1. Data Broadcast in Asymmetric Wireless Environments Nitin H. Vaidya Sohail Hameed

2. SUBJECT OF THE PAPER – Mechanisms that efficiently decide what and when to transmit CHARACTERISTICS OF THE SYSTEM – Wireless communications (server - clients) – Asymmetric environment – Not explicit requests from the clients to server – Minimization of the wait time of clients ALSO COVERED – Environments with errors – Multiple number of Broadcast channels

3. METRICS USED TO EVALUATE THE PERFORMANCE – Access time – Tuning time CONTRIBUTIONS OF THE PAPER – Square root rule – Lower bound on the achievable access time – “on - line” Broadcast Scheduling algorithm – Modified “on - line” algorithm

4. PRELEMINARIES – Database with information Items – Time unit – M = Total number of items – l i = Length of item i – Broadcast cycle with N time units – Instance of an item – Schedule of Broadcast – Frequency of an item – Spacing

5. PRELEMINARIES Continued – Item Mean Access Time – Demand Probability – Overall Mean Access time

6. CONSTRUCTION OF BROADCAST SCHEDULING ALGORITHMS

7. MAPPING DEMAND PROBABILITIES TO ITEM FREQUENCIES Lemma 1: The Broadcast Schedule with minimum Overall Mean Access Time results when the instances of each item are equally spaced Theorem 1 (Square Root Rule): Given the Demand Probability of each item i, the minimum Overall Mean Access Time, t, is achieved when frequency of each item i is proportional to and inversely proportional to, assuming that instances of each item are equally spaced. That is

8. BROADCAST SCHEDULING ALGORITHMS Algorithm A: ON - LINE algorithm: Define Step 1: Determine maximum F(i) over all items i,. Let denote the maximum value of F(i). Step 2: Choose item i such that F(i) =. If this equality holds for more than one item, choose any one of them arbitrarily. Step 3: Broadcast item i at time Q. Step 4: = Q

9. EXAMPLE A: = 1/2= 3/8= 1/8= 1= 2= 4 = 12.5= 9.18= 0.5 EXAMPLE B: ==1= 0.2 + ε= 1 - On - line Algorithm A: Schedule (1,2), t = 1 Schedule (1,2,2), t = 2.9/3 +2ε/3 < 1

10. ON- LINE ALGORITHM B WITH BUCKETING Complexity of algorithm A O(M) Complexity of algorithm B O(k) Divide the database into k buckets Bucket i contains items Average Demand Probability of items in bucket i Average Length of items in bucket i

11. ALGORITHM B Define Step 1: Determine maximum G(i) over all buckets i,. Let denote the maximum value of G(i). Step 2: Choose a bucket i such that G(i) =. If this equality holds for more than one bucket, choose any one of them arbitrarily. Step 3: Broadcast item I j from the front of the bucket B i at time Q. Step 4: Dequeue item I j at the front of the bucket B i and enqueue it at the rear of B i. Step 5: = Q

12. Optimal Mean Access time Heuristic that determines membership of each item into buckets – Calculate R min =, R max = – Divide δ = R min - R max into k equally sized sub - intervals – Calculate for all items. Item i is into bucket j B j if

13. Effect of Transmission Errors on Scheduling Strategy – E(l) – Overall Mean Access Time Theorem 2: Given that the probability of occurrence of uncorrectable errors in an item of length l is E(l), the overall mean access time is minimized when

14. Multiple Broadcast Channels Divide the available bandwidth into c channels Define properly On - line algorithm for channel h, 1 h c Step 1: =, 1 i M Step 2: Determine maximum F(j) over all items j. Let F max denote the maximum value of F(j). Step 3: Choose i such that F(i)= F max. If this equality holds for than one item, choose any one of them arbitrarily. Step 4: Broadcast item i on channel h at time Q. Step 5: Set = Q

15. A heuristic for initializing values Step 1: Set time=1 Step 2: For every item in database { Step 3: For every item { Step 4: if { Step 5: Step 6: time=time+ } Step 7: Step 8: = time Step 9: time=time+ Step 10: For } Step 11: Find,,, by rotating the values of by an amount of

16. Performance Evaluation Demand Probability Distribution Zipf distribution for various values of θ

17. Length Distribution Uniform Length Distribution Increasing Length Distribution Decreasing Length Distribution Length Distribution

18. Performance evaluation in the Absence of Uncorrectable Errors Increasing Length Distribution

19. Decreasing Length Distribution

20. Random Length Distribution

21. Performance evaluation in the Presence of Uncorrectable Errors Increasing Length Distribution

22. Decreasing Length Distribution

23. Performance with Multiple broadcast Channels Uniform Length Distribution