Homework #7

CMSC 611, Spring 2000

Assigned: 4 May 2000
Due: 16 May 2000 at 5:30 PM

NOTE: HW #7 is "officially" due on May 11th, but will be accepted as on time if handed in by May 16th.

1. You’re the I/O system architect for a computer company building high-speed file servers. The average request size is 32 KB (assume the data is all read from the same track). Assume the average seek distance is 30 tracks.
   The CPU you are using runs at 500 MIPS and has a backplane bus capable of transferring 200 MB/s. The operating system needs 50,000 instructions to service a single 32 KB request. The CPU costs $10,000 and comes with a backplane bus with 6 slots.
   You can choose from fast and slow 3.5" disks as described in the following table. Disks must be connected to disk controllers that sit in the backplane bus.
   

   Disk size	Rotation rate	Seek (ms) min/avg/max	Tracks	Surfaces	Sectors per track	Bytes per sector	Cost
   3.5"	7200 RPM	1/8/15	5000	4	500	512	$200
   3.5"	10000 RPM	1/6/12	10000	6	1000	512	$500

   Each controller requires 1 ms to handle a single 32 KB I/O. Controllers can handle one I/O while another I/O hasn’t yet been completed (i.e., if one disk is seeking, the controller can be working on another I/O). Controllers have connections for 2 I/O buses, each of which can support 15 disk drives and transfer data at 40 MB/s. Each controller costs $1000, but I/O buses are free (the disk manufacturer provides the necessary cables with each disk).
   1. How long does a single 32 KB request take to service from start to finish? Assume that time spent in different parts of the system is not overlapped.
   2. What is the maximum capacity (in GB) of a system built from these parts and using only a single CPU and backplane bus?
   3. What is the maximum data rate (in MB/s) of a system built from these parts and using only a single CPU and backplane bus?
   4. How expensive is the cheapest system with a minimum capacity of 300 GB and minimum data rate of 1500 requests per second?
2. Tape libraries were invented as archival storage, and thus have relatively few readers per tape. Assume you have a system that can hold 6000 tapes, each of which stores 40 GB of data. Tapes can be read at 9 MB/s, and there are 8 tape readers. It takes 30 seconds to eject a tape from a reader, put it back on the shelf, and grab a new one.
   1. How long does it take to read a single tape?
   2. How long would it take to read the entire archive? This is often necessary because of advances in technology (how many 9-track tape readers are there today?...)
   3. How long does it take to find and read a 200 MB file in this archive? Assume that files are contiguously stored on tape, and that seek time is randomly distributed betweeen 0 and 60 seconds.
   4. Suppose the tapes were replaced with random access cartridges (high capacity removable magnetic storage, such as that promised by TeraStor). How long would the operation in part (c) take if seek time were 0, assuming that other parameters (load time, transfer rate) stayed the same?
3. The claim has been made that tape libraries are not much cheaper than disks these days. Assume you can buy a 30 GB disk for $200, a PC for $400, and a network hub (100 megabit/second Ethernet) for $1000. Each PC can manage 4 disks, and each hub can be used for 16 PCs. A tape robot costs $250,000, a tape reader costs $20,000, and tape media costs $50 for a 30 GB cartridge.
   1. How much does a 6000 tape system cost? What is its capacity? Assume the system requires 4 tape readers.
   2. How much would a disk system of the same capacity cost?
   3. The disk system would suffer from reliability issues because of all those disks. If the disks were configured as 7+1 RAID systems, how much would it cost to build a disk system with the same capacity as the tape system in (a)?
   4. What would the bandwidth of each system be? Assume the bandwidth of the inexpensive disks from Problem 1, and the tape drives from Problem 2. What other factors might limit overall system bandwidth?