Design of Common Resource Management and Network Simulator in Heterogeneous Radio Access Network Environment

Abstract

By the newly emerging radio access technologies, we face the new heterogeneous network environment. Focusing on the co-existence of multiple access networks and the complex service combinations, the wireless service operators should guarantee good quality of services for every user. Thus, the service operators build a new operation framework which combines the existing networks and newly adopted ones. Our objective is finding the optimal heterogeneous network operation framework. We suggest the market-based marginal cost function for evaluating the relative value of resources for each network and develop a whole new heterogeneous network operation framework. To prove the applicability of the proposed operation framework, we build a large-scale JAVA simulator. We can easily test the various service scenarios in heterogeneous network environment by the simulator.

Appendix A

To prove the difference among marginal costs is converged to zero. We first set up a system of non-linear differential equations according to Traffic Transition Law as follows:

For a transition rate λ,

$$ \begin{gathered} \frac{{du_{1} }}{dt} = - \lambda \sum\limits_{j = 1}^{N} {c_{1j} (f_{1} (u_{j} ) - f_{j} (u_{j} ))} \hfill \\ \frac{{du_{2} }}{dt} = - \lambda \sum\limits_{j = 1}^{N} {c_{2j} (f_{2} (u_{j} ) - f_{j} (u_{j} ))} \hfill \\ \vdots \hfill \\ \frac{{du_{N} }}{dt} = - \lambda \sum\limits_{j = 1}^{N} {c_{Nj} (f_{N} (u_{j} ) - f_{j} (u_{j} ))} \hfill \\ \end{gathered} $$

Let $A_{ij} : = c_{ij} (f_{i} (u_{i} ) - f_{j} (u_{j} )).$ The total traffic $u_{1} + u_{2} + \cdots + u_{N}$ is conserved since

$$ \frac{{d(u_{1} + u_{2} + \cdots + u_{N} )}}{{}} = - \lambda \sum\limits_{i,j} {A_{ij} } = 0\,\left( {\because A_{ij} = - A_{ji} } \right) $$

We measure the “variation among marginal costs” with the following function: $V(t) = \sum\limits_{i,j} {c_{ij} (f_{i} (u_{i} (t)) - f_{j} (u_{j} (t)))^{2} }.$ The load balancing effect by the marginal cost function can be shown by the $V(t) = \sum\limits_{i,j} {c_{ij} (f_{i} (u_{i} (t)) - f_{j} (u_{j} (t)))^{2} } \to 0$ as the dynamics as described by the marginal cost based traffic transition. Using the fact that $A_{ij} = - A_{ji} ,$ we have

$$ \dot{V} = \frac{d}{dt}\sum\limits_{i,j} {c_{ij} (f_{i} (u_{i} ) - f_{j} (u_{j} ))^{2} }= 2\sum\limits_{i,j} {A_{ij} (f'_{i} (u_{i} )\dot{u}_{i} } - f'_{j} (u_{j} )\dot{u}_{j} ) = - 2\lambda \sum\limits_{i,j} {A_{ij} \left( {f'_{i} (u_{i} )\sum\limits_{k} {A_{ik} - f'_{j} (u_{j} )\sum\limits_{k} {A_{jk} } } } \right)} = - 2\lambda \left( {\sum\limits_{i,j} {\sum\limits_{k} {f'_{i} (u_{i} )A_{ij} A_{ik} - \sum\limits_{i,j} {\sum\limits_{k} {f'_{j} (u_{j} )A_{ij} A_{jk} } } } } } \right)= - 4\lambda \left( {\sum\limits_{i} {f'_{i} (u_{i} )\sum\limits_{j,k} {A_{ij} A_{ik} } } } \right) = - 4\lambda \sum\limits_{i} {f'_{i} (u_{i} )\left( {\sum\limits_{k} {A_{ik} } } \right)^{2} }= - \frac{4}{\lambda }\sum\limits_{i} {f'_{i} (u_{i} )(\dot{u}_{i} )^{2} } \le 0$$

$$ \dot{V} = 0 \Leftrightarrow \left( {\sum\limits_{k} {A_{ik} } } \right) = 0 \Leftrightarrow \dot{u}_{i} = 0 \Leftrightarrow f_{i} (u_{i} ) - \frac{{\sum\nolimits_{j = 1}^{N} {c_{ij} f_{j} (u_{j} )} }}{{\sum\nolimits_{j = 1}^{N} {c_{ij} } }}$$

The minimum of V is 0, when $f_{1} \left( {u_{1} } \right) = f_{2} \left( {u_{2} } \right) = \cdots = f_{N} \left( {u_{N} } \right).$ Therefore, we prove the zero convergence of difference among the marginal cost.