Lecture 1: Course Introduction and Overview

Lecture 1: Course Introduction and Overview

CS162 Operating Systems and Systems Programming Lecture 17 Performance Storage Devices, Queueing Theory October 10th, 2015 Prof. John Kubiatowicz http://cs162.eecs.Berkeley.edu Recall: Memory-Mapped Display Controller Memory-Mapped: 0x80020000 Hardware maps control registers and display memory into physical address space Addresses set by hardware jumpers or programming at boot time 0x80010000 Simply writing to display memory (also called the frame buffer) changes image on screen Addr: 0x8000F0000x8000FFFF Graphics Command Queue Display Memory 0x8000F000

Writing graphics description to commandqueue area Say enter a set of triangles that describe 0x0007F004 some scene 0x0007F000 Addr: 0x800100000x8001FFFF Command Status Writing to the command register may cause on-board graphics hardware to do something Say render the above scene Addr: 0x0007F004 Can protect with address translation 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Physical Address Space Lec 17.2 Goals for Today Finish discussion of device interfaces Discussion of performance Disks and SSDs Hardware performance parameters Queuing Theory Note: Some slides and/or pictures in the following are

adapted from slides 2005 Silberschatz, Galvin, and Gagne Many slides generated from my lecture notes Gagne. 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.3 Transferring Data To/From Controller Programmed I/O: Each byte transferred via processor in/out or load/store Pro: Simple hardware, easy to program Con: Consumes processor cycles proportional to data size Direct Memory Access: Give controller access to memory bus Ask it to transfer data blocks to/from memory directly Sample interaction with DMA controller (from OSC): addr len 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.4 I/O Device Notifying the OS

The OS needs to know when: The I/O device has completed an operation The I/O operation has encountered an error I/O Interrupt: Device generates an interrupt whenever it needs service Pro: handles unpredictable events well Con: interrupts relatively high overhead Polling: OS periodically checks a device-specific status register I/O device puts completion information in status register Pro: low overhead Con: may waste many cycles on polling if infrequent or unpredictable I/O operations Actual devices combine both polling and interrupts For instance High-bandwidth network adapter: Interrupt for first incoming packet Poll for following packets until hardware queues are 10/28/15 empty Kubiatowicz CS162 UCB Fall 2015 Lec 17.5

Device Drivers Device Driver: Device-specific code in the kernel that interacts directly with the device hardware Supports a standard, internal interface Same kernel I/O system can interact easily with different device drivers Special device-specific configuration supported with the ioctl() system call Device Drivers typically divided into two pieces: Top half: accessed in call path from system calls implements a set of standard, cross-device calls like open(), close(), read(), write(), ioctl(), strategy() This is the kernels interface to the device driver Top half will start I/O to device, may put thread to sleep until finished Bottom half: run as interrupt routine 10/28/15 Gets input or transfers next block of output May wake sleeping threads if I/O now complete Kubiatowicz CS162 UCB Fall 2015 Lec 17.6 Life Cycle of An I/O Request

User Program Kernel I/O Subsystem Device Driver Top Half Device Driver Bottom Half Device Hardware 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.7 Basic Performance Concepts Response Time or Latency: Time to perform an operation (s) Bandwidth or Throughput: Rate at which operations are performed (op/s) Files: mB/s, Networks: mb/s, Arithmetic: GFLOP/s Start up or Overhead: time to initiate an operation Most I/O operations are roughly linear Latency (n) = Ovhd + n/Bandwidth 10/28/15 Kubiatowicz CS162 UCB Fall 2015

Lec 17.8 Example (fast network) Consider a gpbs link (125 MB/s) With a startup cost S = 1 ms Theorem: half-power point occurs at n=S*B: When transfer time = startup T(S*B) = S + S*B/B 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.9 Example: at 10 ms startup (like Disk) Performanceof gbpslinkwith10msstartup 18,000 50 16,000 45 35 Latency(us) 12,000 30 10,000

25 8,000 20 6,000 15 4,000 Bandwidth(mB/s) 40 14,000 10 2,000 5 0 0 0 50,000 100,000 150,000 200,000 250,000 300,000 350,000 400,000 450,000 500,000 Length(b) 10/28/15 Kubiatowicz CS162 UCB Fall 2015

Lec 17.10 What determines peak BW for I/O ? Bus Speed PCI-X: 1064 MB/s = 133 MHz x 64 bit (per lane) ULTRA WIDE SCSI: 40 MB/s Serial Attached SCSI & Serial ATA & IEEE 1394 (firewire) : 1.6 Gbps full duplex (200 MB/s) USB 1.5 12 mb/s Device Transfer Bandwidth Rotational speed of disk Write / Read rate of NAND flash Signaling rate of network link Whatever is the bottleneck in the path 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.11 Administrivia Midterm I: Grading finished Mean: 62.95, Std: 15.3 Regrades on Midterm I: You have 1 week to request a regrade Be sure: If we receive a request, we may regrade whole exam (could lose points)

Do your own work on Homeworks and Projects! We have seen some incidences of cheating and will be calling people in. JUST SAY NO! 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.12 CS 162 Collaboration Policy Explaining a concept to someone in another group Discussing algorithms/testing strategies with other groups Helping debug someone elses code (in another group) Searching online for generic algorithms (e.g., hash table) Sharing code or test cases with another group Copying OR reading another groups code or test cases Copying OR reading online code or test cases from from prior years We compare all project submissions against prior year submissions and online solutions and will take actions (described on the course overview page) against offenders 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.13 Storage Devices Magnetic disks Storage that rarely becomes corrupted Large capacity at low cost

