Resource Allocation for E-healthcare Applications Qinghua Shen

content Intro: e-healthcare system Research issues Preliminary results conclusion

Intro: e-healthcare system Randomness of the requests Computing: Medical information processing Body channel Limited sensor energy Wban: Remote monitoring Emergency traffic support Wbans: Hospital information collection Mobility distributed

content Intro: e-healthcare system Research issues Preliminary results conclusion

Single sensor WBAN scheduling single sensor application Network model one PDA and one sensor with Pmax Time is partitioned into slots with length T a pilot of duration αT required for transmission. Two decisions made by the sensor at each time slot sleep decision s(i) Transmission decision b(i) Traffic and Channel Model A(i): a maximum Amax and Dmax h(i) : pathloss in power, bounded by minimum hmin and maximum hmax i.i.d, stationary and ergodic Energy Cost Model Queue Update Listening Transmission

Power vs. Delay trade-off Energy Efficient Approaches Opportunistic Transmission exploiting channel dynamics Sleep Scheduling Originate from sensor networks, reduce idle listening Delay requirements Worst case delay Guarantee Dmax deterministic delay requirement Average sense delay little’s law

Power vs. Delay trade-off Relationship between Energy and Delay single link Power-Rate relationship Shannon capacity formulation A practical approximation --monomial function The average power consumption Service rate delay relationship Queue: service process bµ(n) and the arrival rate A(n), service process is determined by transmission policy Q(n)=Q(n-1)+A(n) - bµ(n) Queue of a system is related to the delay Average Delay Worst Case Delay Qmax doesn’t guarantee a Dmax

Power vs. Delay trade-off Problem Formulation Power vs. Delay I (average sense delay [1]) Optimization Objective for V>0, the goal is to find the policy µ to minimize Define the minimal average power can be achieved as the power needed to serve average arrival rate with no delay consideration, denoted by , it’s the solution of the following problem with a policy Ψ(H) . minimize EP(H, Ψ(H)) subject to: E (Ψ(H)) The policy for no delay consideration doesn’t need to take current queue state into decision making. lower bound is proofed[1] and a drift policy achieves it [1] R. Berry and R. Gallager, “Communication over fading channels with delay constraints,” IEEE Trans. Information Theory, vol. 48, no. 5, pp. 1135–1149, 2002.

Power vs. Delay trade-off Problem Formulation Power vs. Delay II (Worst Case Delay ) BT problem: B unit of traffic needed to transmitted by the deadline T Continuous case, Markov Channel, monomial power rate function [2] formulation and solution system updating equation cost function and cost-to-go function solve the Hamilton–Jacobi–Bellman equation backwards to obtain the optimal control policy Discrete case, i.i.d channel [3] monomial: optimal policy Shannon: no closed form scheduling policy characteristics More opportunistically when deadline is far away less opportunistically when queue length is large Transmission policy [2] Murtaza Zafer and Eytan Modiano, Optimal Rate Control for Delay-Constrained Data Transmission over a Wireless Channel. IEEE Transactions on information theory, Vol. 54, No. 9, Sept. 2008. [3] J. Lee and N. Jindal, “Energy-efficient scheduling of delay constrained traffic over fading channels,” IEEE Trans. Wireless Communications, vol. 8, no. 4, pp. 1866–1875, 2009.

Single sensor WBAN scheduling Problem formulation 1) Lyapunov optimization theory[4] adopted why not DP: Curse of dimensionality characteristics of Lyapunov optimization decomposes a time average objective into objectives for each time slot capture the trade-off between different system performance metrics 2) Original Problem goal: average power consumption constraints: bounded delay, feasible rate [4] M. Neely, “Stochastic network optimization with application to communication and queueing systems,” Synthesis Lectures on Communication Networks, vol. 3, no. 1, pp. 1–211, 2010.

Single sensor WBAN scheduling Problem formulation 3) Worst-Case Delay Constraint Transform[5] Why? No direct link between maximum delay and maximum queue a virtual queue Z(t) with a virtual arrival rate Z(t) updates: Lemma: Suppose system is controlled so that Z(i) Zmax, Q(i) Qmax, for all i, for some positive constants Zmax, Qmax. Then all data in queue is transmitted with a maximum delay Dmax: Transform: from bounded delay to bounded queue length [5] M. Neely, A. Tehrani, and A. Dimakis, “Efficient algorithms for renewable energy allocation to delay tolerant consumers,” in Proc. IEEE SmartGridComm’ 10, pp. 549–554, 2010.

Single sensor WBAN scheduling Problem formulation 4) Transform using Lyapunov optimization why? Objectives for each time slot with illustration of the trade-off a. quadratic form Lyapunov function b. one-step Laypunov drift c. upper bound of the drift d. upper bound of the drift plus a weighted cost function New objectives: min Weighted cost function Logic of minimization minimizing the upper bound of the drift controls the delay minimizing cost function is to minimize the energy consumption

Single sensor WBAN scheduling Problem formulation Final problem Objectives: average of all possible states for each time nonlinear Control variables: two decision variables one binary one integer

Single sensor WBAN scheduling Algorithm design two step algorithm sleep scheduling Where , and is the expectation of minimum of Opportunistic Transmission maximal available transmission amount given current channel

Single sensor WBAN scheduling Performance Analysis delay performance Algorithm designed doesn’t guarantee non-positive drift define two conditions necessary for worst case delay guarantee Theorem 1. If above conditions hold, then deterministic upper bounds exist for actual queue and virtual queue as follows: Recall lemma Worst cast delay increase within power consumption performance Theorem 2. Given the minimal power consumption P* that the system can achieve, the average power consumption of our proposed algorithm Pave satisfies: Pave P* + C/V , where C is a constant, at the cost of a worst-case delay increases within O(V ). Stationary randomize policy

Single sensor WBAN scheduling simulation setup Body channel model suggested by IEEE 802.15 task group 6 under the frequency band 2.4GHz Wake up ratio: the fraction of time slots in which the sensor wakes up among the number of total time slots Parameters' Value

Single sensor WBAN scheduling Simulation results Data accumulation: for potential better channel Flat cliff: not in a very good channel condition Sharp cliff: in a good channel condition Delay growth can be bounded a linear function of weighting factor Larger weighting factor, poorer delay

Single sensor WBAN scheduling Simulation results The gap between power consumption of our algorithm and the optimal one can be bounded by a function of the inverse of weighting factor Smaller wakeup ratio, less power consumption Larger virtual arrival rate, smaller delay Larger virtual arrival rate, larger wakeup ratio

Conclusion and Future works A scheduling policy for single sensor WBAN application Address the energy delay trade-off problem for WBAN limited transmission power random traffic and channel worst case delay guarantee Propose a scheduling policy for the problem Utilize both sleep and opportunistic transmission for energy saving Achieve worst case delay Show trade-off between power consumption and delay