## Global Optimal Routing, Scheduling and Power Control for Multi-hop Wireless Networks with Interference

### BibTeX

@MISC{Kazemitabar_globaloptimal,

author = {Javad Kazemitabar},

title = {Global Optimal Routing, Scheduling and Power Control for Multi-hop Wireless Networks with Interference},

year = {}

}

### OpenURL

### Abstract

Abstract — We consider the problem of joint routing, scheduling and power control in multi-hop wireless networks. We use a linear relation between link capacity and signal to interference noise ratio in our formulation. In a previous work, using a duality approach, the optimal link scheduling and power control that minimizes the total average transmission power is found. We formulate this problem as a linear programming problem with exponential number of constraints. To cope with the exponential number of constraints, we propose an iterative algorithm based on the cutting plane method. The separation Oracle for the cutting plane algorithm turns out to be an element-wise concave optimization problem that can be effectively solved using branch and bound algorithm. We extend the same method to find the optimal routing scheduling and power control. Simulation results show that this methodology is more efficient and scalable compare to the previously proposed algorithm. I.

### Citations

3668 |
Convex optimization
- Boyd, Vandenberghe
- 2004
(Show Context)
Citation Context ...teration that leads to convergence. We use the standard form of convex optimization, i.e. cost-constraint format. We denote the cost function of the LP problem by f and the constraint functions by hi =-=[17]-=-. f(T, β(1), · · · , β(L)) = T h1(T, β(1), · · · , β(L)) = T − � l β(l)(C(l) − X1 (l)) − � l P 1 (l) ≤ 0 hm(T, β(1), · · · , β(L)) = T − � l β(l)(C(l) − Xm (l)) − � l P m (l) ≤ 0 . (26) Since the line... |

673 | MACAW: a media access protocol for wireless LAN’s
- Bharghavan
(Show Context)
Citation Context ... more challenging to provide short term performance guarantees with these algorithms [6] [7]. This becomes even more dramatic if we use random access methods such as 802.11 for distributed scheduling =-=[8]-=- [9], where starvation of some connections may occur. Under these circumstances a combination of centralized algorithms for minimum bandwidth guarantees and distributed algorithms for the rest of the ... |

223 | The impact of imperfect scheduling on cross-layer congestion control in wireless networks
- Lin, Shroff
- 2006
(Show Context)
Citation Context ...ths. We can use the centralized algorithm proposed in this paper to select a good candidate set of the paths and then use distributed scheduling algorithms to distribute the load among selected paths =-=[10]-=-. Furthermore, our algorithm will also provide good set of the links that can be scheduled together in order to simplify the distributed scheduling. • Bench-marking: Our algorithm can be used to study... |

134 |
Characterizing achievable rates in multi-hop wireless networks: the joint routing and scheduling problem, in
- Kodialam, Nandagopal
- 2003
(Show Context)
Citation Context ...thms for routing, scheduling and power control is even much more efficient than the direct approach proposed in [1], [2] for scheduling and power control (with fixed routing). Kodialam and Nandagopal =-=[3]-=- consider the problem of determining the achievable rates in multi-hop wireless networks. They consider a node-exclusive interference model, which means that transmitters use orthogonal channels and t... |

97 | Crosslayer congestion control, routing and scheduling design in ad hoc wireless networks - Chen, Low, et al. - 2006 |

89 | Energy optimal control for time varying wireless networks - Neely - 2006 |

57 | Modeling media access in embedded two-flow topologies of multi-hop wireless networks
- Garetto, Shi, et al.
- 2005
(Show Context)
Citation Context ...e challenging to provide short term performance guarantees with these algorithms [6] [7]. This becomes even more dramatic if we use random access methods such as 802.11 for distributed scheduling [8] =-=[9]-=-, where starvation of some connections may occur. Under these circumstances a combination of centralized algorithms for minimum bandwidth guarantees and distributed algorithms for the rest of the capa... |

56 |
Computer Networks, Fourth Edition
- Tanenbaum
- 2002
(Show Context)
Citation Context ...ify the last step as follows. The potential function in (23) is separable to two functions. The first one, i.e. ∑ l βk(l)C(l), is the sum of weighted C(l)s and can be minimized via Dijkstra algorithm =-=[11]-=-. The second one is simply the potential function in the previous subsection minus a constant value. Therefore, it does not require a new technique to find the minimum. Similar to the scheduling-only ... |

50 | Kodialam,“On power efficient communication over multihop wireless networks: joint routing, scheduling and power control
- Bhatia, M
- 2004
(Show Context)
Citation Context ... routing problem and rely on graph edge coloring methods for scheduling. In their model the transmission power over each link is fixed and hence there is no power control problem. Bhatia and Kodialam =-=[4]-=- consider the problem of joint routing, scheduling and power control for wireless multihop networks. They derive a performance guaranteed polynomial time approximation algorithm for jointly solving th... |

9 | Low-complexity and distributed energy minimization in multi-hop wireless networks
- Lin, Lin, et al.
- 2007
(Show Context)
Citation Context ...time approximation algorithm for jointly solving these three problems. Similar to [3] they also assume orthogonal channels and hence there is no interference between the channels. Lin, Lin and Shroff =-=[6]-=- use the same model presented in [4] and find a low complexity distributed algorithm for routing, scheduling and power control. Their proposed algorithm is sub-optimal and its power consumption can be... |

8 |
Optimal Routing, Link Scheduling and
- Cruz, Santhanam
- 2003
(Show Context)
Citation Context ... network and consider non-convex inter-dependent model for wireless links. Optimization approaches for wireless network resource allocation are developed in several papers. Our approach is similar to =-=[1]-=-, where the problem of joint routing, scheduling and power control for wireless multi-hop network is considered. They present a centralized algorithm to find optimal scheduling and power control to mi... |

4 |
The Cutting Plane Method for Solving Convex Programs
- Kelly
- 1960
(Show Context)
Citation Context ...nks in the network, andstherefore it is not possible to find the solution for large values of M. A common approach to deal with large number of constraints in linear programs is cutting plane methods =-=[14]-=- 1 . Instead of dealing with all constraints, cutting plane algorithm considers a subset of constraints I and form the relaxed problem: max T s.t. T − � l∈ɛ P m (l) − � β(l)(C(l) − Xm (l)) ≤ 0 l∈ɛ m ∈... |

1 |
Joint Optimization of Radio Resources in Wireless Multi-Hop Networks
- Sanathanam
(Show Context)
Citation Context ...ng the peak power constraint in every slot. However, since the potential function V is linear in −→ P , −→ C , and −→ X, it follows that (9) can be computed by an optimization over a single slot [1], =-=[2]-=-. Therefore, we can just focus on solving maxβ≥0{min−→ P V ( −→ P , β)} s.t. −→ P ∈ P (10) It can be shown [1] that V is element-wise concave in terms of −→ P . Therefore, the minimization problem tak... |

1 |
Outage Probability Metrics of Connectivity for MIMO Fading Ad-Hoc Networks
- Yousefi’zadeh, Jafarkhani, et al.
- 2005
(Show Context)
Citation Context ...le N(N − 1) links between nodes, make a network topology. These active links are chosen based on the distance, Signal to Interference Noise Ratio (SINR) or some other connectivity measure [11], [12], =-=[13]-=-. For simplicity, we assume in this paper that two nodes constitute a link if the distance between them is less than a threshold. For a given link l = (i, j), the transmitter node i uses a signal powe... |