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

Outline

MotivationWhen a VCR operation is performed,

how to deal with this condition?Dimensioning the number of channels in an interactive VoD systemAccuracy of approximation modelSimulation results

Service Model

In a interactive VoD system (true VoD)With both batching and piggybacking techniqueSupport VCR operations

• Ex: Pause, rewind (REW), and fast forward (FF)

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

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 h

andle VCR operationsNo provision a pool of channels for VCR operations

• No guarantee of QoS• No sources are unnecessarily wasted

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 VC

R operations– Arrival of requests is followed by a poisson process– Use Zipf distribution to show user preference

An Erlang B queue

Is a M/M/c/c queue1st ‘M’: arrival according to a Poisson process2nd ‘M’: exponential distribution of service time (Holding time)1st ‘c’: the number of servers2nd ‘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

To determine the arrival rateTwo user states

Playback and VCRThe 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

To determine the mean holding time (H)

Includes:The duration of the VCR operationResynchronization 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

The holding time h(n) (1/2)Assuming

the duration of a VCR operation is t secondsthe request is issued at the sth frame

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).

Accuracy of approximation modelTo 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 operationBut merges with original stream will be impossible

• Have a long holding time

overestimation

Simulation results

Issues:The number of users admitted into the systemThe probability of renegingThe percentage of VCR operations denied

For high loadsIn 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 poolU: degree of user interactivity

The number of users admitted into the system ◆For low loads (10 requests/min) ◆ For high loads (60 requests/ min)

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)◆ ◆

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

In high load conditionAverage of 25% of the channels being wasted

In low load conditionAverage of 45% of the channels being wasted

As the number of contingency channels increasesthe number of channels admitting new batches of users decreaseincreasing the probability of reneging decreasing the number of VCR operations denied.