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

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

Existing Congestion Control Originally, wired networks rate is the only variable to maximize network utility with fixed link capacity 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 Congestion Control Via Network Utility Maximization Maximize the network utility Utility = U(flow rates) So far, Congestion Control = Joint optimization (rate, power) (Kelly, Low) (Chiang)

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

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

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 2. Capacity for a transmission (n,f) One parent broadcast to multiple children Bottleneck child defines capacity Capacity of (3,1) = 5 1. (n,f) one multicast transmission C=5C=10 C(3,1)=5 Something special with multicast

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

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

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

The capacity function C n,f (P) is concave –The Hessian matrix of C n,f < 0 The capacity function α n,f C n,f (P) is concave –Relative entropy –Preserves the convexity For any given vector V Concavity of POWER-TIME H is definite negative

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

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

Numerical results -Multicast scenarios AAS works with multicast as well The joint congestion control converges AAS improves network utility Optimal time-allocation at nodes can improve flow rates while saving power

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 Conclusions and future work

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