1. Broadcast Information Dissemination
3/21/2004
Richard Yang

2. Outline
Admin. and recap
Broadcast information dissemination

3. Recap Routing protocols “Traditional” routing Geographic routing
find a path from a source to a destination
“Traditional” routing
DSR, DSDV, AODV, TORA
Geographic routing
Greedy routing
GPSR
Geographic routing without location
A comparison of all routing protocols can be an interesting project
in particular, a comprehensive comparison of traditional routing and geographic routing

4. Motivation
The previous routing protocols assume unicast information dissemination
a source sends data to a destination
There are other communication patterns
broadcast (multicast)
one transmission serves multiple receivers
we consider only one hop in this course
concast
many senders send to a single receiver
likely to happen in sensor networks where the receiver is an information center
anycast
send to any one of the receivers

5. Outline
Admin. and recap
Broadcast dissemination
motivation

6. Examples Location aware computing Digital Audio Broadcast (DAB)
sending power: 6.1 kW (VHF, Ø 120 km) or 4 kW (L-band, Ø 30 km)
date-rates: Mbit/s (net 1.2 to Mbit/s)
sends multiple radio programs using same frequency
sends data items
Electronic Programme Guide (EPG)
traffic, weather, stock prices, sports, news items
Collections of HTML pages and digital images (Known as 'Broadcast Web Sites')
Slideshows, which may be synchronised with audio broadcasts

7. Examples for DAB Coverage
Germany
DAB World Coverage Map (January 2003) UK

8. Asymmetric Channel - High bandwidth down link
service provider
service users A
receiver B A
unidirectional
distribution
medium A B
receiver A A B
sender . A B A
receiver
- High bandwidth down link
- Low bandwidth up link (or no up link at all)

9. Flat Data Disk
- It is called data disk because you can think of the cyclic transmission as disk rotation
- Also called data carousel
Question: what are the problems of flat disk broadcast?

10. Outline Admin. and recap Broadcast information dissemination
motivation
broadcast disk

11. Broadcast Disks
Flat broadcast disk does not consider that different items have different access probabilities
The intuition is that we should broadcast “hot” items more often
Broadcast disk proposed by M. Franklin’s group in 1995

12. Constructing Broadcast Disks
Following convention, we assume that data items are “pages,”; that is they are of a uniform, fixed length
Order the pages from hottest (most popular) to coldest
Partition the list of pages into “disks”
each disk contains pages with similar access probabilities
Choose the relative frequency of broadcast for each disk
for example, given two disks, disk 1 could be broadcast three times for every two times disk 2 is broadcast, then rel_freq(1) = 3, rel_freq(2) = 2
all relative frequencies are integers

13. Constructing Broadcast Disks
Compute max_chunks as the Least Common Multiple (LCM) of all relative frequencies
Split disk i into chunks: num_chunks(i) = max_chunks / rel_freq(i) for the previous example, max_chunks = LCM(3, 2) = 6, num_chunks(1) = 6 / 3 = 2, num_chunks(2) = 6 / 2 = 3.

14. Constructing Broadcast Disks
Create broadcast program by interleaving chunks from different disks, where Cj,k is the k-th chunk of disk j

15. An Example 4
Rel_freq 2 1

16. Discussion
What are the problems with the broadcast disk discussion so far?

17. Outline Admin. and recap Broadcast information dissemination
motivation
broadcast disk
optimal broadcast schedule

18. Designing a Broadcast System: A General Model
Server has M information items to broadcast
Item i has length li
The probability that item i is requested in any request is pi (called demand probability or popularity)
for a large number of “requests” for the information items, pi of them are for item i
The arrival of requests to each item arrives randomly

19. Model
Item 1
Item 2
Item M
Client
Client
Server

20. Objectives Minimizing mean access time tune-in time
The weighted wait time to receive each item
The weight of item i is the demand probability of item I
tune-in time
The time to tune in to the broadcast until a receiver receives the item it waits for

