Resource Allocation for E-healthcare Applications

1. Resource Allocation for E-healthcare Applications QinghuaShen

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

3. 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

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

5. 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

6. 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

7. 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 Qmaxdoesn’t guarantee a Dmax

8. 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.

9. 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] MurtazaZafer and EytanModiano, 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.

10. 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.

11. 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.

12. 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

13. 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

14. 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

15. 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

16. 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

17. 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

18. 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

19. 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