1. On G-network and resource allocation in multimedia systems 報告者 : 王敬育

2. The multimedia server system strict timing requirements Large database of multimedia documents is stored at a centralized server High-speed communication network Small latency & constant transfer rate Multicasting Batching schemes

4. Modeling and mathematical preliminaries Consider a database: M : video documents Λ : user requests arrive as Poisson process rate : the probability of a user chooses to view document i, 0< <1 and : = Λ, the customer join queue i

6. Round-Robin scheduling of the multimedia server(1) L i : length of a service of queue i, L i = L 1 i M D : inspection frequency parameter The RR scheme : a list of available servers and a pointer to queue i, start at t = rD, r 0 The next available server inspects the queues in the order i+1,…M,1…i-1,i

7. If all the queues were found empty, then the server remains idle and starts another circular inspection of the queues as time t = (r+1)D

9. Round-Robin scheduling of the multimedia server(2) : the steady state probability that the jth queue is non-empty : the expected delay between visit to queue i i : total average service time perceived at the ith queue, i =, and the service rate is i = [ i ]

10. Round-Robin scheduling of the multimedia server(3) The calculation of the queue length distribution for each document : our queuing system is a special case of a product form G-network. In particular, when there are n i requests in queue i,the queue length can, Increase (with rate ) to (n i+ 1),due to arrive of a positive customer Decrease (with rate λ i ) to (n i- 1), due to arrive of a negative customer that ‘kills’ a single positive customer Decrease to zero (with rate μ i ),due to arrival of a negative customer, that kills all the positive customer in the queue

11. Round-Robin scheduling of the multimedia server(4) p(n i ) : the steady state probability for n i requests in queue i For n i > 0 the global balance equation for p(n i ) is

12. Round-Robin scheduling of the multimedia server(5) The solution to this system of equations can be written as :

13. Multimedia scheduling and the resource allocation problem(1) assignment of a fixed portion of the server capacity to each of the queues

14. Multimedia scheduling and the resource allocation problem(2) the implementation of LRR consists of two phases: 1.Preprocessing phase : find an efficient allocation of server capacity to the M queues (DP) 2.Scheduling phase : for i =1…M, let L i denote the length of document i, schedule queue i at time instances rD i, r ≥ 0, where D i = L i /N i, by the algorithm RR

15. T : waiting an amount of time given by the wait threshold