Soft Scheduling - Scalable Continuous Media Streaming Systems - page 63

Table 4.1 Summary of notations

Description Symbol Notes

Average media bit-rate R 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

Disk transfer rate r Random variable in bytes per second

r i Transfer rate for the i th request

r min Minimum transfer rate

(i.e. of innermost track)

Fixed overhead in disk read α Constant in seconds

Seek time in disk read t seek Random variable in seconds

t seek Seek time for the i th request

Rotational latency in disk read t latency Random variable in seconds

t latency Rotational latency for the i th request

t end
seek

Head repositioning delay Random variable in seconds

Service time for a request t request Random variable in seconds

t request ( i ) Service time for request i

Length of a service round serving k
requests

t round ( k ) Random variable in seconds

Disk platter rotation rate W Constant in cycles per second

t max Worst-case seek time for serving k

requests

seek ( k )

Computed, in seconds

t max An upper bound for service round

length serving k requests

round ( k )

Computed, in seconds

Usable disk capacity under
hard scheduling

C Computed, in number of requests

(served in a service round)

C ( ε ) Usable disk capacity under soft

scheduling

Computed, in number of requests
(served in a service round)

Usable disk capacity under
Dual-Round Scheduling

C DRS ( ε ) Computed, in number of requests

(served in a service round)

Number of disk tracks N Parameter in numbers

Seek distance for request i n i Variable in number of tracks

Overflow probability constraint ε Parameter

Extra number of buffers for
Dual-Round Scheduling

B early Computed, in number of Q -bytes

buffers

Probability density function for
round length serving k requests

f round ( t , k ) Parameter

Probability distribution function for
round length serving k requests

F round ( t , k ) Parameter

Overflow probability for serving k
requests in a round

( k ) Computed

Size of track i z i Parameter in bytes

Probability of disk head located at
track i

p i Computed

Track number for request i v i Parameter

Variable in seconds:

(Continued)