1. Presented by Jason L.Y. Lin
Modelling and Performance Analysis of the Distributed Scheduler in IEEE Mesh Mode
Min Cao, Dept. Electrical & Computer Engineering
University of Illinois, Urbana-Champaign
Wenchao Ma, Microsoft Research Asia
Qian Zhang, Microsoft Research Asia
Xiaodong Wang, Dept. Electrical Engineering Columbia University
Wenwu Zhu, Intel China Research Center
Proceedings of the 6th ACM international symposium on Mobile
ad hoc networking and computing MobiHoc '05
Presented by Jason L.Y. Lin
2018/12/4
OPLab, Dept. of IM, NTU

2. Outline Introduction Background on IEEE 802.16 Mesh mode
Modelling and Performance Analysis
Simulation Results
Conclusions and Future Work
2018/12/4
OPLab, Dept. of IM, NTU

3. Introduction (1/3) IEEE 802.16 MAC has two mode
- point-to-multipoint (PMP) mode
- multipoint-to-multipoint (mesh) mode
In the mesh mode
- nodes are organized in an ad-hoc fashion
- there still be certain nodes that provide the BS function
2018/12/4
OPLab, Dept. of IM, NTU

4. Introduction (2/3)
IEEE has two mechanisms to schedule the data transmission in mesh mode
- centralized scheduling
- distributed scheduling
In centralized scheduling
- all the control and data packets need to go through the BS
- the scheduling procedure is simple
- but the connection setup delay is long
2018/12/4
OPLab, Dept. of IM, NTU

5. Introduction (3/3) In distributed scheduling
- every node competes for channel access using a pseudo-random election algorithm based on the scheduling information of the two-hop neighbors
- exhibits better flexibility and scalability
- but distributed channel access control is more complex
2018/12/4
OPLab, Dept. of IM, NTU

6. Outline Introduction Background on IEEE 802.16 Mesh mode
Modelling and Performance Analysis
Simulation Results
Conclusions and Future Work
2018/12/4
OPLab, Dept. of IM, NTU

7. Background on IEEE 802.16 Mesh mode
the difference between and
is a slotted system, and all transmissions must be synchronized
uses a three-way handshaking to set up connection before data transmission
- the control channel and data channel are separated in
- in , nodes can reserve multiple slots for the following packets without exchanging control message again
2018/12/4
OPLab, Dept. of IM, NTU

8. IEEE 802.16 Distributed Scheduling Algorithm (1/6)
IEEE distributed scheduling behavior
- the control message and data packet are allocated in different time slots in a frame
- there is no contention in the data time slots
- employs a request/grant/confirm three-way handshaking procedure
2018/12/4
OPLab, Dept. of IM, NTU

9. IEEE 802.16 Distributed Scheduling Algorithm (2/6)
2018/12/4
OPLab, Dept. of IM, NTU

10. IEEE 802.16 Distributed Scheduling Algorithm (3/6)
The Scheduling message, MSH-DSCH, contains the schedule and data subframe allocation information of the neighborhood.
- NextXmtMx and XmtHoldoffExponent
The transmission time for a station is an aggregate of some sequential transmission opportunities called eligibility interval
The eligible interval length for a node is
transmission opportunities.
2018/12/4
OPLab, Dept. of IM, NTU

11. IEEE 802.16 Distributed Scheduling Algorithm (4/6)
After one eligibility interval, a station must hold off at least
One station sets the first transmission slot after the holdoff time as the temporary next transmission opportunity
2018/12/4
OPLab, Dept. of IM, NTU

12. IEEE 802.16 Distributed Scheduling Algorithm (5/6)
2018/12/4
OPLab, Dept. of IM, NTU

13. IEEE 802.16 Distributed Scheduling Algorithm (6/6)
Pseudo-random function
mixing value : with the current node ID and the slot number as the inputs
The channel contention result is correlated with the total node number, exponent value and network topology.
Assumes the transmit time sequences of all the nodes in the control subframe form statistically independent renewal processes
2018/12/4
OPLab, Dept. of IM, NTU

14. Outline Introduction Background on IEEE 802.16 Mesh mode
Modelling and Performance Analysis
Simulation Results
Conclusions and Future Work
2018/12/4
OPLab, Dept. of IM, NTU

