1. Resource Allocation for E-healthcare Applications
Qinghua Shen

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 Qmax doesn’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] 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
[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 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