In today's practical wireless networks, one of the most important issues is how to jointly optimize various functions at different layers (e.g., routing, scheduling and power control) for high performance.
To illustrate this point, researchers usually present what they call a cross-layer design.
Cross-layer design can help to exploit the interactions between layers and promotes adaptability at various layers based on information exchanged.
However, it is often hard to characterize the interactions between protocols at different layers, and the joint optimization across layers may lead to complex schemes.
Furthermore, in wireless networks, available resources (for scheduling or routing) are generally restricted, and profits between nodes are often structurally twisted and complicated.
Thus, it is considerably difficult to take various functions at different layers and profits between the nodes into consideration jointly and to optimize the network.
In this context, mathematical programming such as linear programming (LP, or linear optimization) can be a nice approach to the cross-layer optimization problem.
LP is a mathematical method for determining a way to achieve the best outcome such as maximum profit or minimum cost in a given mathematical model for some list of requirements represented as linear relationships.
It is applied to various fields of study, and it is also useful in optimizing the network due to proven usefulness in planning (e.g., routing, scheduling, assignment, and design), fast derivation of the solution, intuitive formulation, and handling of many variables.
Our study for cross-layer optimization design in wireless networks has a straightforward linear programming formulation and, it will be the main theme of this thesis.
The main idea of our study is to represent the acceptance or rejection of resource assignment (i.e., time and/or channel allocation) for each node as a binary integer variable which can only take on the value of 0 or 1 (rather than arbitrary integers).
Then, we consider the characteristics of wireless networks (such as RFID system and ad hoc network) and formulate the linear program that sequentially achieves several objectives (such as minimum frame size, maximum utilization, energy efficiency, etc.) while taking the controls (such as scheduling, routing and power control, etc.) in different layers into consideration jointly.
Numerical results demonstrate the effectiveness of the proposed optimization designs.