Continuous Media Storage and Retrieval - Scalable Continuous Media Streaming Systems - page 47

where i denotes the i th request in a service round; t seek and t seek are the seek time and rotational
latency incurred in serving request i ; and t end

seek is the time to position the disk head to the last
track to prepare for the next scan. We will use this generic diskmodel for capacity dimensioning
in the next section.

3.2.2 Capacity Dimensioning
The goal of capacity dimensioning is to determine the maximum number of concurrent me-
dia streams that can be sustained with deterministic performance guarantee so that proper
admission control can be performed to prevent system overload. Consider a system with a
homogeneous media bit-rate of R bytes per second and a constant request size of Q bytes.
Using double buffering as shown in Figure 3.3, data blocks retrieved in a disk service round
will be transmitted in the next round at the media bit-rate R . In other words, the retrievals in
a service round must be completed within a duration of Q / R seconds or else the transmission
will be delayed, possibly leading to playback jitter at the client. This is also known as the
continuity condition in the literature.
Formally, this condition can be expressed as

Q
R

t round ( k ) ≤ (3.4)

which must be met for all disk service rounds. In other words, the worst-case disk service
round length must not exceed the duration of one transmission round of Q / R seconds.
Now consider equation (3.3) again. The worst-case rotational latency can be computed from
the disk's rate of rotation. If the disk spins at a rate of W cycles per second, then the worst-
case rotational latency is just one complete rotation, i.e., W − 1 seconds. For seek time, it can
be shown that worst-case seek overheads are incurred when requests are evenly spaced across
the disk surface, provided that the seek function is concave.
Modifying equation (3.3) with the previous worst-case values, we can compute the worst-
case service round duration:

t max

round ( k )

= max { t round ( k ) }

1)

N track −

k T latency +

1 Q

R disk

= ( k + α + β + (3.5)

k + 1

and then dimension the disk streaming capacity accordingly:

max k

Q
R ,

t max C = |

round ( k )

≤ k = 1 , 2 ,... (3.6)

where C denotes the dimensioned worst-case disk capacity in number of concurrent media
streams.
Note that by using the worst-case values we guarantee that the disk will be able to sustain
C concurrent media streams regardless of the actual placement of the requested data blocks.
In other words, it does not matter whether a media stream's data are stored sequentially from
sector to sector, track to track on the disk, or simply placed randomly over the disk surface.