21. Defining Mean Access Time of One Item1 1 1 1 1
Consider item 1
Assume in time T item 1 appears K times:
Assume a request for item 1 arrives randomly
Then the mean access time for item 1 is
The mean access time is minimum
if equal spacing, namely s1j = s1

22. Broadcast Multiple Items
spacing between two instances of Item 1 l0 8 4 10 7
Item 1
Item 2
Item 3
Item 1
Item 4
an instance of Item 1
an instance of Item 1

23. Overall Mean Access Time
Constraint on feasible broadcast schedule
where C is the bandwidth.

24. Minimizing Overall Mean Access Time
under the constraint
where C is the bandwidth, and bi = li/si.

25. Minimizing Overall Mean Access Time
Since Cauchy’s inequality:
where the equality is true iff xi = c yi

26. The Square-Root Rule
Given demand probability pi of each item i, the minimum overall mean access time is achieved when si of each item i is proportional to and inversely proportional to , assuming that instances of each item are equally spaced. That is,
This is a rule that has been rediscovered multiple times, for example in 2002 in the context of overlay networks.

27. An On-line Scheduling Algorithm
From Square-Root Rule,
Define:
Here Q is the current time, R(i) is the time at which an instance of item i was most recently transmitted.
Algorithm A: On-line Algorithm
Step 1: Find Gmax = max{G(i), 1 ≤ i ≤ M}.
Step 2: Choose k such that G(k) = Gmax. If find multiple k, select one of them randomly.
Step 3: Broadcast item k at time Q.
Step 4. R(k) = Q.

28. Illustration of the Algorithm
spacing
Item 1
Item 1
R(1) Q
Question: what is the complexity of the algorithm? How to reduce complexity?

29. On-line Algorithm with Bucketing
M items are divided into K buckets. m 1 m 1 m K
Bucket 1
Bucket 2
Bucket K
Let bucket j contains mj items. Define:
In this case, for optimality, the following condition holds:

30. On-line Algorithm with Bucketing
Algorithm B: On-line Algorithm with Bucketing
Step 1: Find Gmax = max{G(j), 1 ≤ j ≤ K}.
Step 2: Choose k such that G(k) = Gmax. If find multiple k, select one of them randomly.
Step 3: Broadcast item Ik at time Q, where Ik is the item at the front of bucket Bk.
Step 4: Move item Ik from the front of the bucket Bk to the end.
Step 5: R(Ik) = Q.

31. On-line Algorithm with Bucketing
To carry out bucketing algorithm, M items can be divided into K buckets in the following way:
Amin
Amax
Bucket BK
Bucket B1
Bucket B2

32. Evaluation: Demand Probability
Demand probabilities follow the Zipf distribution:
where θ is access skew coefficient. When θ = 0, Zipf distribution reduces to uniform distribution.

33. Performance Evaluation (Constant Item Length)
The curve of the online algorithm overlaps the optimal curve
The simulation results are within 0.5% of analytical results
Bucketing algorithm can significantly reduce time complexity with only small performance degradation.

34. Considering Transmission Errors
Suppose that uncorrectable errors occur in item i with probability ei.

35. Calculation

36. Broadcast with Transmission Errors
Thus in an optimal schedule
Online scheduling:

37. Client Cache Management
A client should not cache the item with its highest access probability
Pick the one with the minimum PIX value probability of access PIX = frequency of broadcast

38. Minimizing Tune-in Time
Broadcast schedule (index) so that receivers can go to sleep

39. Backup Slides

40. An Example Showing that the Online Algorithm is not Optimal1 2 1 2 1
In this case, the On-line scheduling algorithm produces
cyclic schedule (1,2,1,2,…). The overall mean access time
is 1.
On the other hand, cyclic schedule (1,2,2,1,2,2,…) has
overall mean access time 2.9/3 + 2ε/3 < 1.