Mission-based Joint Optimal Resource Allocation in Wireless Multicast Sensor Networks

1. Mission-based Joint Optimal Resource Allocation in Wireless Multicast Sensor Networks Yun Hou Prof Kin K. Leung Archan Misra

2. Existing Congestion Control • Congestion Control Via Network Utility Maximization • Maximize the network utility • Utility = U(flow rates) • Recently, wireless networks • Power defines capacity • Power as another variable • Alleviating bottlenecks • More power on congested nodes • Less power on non-congested nodes • Conserving energy • Originally, wired networks • rate is the only variable • to maximize network utility • with fixed link capacity (Chiang) (Kelly, Low) So far, Congestion Control = Joint optimization (rate, power)

3. Issue with Single-radio Wireless Sensor Networks Single-radio Sensor: A node can transmit for one flow at a time Multiple flows going through the same node Flows are scheduled one by one Flow 2 Flow 1 All flows ”share” the air-time of the node Question : how much air-time to spend on each flows?

4. Motivation – Adaptive airtime-sharing More then needed Less than needed Equal time sharing = Suboptimal Objective : How to jointly adapt rate, power with airtime-sharing? Effective C = C * time fraction Biased time sharing = Optimal

5. Multi-cast networks Two flows: [1, 2] = sources [3, 4, 5] = forwarding nodes [6, 7, 8, 9] = sinks One parent has multiple next-hop children nodes C=5 C=10 C(3,1)=5 Something special with multicast 1. (n,f)<-> one multicast transmission • 2. Capacity for a transmission (n,f) • One parent broadcast to multiple children • Bottleneck child defines capacity •  Capacity of (3,1) = 5

6. Challenges and assumptions challenges: • the non-linear rate constraint – explicit time fractions sharing scheme • the non-concavity – High SINR • Unknown bottleneck child -- known network schedule The original problem Objective function = strictly concave s.t. where : fixed time fraction for transmission (n,f) : set of flows passing through node n

7. Problem formulation: Penalty of power Utility of flows Congestion control with adaptive air-time sharing (AAS) Airtime Sharing: Multiple flows passing one node share the airtime of node The time fraction for flow f at n: Capacity constraint with time sharing s.t. Capacity is a function of power where

8. Decomposition s.t. where The Lagrangian of the problem: POWER-TIME sub-problem: C is to be optimized The RATE problem is concave by definition What about the POWER-TIME problem? RATE sub-problem: C is known constant here

9. Concavity of POWER-TIME • The capacity function Cn,f (P) is concave • The Hessian matrix of Cn,f< 0 • The capacity function αn,f Cn,f(P) is concave • Relative entropy • Preserves the convexity H is definite negative For any given vector V

10. Updating the airtime fractions Review the Lagrangian: At the optimum, we have Insight:More time to saturated flows Less time to low-demand flows The airtime constraint Towards the optimal , an iterative algorithm to update is: Insight:requires local info only works with existing congestion control readily

11. The joint rate and power allocation algorithm (JRPA) Adaptive air-time sharing (AAS) with optimal rate and power allocation Airtime allocation based on local info. (rate and capacity) only Distributed AAS generally work with most kind of rate and power control.

12. Numerical results -Multicastscenarios • AAS works with multicast as well • The joint congestion control converges • AAS improves network utility • Optimal time-allocation at nodes can improveflow rates while saving power

13. Conclusions and future work • Formulated a joint rate, power and per-node airtime optimization problem for multicast wireless networks • Showed the concavity and convergence • Fully distributed AAS working with existing congestion control algorithms • Optimal airtime sharing improves the congestion control algorithms • Future work • Adaptive network schedule • Optimal rate and power allocation with sensor selection

14. Thank you