Broadcast Information Dissemination 3/21/2004 Richard Yang

Outline Admin. and recap Broadcast information dissemination

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

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

Outline Admin. and recap Broadcast dissemination motivation

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: 2.304 Mbit/s (net 1.2 to 1.536 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

Examples for DAB Coverage Germany DAB World Coverage Map (January 2003) http://www.worlddab.org UK

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)

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?

Outline Admin. and recap Broadcast information dissemination motivation broadcast disk

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

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

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.

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

An Example 4 Rel_freq 2 1

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

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

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

Model Item 1 Item 2 Item M Client Client Server

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

Defining Mean Access Time of One Item 1 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

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

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

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

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

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.

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.

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

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:

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.

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

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

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.

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

Calculation

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

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

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

Backup Slides

An Example Showing that the Online Algorithm is not Optimal 1 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.