1. Dimensioning the Capacity of True Video-on-Demand Servers Nelson L. S. da Fonseca, Senior Member, IEEE, and Hana Karina S. Rubinsztejn IEEE TRANSACTIONS ON MULTIMEDIA, OCTOBER 2005

2. Outline Motivation When a VCR operation is performed, how to deal with this condition? Dimensioning the number of channels in an interactive VoD system Accuracy of approximation model Simulation results

3. Service Model In a interactive VoD system (true VoD) With both batching and piggybacking technique Support VCR operations Ex: Pause, rewind (REW), and fast forward (FF)

4. Motivation Problems: When a VCR operation is performed become unsychronized with its multicast group How to handle these events? Goals: maintain Qos for VCR operations Minimize the number of requests which denied a VCR operation

5. When a VCR operation is performed Will become unsychronized with its multicast group Require a private channel to support, until resynchronization with another stream Considerations: Reservation of a pool of channels for VCR operations Assure the VCR operations will not be denied Resources are unnecessarily wasted A batch stream is admitted if there are enough channels to handle VCR operations No provision a pool of channels for VCR operations No guarantee of QoS No sources are unnecessarily wasted

6. Dimensioning the number of channels in a interactive VoD system Characteristics: The size of channels for VCR operators are changed When a batch of users is admitted into, or leaves the system How to determine the number of reserved channels? Use an Erlang B queue Minimize the probability of rejection of requests for VCR operations –Arrival of requests is followed by a poisson process –Use Zipf distribution to show user preference

7. An Erlang B queue Is a M/M/c/c queue 1 st ‘ M ’ : arrival according to a Poisson process 2 nd ‘ M ’ : exponential distribution of service time (Holding time) 1 st ‘ c ’ : the number of servers 2 nd ‘ c ’ : the limit on the clients in the queue How to determine the number of reserved channels? The flowchart is: arrival rate The number of servers Required channels

8. To determine the arrival rate Two user states Playback and VCR The mean arrival rate of VCR requests is : The mean arrival rate of VCR requests : Number of users performing VCR operators : rate of VCR requests per user : probability of a user being in the playback state

9. To determine the mean holding time (H) Includes: The duration of the VCR operation Resynchronization with another stream In this paper, the unsynchronized stream merge with its original stream The mean holding time is : the holding time of a channel per VCR operation given that n operations are issued during a video display : is the probability of a user requesting n VCR operations during the video display

10. The holding time h(n) (1/2) Assuming the duration of a VCR operation is t seconds the request is issued at the sth frame

11. The holding time h(n) (2/2) :Holding time of a channel conditioned only on the frame position :maximum duration of an operation op which can occur at the sth frame :probability density function for the duration of operation op, :is the probability of any specific type of VCR operation (PAUSE, FF, or REW).

12. Accuracy of approximation model To vary the mean arrival rate, different values of and were chosen = number of VCR operations issued per user varying from 50 to 2000 and varying from of 1 to 10 The higher the is, the closer the estimated value is to the maximum, and then Increases the chances that a request for a VCR operation But merges with original stream will be impossible Have a long holding time overestimation

13. Simulation results Issues: The number of users admitted into the system The probability of reneging The percentage of VCR operations denied

14. For high loads In a medium to high degree of interactivity The different between a system with no pool and with a reserved pool is larger than when low loads are involved WC: with a contingency pool U: degree of user interactivity The number of users admitted into the system ◆ For low loads (10 requests/min) ◆ For high loads (60 requests/ min)

15. The probability of reneging in a system with no pool is always less than with a reserved pool The probability of reneging ◆ For low loads (10 requests/min) ◆ For high loads (60 requests/min)

16. The percentage of VCR operations denied ◆ For low loads (10 requests/min) ◆ For high loads (60 requests/ min)

17. In high load condition Average of 25% of the channels being wasted In low load condition Average of 45% of the channels being wasted As the number of contingency channels increases the number of channels admitting new batches of users decrease increasing the probability of reneging decreasing the number of VCR operations denied.

18. Batching (1993) 0t1t1 t2t2 t3t3 Client requests time

19. piggybacking merged stream t0t0 t1t1 t2t2 time Media file position