flexible SLA-Oriented Slice Isolation

et al. 2020

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Network slicing is a novel key technology in 5G networks which permits to provide a multitude of heterogeneous communication services over a common network infrastructure while satisfying strict Quality of Service (QoS) requirements. Since radio spectrum resources are inherently scarce, the slicing of the radio access network should rely on a flexible resource sharing policy that provides efficient resource usage, fairness and slice isolation. In this article, we propose such a policy for bandwidth-greedy communication services. The policy implies a convex programming problem and is formalized to allow for session-level stochastic modeling. We developed a multi-class service system with service rates obtained as a solution to the optimization problem, a Markovian Arrival Process and state-dependent preemptive priorities. We use matrix-analytic methods to find the steady state distribution of the resulting continuous-time Markov chain and the expressions for important performance metrics, such as data rates. Numerical analysis illustrates the efficiency of the proposed slicing scheme compared to the complete sharing and complete partitioning policies, showing that our approach leads to a data rate about the double of that obtained under complete partitioning for the analyzed scenario.

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Section: Stationary State Distributionmentioning

confidence: 99%