Soft Scheduling - Scalable Continuous Media Streaming Systems - page 71

smaller than D max :

Q
R (0

. 5 + δ ) ≤ D max (4.21)

Rearranging gives the largest block size that can be used:

RD max
0

Q ≤ (4.22)

. 5 + δ

Note that we also need to round Q computed from equation (4.22) to integral multiples of disk
sector size.

4.5 Overflow Management
The previous sections focus on the cases when there is no overflow. In this section, we turn the
focus to operational issues in implementing soft scheduling and tackle the issue of overflow
detection and recovery.

4.5.1 Deadline-Driven Detection
The analytical models in Sections 4.2 and 4.3 give the probability of experiencing a round
overflow during system operation. This means that overflow can eventually occur and so the
system must detect any overflow condition and take corrective actions. To illustrate, consider
the scenario in Figure 4.3 where overflow occurs in round i . Consequently, transmission for
the last block retrieved in round i cannot proceed normally as it has missed the transmission
cycle. Moreover, schedule for the next round is also delayed, further increasing the likelihood
of overflow in subsequent rounds. Clearly, we need to contain the problems caused by overflow
to prevent overflow propagation.

Transmission cycle missed

u u

2 2

Transmission

1 1

. . . . . .

4 2 1 3 1 5

Disk Retrieval

round i round i+1

Figure 4.3 An overflow in round i can delay the start of the next round, increasing the likelihood of
overflow in round i + 1