Consider a disk with the $$100$$ tracks numbered from $$0$$ to $$99$$ rotating at $$3000$$ $$rpm.$$ The number of sectors per track is $$100.$$ the time to move the head between two successive tracks is $$0.2$$ milliseconds.

(a) Consider a set of disk requests to read data from tracks $$32, 7, 45, 5$$ and $$10.$$ Assuming that the elevator algorithm is used to schedule disk requests, and the head is initially at track $$25$$ moving up (towards larger track numbers), what is the total seek time for servicing the requests?
(b) Consider an initial set of $$100$$ arbitrary disk requests and assume that no new disk requests arrive while servicing these requests. If the head is initially at track $$0$$ and the elevator algorithm is used to schedule disk requests, what is the worst case time to complete all the requests?

Consider a disk with following specifications: $$20$$ surface, $$1000$$ tracks/surface, $$16$$ sectors/track, data density $$1$$ $$KB/sector,$$ rotation speed $$3000$$ $$rpm.$$ The operating system initiates the transfer between the disk and the memory sector-wise. Once the head has been placed on the right track, the disk reads a sector in a single scan. It reads bits from the sector while the head is passing over the sector. The read bits are formed into bytes in a serial $$=$$in-parallel-out buffer and each byte is then transferred to memory. The disk writing is exactly a complementary process. For parts $$(c)$$ and $$(d)$$ below, assume memory read-write time $$= 0.1$$ micro-second/ byte, interrupt driven transfer has an interrupt overhead $$= 0.4$$ microseconds, the $$DMA$$ initialization and termination overhead is negligible compared to the total sector transfer time. $$DMA$$ requests are always granted.

(a) What is the total capacity of the disk?
(b) What is the data transfer rate?
(c) What is the percentage of time the $$CPU$$ is required for this disk $${\rm I}/O$$ for byte-wise interrupts driven transfer?
(d) What is the maximum percentage of time the $$CPU$$ is held up for this disk $${\rm I}/O$$ for cycle-stealing $$DMA$$ transfer ?

A file system with a one-level directory structure is implemented on a disk with disk block size of $$4$$ K bytes. The disk is used as follows:

Disk-block $$0:$$ File Allocation Table, consisting of one $$8$$-bit entry per date block, representing the data block address of the next date block in the file:

Disk block $$1:$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ Directory, with one $$32$$ bit entry per file:
Disk block $$2:$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ Data block $$1;$$
Disk block $$3:$$ $$\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,$$ Data block $$2;$$ etc.

(a) What is the maximum possible number of files?
(b) What is the maximum possible file size in blocks?

The head of a moving head disk with $$100$$ tracks numbered $$0$$ to $$99$$ is currently serving a request at tract $$55.$$ If the queue of requests kept in $$FIFO$$ order is $$10, 70, 75, 23, 65$$ Which of the two disk scheduling algorithms $$FCFS$$ (First Come First Served) and $$SSTF$$ (Shortest Seek Time First) will require less head movement? Find the head movement for each of the algorithms.