15. Modelling and Performance Analysis
Model and approach
Two scenario
- Collocated scenario
* identical holdoff time
* nonidentical holdoff exponents
- General topology scenario
Performance metrics estimation
2018/12/4
OPLab, Dept. of IM, NTU

16. Model and Approach (1/4) Assumptions
(1) the counting process, , of each node eventually reaches its steady state and the intervals are i.i.d., that is, forms a stationary and ergodic renewal process
(2) the renewal processes of different nodes are mutually independent at their steady states
(3) when all the processes reach their steady states, we can assume that all the processes are initiated at t=-∞ and the time of renewal events of different processes are uncorrelated
2018/12/4
OPLab, Dept. of IM, NTU

17. Model and Approach (2/4)
2018/12/4
OPLab, Dept. of IM, NTU

18. Model and Approach (4/4)
：the expected number of competing nodes in slot s for the
node of interest
The probability that this node wins the slot is
So the p.m.f. of S is
2018/12/4
OPLab, Dept. of IM, NTU

19. Collocated Scenario - Indentical Holdoff Exponent (1/15)
In collocated scenario
- all nodes are one-hop neighbors of each other
Identical Holdoff Exponent
- assume equal holdoff exponents
- hence when the node are collocated, the transmission interval has the same distribution
2018/12/4
OPLab, Dept. of IM, NTU

20. Collocated Scenario - Indentical Holdoff Exponent (2/15)
2018/12/4
OPLab, Dept. of IM, NTU

21. Collocated Scenario - Indentical Holdoff Exponent (3/15)
LEMMA 1. (Limiting Distribution of Excess Time)
Let τ be the renewal interval, the limiting distribution of the
excess time is
for fixed , where and is an indicator function.
By the stationary and ergodic assumption,
2018/12/4
OPLab, Dept. of IM, NTU

22. Collocated Scenario - Indentical Holdoff Exponent (4/15)
2018/12/4
OPLab, Dept. of IM, NTU

23. Collocated Scenario - Indentical Holdoff Exponent (5/15)
Figure 4:T he interval τ between two successive transmissions.
2018/12/4
OPLab, Dept. of IM, NTU

24. Collocated Scenario - Indentical Holdoff Exponent (6/15)
By the assumption that the renewal process is stationary and that the distributions of are identical, we can simply denote as .
2018/12/4
OPLab, Dept. of IM, NTU

25. Collocated Scenario - Indentical Holdoff Exponent (7/15)
2018/12/4
OPLab, Dept. of IM, NTU

26. Collocated Scenario - Indentical Holdoff Exponent (8/15)
2018/12/4
OPLab, Dept. of IM, NTU

27. Collocated Scenario - Indentical Holdoff Exponent (9/15)
2018/12/4
OPLab, Dept. of IM, NTU

28. Collocated Scenario - Indentical Holdoff Exponent (10/15)
denote as the number of nodes (among N-1 neighbors) which compete with node k in slot s.
Denote as
The expected number of nodes competing with node k in slot s is
2018/12/4
OPLab, Dept. of IM, NTU

29. Collocated Scenario - Indentical Holdoff Exponent (11/15)
The competing nodes in slot s for node k is
Substituting (9) into (1) we get
2018/12/4
OPLab, Dept. of IM, NTU

30. Collocated Scenario - Indentical Holdoff Exponent (12/15)
we make a further approximation that
2018/12/4
OPLab, Dept. of IM, NTU

31. Collocated Scenario - Indentical Holdoff Exponent (13/15)
2018/12/4
OPLab, Dept. of IM, NTU

32. Collocated Scenario - Indentical Holdoff Exponent (14/15)
2018/12/4
OPLab, Dept. of IM, NTU

33. Collocated Scenario - Indentical Holdoff Exponent (15/15)
Substitute and into (17)
2018/12/4
OPLab, Dept. of IM, NTU

34. Collocated Scenario - Nondentical Holdoff Exponents (1/9)
2018/12/4
OPLab, Dept. of IM, NTU

35. Collocated Scenario - Nondentical Holdoff Exponents (2/9)
2018/12/4
OPLab, Dept. of IM, NTU

36. Collocated Scenario - Nondentical Holdoff Exponents (3/9)
2018/12/4
OPLab, Dept. of IM, NTU

37. Collocated Scenario - Nondentical Holdoff Exponents (4/9)
2018/12/4
OPLab, Dept. of IM, NTU

38. Collocated Scenario - Nondentical Holdoff Exponents (5/9)
Assume that are geometrical distributed, that
is, assume
2018/12/4
OPLab, Dept. of IM, NTU

