1. DRAND: Distributed Randomized TDMA Scheduling for Wireless Ad-Hoc Networks
Injong Rhee
(with Ajit Warrier, Jeongki Min, Lisong Xu)
Department of Computer Science
North Carolina State University

2. CSMA Protocols When are they useful? When are they a bad idea?
Can TDMA be a better solution?
Why? Why not?

3. Static Channel Assignment Problem (for stationary networks)
Finding a time slot for each node such that any two nodes within an interference range do not have the same transmission time slot.
G=(V,E), V: set of nodes, E: set of edges
Edge e =(u,v) is exists iff u and v can talk A B C

4. TDMA Scheduling - Example (Broadcast: 2 hop interference)
Radio Interference/Communication Map C D B F
Need to clarify:
- Radio ranges usually never well defined
- Assuming communication range = interference range E E 2 3 A A C D C D 1 1 B F B F
Input Graph
TDMA Slot Assignment

5. Performance goals for TDMA Scheduling
Efficient: Use as few slots as possible. More slots would imply less spatial reuse and longer delay.
Distributed: The algorithm must not require global information or global coordination of any kind.
Simple: Low Time/Message Complexity. The algorithm must be simple to implement.

6. RAND by Ramanathan [Infocom97]
TDMA scheduling is a coloring problem.
Hence Optimal TDMA scheduling is NP-Hard.
RAND: So a heuristic, but centralized algorithm:
Total-order all the nodes in a random order.
Assign to each node in that order the minimum color that has not been been assigned to its two-hop neighbors in the graph.
Gives “pretty” good efficiency: at most d+1 colors, but mostly much fewer colors (d is the number of conflicting neighbors).

7. DRAND: Distributed RAND
Performance
as efficient as RAND
The first distributed version of RAND
Simple, Running time/msg complexity O(d) – d is the max number of contenders (two-hop nodes)
Key assumption
Each node knows its neighbors.
Packet losses are possible
No time synchronization is required.
Key idea
When a node is selecting a color, it ensures that no other neighboring nodes are selecting.

8. DRAND: How it works Algorithm runs by rounds
With some probability, node C sends request message if C does not have time slot.
Neighbor B sends grant(containing its one-hop neighbors’ slot info) if it is not aware of any of B’s neighbors that has sent a request. C
Request A B
Grant C A B

9. DRAND: How it works (cont.)
If and when C receives grant messages from its entire one-hop neighbors,
it chooses the minimum of the time slots that have not been taken by its two-hop neighbors, and then broadcast a release message.
Release C A B

10. Main Idea
Each transmitter ensures that interferer is at least three hops away from it
I.e., interferer is at least two hops away from the intended receiver A B C D

11. DRAND: How it works (Cont.)
When a node has granted to another node, it sends back a reject.
If a node receives reject or timeout, then it sends release (but with failure indication).
Reject C D
Grant A B
Release C A B

12. DRAND – Complexity Results
Running time is O(d) – d is the maximum number of nodes within two hops for the entire graph.
Message complexity is O(d).
Achieves the same slot efficiency as RAND

13. DRAND Experimental Evaluation Methods
Verification of analysis
DRAND performance overhead on a small scale mote test bed
DRAND performance comparison with existing TDMA assignment schemes

14. Experimental Setup – Single/Multiple Hop
Single-Hop Experiments:
Mica2 motes equidistant from one node in the middle.
All nodes within one-hop transmission range.
Tests repeated 10 times and average/standard deviation errors reported.
NS simulation

15. DRAND – Time Complexity
Running Time
One Hop Mica2 Experiment
Multi Hop NS2 Experiment
Need to mention that run time curve is quadratic since the message delays are not a constant, but increase linearly with neighborhood size, as seen in next slide
Number of rounds is linear
Num of neighbors
Rounds

16. DRAND – Maximum Number of Slots
Y = d
Need to mention that actual number of slots assigned is much less than neighborhood size.
Maximum number of slots in the multi hop NS simulation

17. Experimental Setup - Testbed
40 Mica2 sensor motes in Withers Lab.
Wall-powered and connected to the Internet via Ethernet ports.
Programs uploaded via the Internet, all mote interaction via wireless.
Links vary in quality, some have loss rates up to 30-40%.
Asymmetric links also present.

