Reliable and Fault-Tolerant Storage Systems - Scalable Continuous Media Streaming Systems - page 87

Table 5.1 Summary of notations

Description Symbol Notes

Average media bit-rate R v Parameter in bytes per second (e.g.,

150,000 Bps)

Media block size Q Parameter in bytes (e.g. 65,336 bytes)

Length of a transmission cycle T r Computed from Q / R , in seconds

Number of disks N D Parameter

Disk storage capacity G Parameter in bytes

Number of recording surfaces in a disk N suf Parameter in numbers

Number of tracks per recording surface
in a disk

N trk Parameter in numbers

Size of a disk sector S Parameter in bytes

Number of zones in a disk N zone Parameter in numbers

Number of sectors per track in zone i Y i Parameter in numbers

Minimum number of sectors per track Y min Parameter in numbers

Maximum number of sectors per track Y max Parameter in numbers

Transfer rate in zone i X i Computed, in bytes per second

Minimum transfer rate X min Computed, in bytes per second

Disk platter rotation rate W Parameter in cycles per second

Fixed overhead in disk read α Parameter in seconds

Seek time in disk read t seek Random variable in seconds

Rotational latency in disk read t rot Random variable in seconds

Transfer time in disk read t xfr Random variable in seconds

Disk seek function f seek ( n ) Seek time for a seek distance of n tracks

Maximum number of requests that can be
served in a service round

K Computed, in number of requests

Head-switching time in disk t hsw Parameter in seconds

Total track-to-track seek time in serving
a request

t track Random variable, in seconds

Earliest completion time for retrieving track i e i Random variable, in seconds

Latest completion time for retrieving track i l i Random variable, in seconds

Minimum time for retrieving one track Parameter in seconds

Deviation bound for track-retrieval
completion times

D asyn Parameter in seconds

Server load/utilization u Variable, in number of streams

Number of active streams for a server U Variable, in number of streams

Server utilization ρ Variable, real number ranging from 0 to 1

Number of rebuild blocks retrieved by a
working disk in a round

n b Computed, in number of media blocks

Rate at which rebuild data are retrieved from
the working disks

R rb Computed, in bytes per second

Rate at which lost data are rebuilt R rebuild Computed, in bytes per second

Buffer requirement for playback process B p Computed, in bytes

Buffer requirement for rebuild process B r Computed, in bytes

Total buffer requirement without buffer
sharing

B sum Computed, in bytes

Total buffer requirement with buffer sharing B share Computed, in bytes