39. Collocated Scenario - Nondentical Holdoff Exponents (6/9)
2018/12/4
OPLab, Dept. of IM, NTU

40. Collocated Scenario - Nondentical Holdoff Exponents (7/9)
2018/12/4
OPLab, Dept. of IM, NTU

41. Collocated Scenario - Nondentical Holdoff Exponents (8/9)
2018/12/4
OPLab, Dept. of IM, NTU

42. Collocated Scenario - Nondentical Holdoff Exponents (9/9)
2018/12/4
OPLab, Dept. of IM, NTU

43. General topology scenario (1/3)
2018/12/4
OPLab, Dept. of IM, NTU

44. General topology scenario (2/3)
2018/12/4
OPLab, Dept. of IM, NTU

45. General topology scenario (3/3)4 1 3 3 2 4 1 2 1 2 3
2018/12/4
OPLab, Dept. of IM, NTU

46. Performance metrics estimation
Let denote the time node A need to accomplish a three-way handshaking with node B.
2018/12/4
OPLab, Dept. of IM, NTU

47. Performance metrics estimation
Assumptions
- the renewal process of node A and B have run for a long time
follows a limiting distribution as the excess time
when , we can assume that
2018/12/4
OPLab, Dept. of IM, NTU

48. Performance metrics estimation
where α is a compromising factor.
is a good choice for the identical holdoff exponent
case and for the nonidentical holdoff exponents
case
2018/12/4
OPLab, Dept. of IM, NTU

49. Performance metrics estimation
2018/12/4
OPLab, Dept. of IM, NTU

50. Outline Introduction Background on IEEE 802.16 Mesh mode
Modelling and Performance Analysis
Simulation Results
Conclusions and Future Work
2018/12/4
OPLab, Dept. of IM, NTU

51. Simulation Results ns-2 simulator - network controller
- scheduling controller
- data channel component
The set of possible exponent values is {0,1,2,3,4}
2018/12/4
OPLab, Dept. of IM, NTU

52. Transmission interval
Figure 9:Simulation and analytical results on the expected transmission intervals for the identical exponent
2018/12/4
OPLab, Dept. of IM, NTU

53. Transmission interval
Figure 10:Simulation and analytical results on the expected transmission intervals for the nonidentical exponent
2018/12/4
OPLab, Dept. of IM, NTU

54. Three-way Handshaking Time
Figure 11:Simulation and analytical results on the three-way handshaking time for the identical exponent case
2018/12/4
OPLab, Dept. of IM, NTU

55. Three-way Handshaking Time
Figure 12:Simulation and analytical results on the three-way handshaking time for the nonidentical exponent case with N = 10
2018/12/4
OPLab, Dept. of IM, NTU

56. Three-way Handshaking Time
Figure 13:Simulation and analytical results on the three-way handshaking time for the nonidentical exponent case with N = 100
2018/12/4
OPLab, Dept. of IM, NTU

57. General Topology Scenario
Table 1:Simulation and analytical results on the expected transmission intervals for the general topology
2018/12/4
OPLab, Dept. of IM, NTU

58. Outline Introduction Background on IEEE 802.16 Mesh mode
Modelling and Performance Analysis
Simulation Results
Conclusions and Future Work
2018/12/4
OPLab, Dept. of IM, NTU

59. Conclusions and Future Work (1/2)
The channel contention result is correlated with the total node number, exponent value and network topology.
developed methods for estimating the distributions of the node transmission interval and connection setup delay
also shed some light on the data subframe reservation scheme
2018/12/4
OPLab, Dept. of IM, NTU

60. Conclusions and Future Work (2/2)
- to propose such a reservation scheme taking into account the tradeoff between system resource utilization and the connection QoS requirements
2018/12/4
OPLab, Dept. of IM, NTU

61. Thanks for your listening
2018/12/4
OPLab, Dept. of IM, NTU