18. DRAND – Time and Energy for each phase
Operation
Average Running Time
Average Energy Cost
Neighbor Discovery
30s
0.732J
DRAND Assignment
194.38s
4.88J
Slot Dissemination
60s
1.33J
Total Energy (6.942J) is 0.02% of the total battery capacity of a node with 2500mAh and 3V.

19. Comparison with existing TDMA schemes: Throughput/Loss Rate
DRAND
RANDOM
SEEDEX
DRAND
DRAND
DRAND performs pure TDMA, so has lowest loss rate
Some perceptible loss rate is due to time sync errors
SEEDEX has only slightly better throughput than RANDOM
SEEDEX transmission probability P chosen to be which is optimal for neighborhood size of 21, also test for other values of P, but did not affect the result by much, so do not show the results
Throughput
Loss Rate

20. DRAND - Adapting to Changes
As new nodes join or topology changes, it requires only local adjustment.
We measure the overhead as nodes restart after crash.

21. Conclusion DRAND is a distributed implementation of RAND
Efficiency, Running time and Msg Complexity : O(d)
Can also be applicable to other problems such as
ID assignments
Frequency channel assignment.

22. Experimental Topologies for Verification of Analysis
Report DRAND running time, message complexity, maximum number of slots assigned for each run.
One Hop Mica2 Experiments
20 Mica2 motes within radio range of each other.
Multi-Hop NS2 Simulations
nodes placed randomly on a 300x300 grid, creating node densities between 5 and 60.
Radio range 40m
Bandwidth 2Mbps
MAC

23. Support Slides

24. Performance Comparison with Existing Schemes
Compare:
Algorithm Complexity (on NS2 topology)
Number of slots assigned
Run time
Number of messages transmitted
Transmission efficiency (on two-hop topology)
How well other schemes utilize the TDMA slots assigned to them

25. Number of Slots Assigned
FPRP (Five Phase Reservation Protocol)
Series of reservation/transmission phases
For each time slot of transmission phase, run five phases for a number of times (cycles) to pick a winner
FPRP-x indicates that we run FPRP for x cycles to determine the ownership of each slot
More cycles => more nodes get a slot, but correspondingly increases running time

26. Algorithm Complexity – FPRP and DRAND
By increasing number of cycles, we can get less number of message transmissions, and smaller frame size, but the running time increases
For ad-hoc networks, it may be difficult to find the optimal number of cycles required
Maximum Slot Number
Message Transmissions
Run Time

27. Transmission Efficiency
SEEDEX:
Nodes send in a slot with probability P.
Random number generator seeds of every node in two hop neighborhood known, through message passing
Hence each node knows the number of nodes eligible to send in a slot = C
Send in that slot with probability 1/C
Randomized Slotting:
At the beginning of the frame, select slot randomly
Transmit

28. Two Hop Mica2 Topology for Transmission Efficiency Experoments1 11 2 12
Sink 3 13
20 nodes, 10 clusters each
Chosen from lower left of the mote test bed, with sink node as 36
Nodes transmit data to sink, throughput and loss rate measured at sink 10 20

29. Interference in Wireless Networks
Primary Interference
A station cannot transmit/receive at the same time
Secondary Interference
Two stations within radio range cannot transmit at the same time (single-hop interference)
Two stations within radio range of a common node will cause collision if they transmit at the same time (hidden terminal problem)

30. Scheduling in Wireless Networks
Broadcast Scheduling
The stations themselves are scheduled
The transmission of a station must be received collision-free by all its one-hop neighbors
Link Scheduling
The links between stations are scheduled
The transmission of a station must be received collision-free by one particular neighbor.

31. Announcements G=(V,E), V: set of nodes, E: set of edges
Finding a time slot for each node such that any two nodes within an interference range do not have the same transmission time slot.
G=(V,E), V: set of nodes, E: set of edges
Edge e =(u,v) is exists iff u and v can hear each other. A B C

32. Comparison with CSMA ZMAC [Sensys05]. A hybrid of CSMA and TDMA
Throughput
ZMAC [Sensys05].
A hybrid of CSMA and TDMA
High throughput
Highly fair (reduce a lot of location and topology dependency)
Implemented over IEEE
ZMAC
CSMA
Num of Contenders
ZMAC
Fairness
CSMA
Num of Contenders