Rate-delay analysis of radio access network slices

Based on wireless network virtualization, radio access network (RAN) slicing is developed to provide services for the different users' requirements. Moreover, the users' sum data rate and delay are two significant metrics to guarantee quality of services. In this paper, we first establish an optimization problem to maximize the downlink sum rate while guaranteeing users' delay for RAN slices, where the base stations and user equipments are randomly distributed. Then we analyze the performance tradeoff between the sum rate maximization and delay tolerance. With the aid of Lyapunov optimization, the upper bounds of the achievable rate and delay are derived, through which the existence of tradeoff in performance is obvious and verified by numerical results

Energy-efficiency versus delay tradeoff in wireless networks virtualization

This paper studies the issues on wireless networks virtualization in terms of two important performance metrics, i.e., energy efficiency (EE) and delay. Different from existing works on physical layer, we aim to achieve a good tradeoff between EE and delay in wireless networks virtualization using cross-layer stochastic optimization approach. In particular, we formulate a cross-layer problem using fractional programming and Lyapunov optimization method. The EE and delay tradeoff solution is given explicitly by deriving their analytical bounds that are verified by simulation results

Hopf Bifurcation of an Epidemic Model with Delay

<div><p>A spatiotemporal epidemic model with nonlinear incidence rate and Neumann boundary conditions is investigated. On the basis of the analysis of eigenvalues of the eigenpolynomial, we derive the conditions of the existence of Hopf bifurcation in one dimension space. By utilizing the normal form theory and the center manifold theorem of partial functional differential equations (PFDs), the properties of bifurcating periodic solutions are analyzed. Moreover, according to numerical simulations, it is found that the periodic solutions can emerge in delayed epidemic model with spatial diffusion, which is consistent with our theoretical results. The obtained results may provide a new viewpoint for the recurrent outbreak of disease.</p></div

Hopf bifurcation with <i>k</i> = 0.

<p>(a) The constant steady state <i>E</i>* is asymptotically stable for <i>τ</i> = 1.2 with initial conditions <i>S</i>(<i>x</i>, <i>t</i>) = 0.42, <i>I</i>(<i>x</i>, <i>t</i>) = 0.20, (<i>x</i>, <i>t</i>) ∈ [0, <i>π</i>] × [−1.2, 0]; (b) The bifurcating periodic solutions are asymptotically stable for <i>τ</i> = 1.6 with initial conditions <i>S</i>(<i>x</i>, <i>t</i>) = 0.42, <i>I</i>(<i>x</i>, <i>t</i>) = 0.20, (<i>x</i>, <i>t</i>) ∈ [0, <i>π</i>] × [−1.6, 0].</p

The phylogenetic tree of <i>Conus</i> species based on 13 complete mitogenome sequences.

<p>GenBank accession numbers: NC_008098.1 for <i>L</i>. <i>cerithiformis</i>, NC_008797.1 for <i>C</i>. <i>textile</i>, NC_013239.1 for <i>O</i>. <i>dimidiate</i>, NC_013242.1 for <i>F</i>. <i>similis</i>, NC_013243.1 for <i>C</i>. <i>borgesi</i>, NC_023460.1 for <i>C</i>. <i>consors</i>, NC_027518.2 for <i>C</i>. <i>tulipa</i>, NC_027957.1 for <i>C</i>. <i>tribblei</i>, NC_030213.1 for <i>C</i>. <i>gloriamaris</i>, NC_030354.1 for <i>C</i>. <i>capitaneus</i>, NC_030536.1 for <i>C</i>. <i>striatus</i>, and NC_032377.1 for <i>C</i>. <i>californicus</i>. The red branch highlights our present study of <i>C</i>. <i>quercinus</i>. Please note that the outgroups <i>L</i>. <i>cerithiformis</i>, <i>O</i>. <i>dimidiata</i> and <i>F</i>. <i>similis</i> are allochthonous species. Branch lengths and topologies were obtained using the Bayesian inference analysis.</p

Scheme of the D-loop region in <i>C</i>. <i>quercinus</i> compared with <i>C</i>. <i>consors</i>.

<p>The region spans 943 bp and exhibits several outstanding motifs. The upper and lower red boxes denote the tRNA-Phe and COX3, and the blue box points to a long AT tandem repeat stretch.</p

RSCU values in the mitogenome of <i>Conus quercinus</i>.

<p>Codon families are indicated below the X-axis.</p

Nucleotide composition of <i>Conus</i> mitogenomes.

<p>Nucleotide composition of <i>Conus</i> mitogenomes.</p

The detailed mitogenome structure of <i>Conus quercinus</i>.

<p>The detailed mitogenome structure of <i>Conus quercinus</i>.</p

Ka/Ks ratios for the 13 mitochondrial PCGs among three representative <i>Conus</i> species.

<p>GenBank accession numbers: KY609509 for <i>C</i>. <i>quercinus</i>, NC_008797 for <i>C</i>. <i>textile</i>, and NC_030536 for <i>C</i>. <i>striatus</i>.</p