optimal Scheduling Algorithms for ad hoc Wireless Networks

1. optimal Scheduling Algorithms for ad hoc Wireless Networks Siva Theja Maguluri Qualifying Exam

2. Setting • Adhoc Wireless Network – Interference Graph • Time is slotted – Packets are of same size • Schedule – Binary Vector – Independent Set 0 0 1 0 1 0 1 0 1 0 0

3. Throughput Optimality • Consider the Co(M[L])- Convex hull of Maximal Schedules • Any vector strictly dominated by this is feasible (Capacity Region) • Throughput Optimality • Algorithm based only on current queue length and not arrival rate

4. Scheduling Algorithms • Max Weight (Tassiulas & Ephremides) • Throughput Optimal • Excellent Performance • High complexity; Centralized Implementation • Q-CSMA • Each node tries to transmit after an exponential back-off time with rate proportional to its queue length (Jiang and Walrand) • Distributed Implementation; Asynchronous • Throughput Optimal • Poor Delay performance

5. Longest Queue First (LQF) • Approximate Greedy implementation of Max Weight - Greedy Maximal Scheduling aka LQF • Greedily try to add longest queue link in the schedule • Low complexity • Distributed Implementation of LQF • Data Slot and Control Slot Control Slot Data Slot

6. Longest Queue First • Throughput optimal under a topological condition called local pooling (Dimakis and Walrand) • Local pooling No vector in Co(M[L]) strictly dominates another • Works well for practical networks • QoS Performance of Queue Lengths? • Variable Packet Sizes – Many Practical Scenarios like 802.11 ?

7. Large Deviation Optimality • Second Order Performance Measure • Probability of Buffer Overflow of the maximum queue • Largest set of allowed rates under upper bound on probability of buffer overflow • To find a schedule with the Largest Large Deviation Exponent

8. Large Deviation Optimality • Bernoulli Arrivals with mean p • If q is empirical mean, the LD cost for that event is D(p||q) • Overflow happens along the path with the lowest cost • Reduces to deterministic problem of finding minimum cost path to overflow • Further reduced to one dimension by considering the path of a Lyapunov function

9. Large Deviation optimality of LQF • Greedily try to minimize increase of the Lyapunov function (Venkataraman and X Lin ‘09) • Use max as Lyapunov Function • Under localpooling, LQF is large deviation optimal for overflow of max queue length • Compare with any other algorithm

10. LQF with variable packet sizes • Variable Packet Sizes – Exponential Distribution • Discrete time to Continous time • Add longest queue in the schedule whenever possible • Exponential wait time – required ? • Throughput Optimal

11. Further Work • Is the wait period required? • Is Asynchronous LQF large deviation optimal?

12. Conclusion • Asynchronous version of LQF, with small wait is proved to be throughput optimal • To investigate if it works without the delay • LQF is found to be Large Deviation Optimal in the synchronous case • To find if asynchronous LQF is also Large Deviation Optimal