Block level random access (except for SMR later!) Slow performance for random access Better performance for streaming access Flash memory Storage that rarely becomes corrupted Capacity at intermediate cost (50x disk ???) Block level random access Good performance for reads; worse for random writes Erasure requirement in large blocks Wear patterns 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.14 Are we in an inflection point? 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.15 Hard Disk Drives (HDDs) Read/Write Head Side View

Western Digital Drive http://www.storagereview.com/guide/ IBM Personal Computer/AT (1986) 30 MB hard disk - $500 30-40ms seek time 0.7-1 MB/s (est.) 10/28/15 IBM/Hitachi Microdrive Kubiatowicz CS162 UCB Fall 2015 Lec 17.16 The Amazing Magnetic Disk Unit of Transfer: Sector Ring of sectors form a track Stack of tracks form a cylinder Heads position on cylinders Disk Tracks ~ 1m (micron) wide Wavelength of light is ~ 0.5m Resolution of human eye: 50m 100K on a typical 2.5 disk Separated by unused guard regions Reduces likelihood neighboring tracks are corrupted during writes Track length varies across disk Outside: More sectors per track, higher bandwidth

Disk is organized into regions of tracks with same # of sectors/track Only outer half of radius is used Most of the disk area in the outer regions of the disk New: Shingled Magnetic Recording (SMR) Overlapping tracks greater density, restrictions on writing Seagate (8TB), Hitachi (10TB) 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.17 Magnetic Disk Characteristic Sector Cylinder: all the tracks under the Track Head head at a given point on all surfaces Cylinder Read/write: three-stage process: Platter Seek time: position the head/arm over the proper track (into proper cylinder) Rotational latency: wait for the desired sector to rotate under the read/write head Transfer time: transfer a block of bits (sector) under the read-write head

Disk Latency = Queuing Time + Controller time + Seek Time + Rotation Time + Xfer Time Media Time (Seek+Rot+Xfer) Result Highest Bandwidth: Hardware Controller Request Software Queue (Device Driver) Transfer large group of blocks sequentially from one track 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.18 Typical Numbers for Magnetic Disk Parameter Info / Range Space/Density

Space: 8TB (Seagate), 10TB (Hitachi) in 3 inch form factor! (Introduced in Fall of 2014) Areal Density: 1Terabit/square inch! (SMR, Helium, ) Average seek time Typically 5-10 milliseconds. Depending on reference locality, actual cost may be 25-33% of this number. Average rotational latency Most laptop/desktop disks rotate at 3600-7200 RPM (16-8 ms/rotation). Server disks up to 15,000 RPM. Average latency is halfway around disk yielding corresponding times of 8-4 milliseconds Controller time Depends on controller hardware Typically 50 to 100 MB/s. Depends on: Transfer size (usually a sector): 512B 1KB per sector Rotation speed: 3600 RPM to 15000 RPM Recording density: bits per inch on a track Diameter: ranges from 1 in to 5.25 in

Transfer time Cost 10/28/15 Drops by a factor ofUCB two every 1.5 years (or even Kubiatowicz CS162 Fall 2015 Lec 17.19 Disk Performance Example Assumptions: Ignoring queuing and controller times for now Avg seek time of 5ms, 7200RPM Time for rotation: 60000(ms/M)/7200(rev/M) ~= 8ms Transfer rate of 4MByte/s, sector size of 1 Kbyte 1024 bytes/4106 (bytes/s) = 256 10-6 sec .26 ms Read sector from random place on disk: Seek (5ms) + Rot. Delay (4ms) + Transfer (0.26ms) Approx 10ms to fetch/put data: 100 KByte/sec Read sector from random place in same cylinder: Rot. Delay (4ms) + Transfer (0.26ms) Approx 5ms to fetch/put data: 200 KByte/sec

Read next sector on same track: Transfer (0.26ms): 4 MByte/sec Key to using disk effectively (especially for file systems) is to minimize seek and rotational 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.20 Intelligence in the controller Sectors contain sophisticated error correcting codes Disk head magnet has a field wider than track Hide corruptions due to neighboring track writes Sector sparing Remap bad sectors transparently to spare sectors on the same surface Slip sparing Remap all sectors (when there is a bad sector) to preserve sequential behavior Track skewing Sector numbers offset from one track to the next, to allow for disk head movement for sequential ops 10/28/15 Kubiatowicz CS162 UCB Fall 2015

Lec 17.21 Solid State Disks (SSDs) 1995 Replace rotating magnetic media with nonvolatile memory (battery backed DRAM) 2009 Use NAND Multi-Level Cell (2 or 3-bit/cell) flash memory Sector (4 KB page) addressable, but stores 4-64 pages per memory block Trapped electrons distinguish between 1 and 0 No moving parts (no rotate/seek motors) Eliminates seek and rotational delay (0.1-0.2ms access time) Very low power and lightweight Limited write cycles Rapid 10/28/15 advance Kubiatowicz in capacity ever since CS162and UCBcost Fall 2015 Lec 17.22 SSD Architecture Reads Host

SATA Buffer Manager (software Queue) Flash Memory Controller DRAM Read 4 KB Page: ~25 usec NAND NAND NAND NAND NAND NAND NAND NAND NAND NAND NAND NAND NAND NAND NAND

NAND NAND NAND NAND NAND NAND NAND NAND NAND NAND NAND NAND NAND NAND NAND NAND NAND No seek or rotational latency Transfer time: transfer a 4KB page SATA: 300-600MB/s => ~4 x103 b / 400 x 106 bps => 10 us Latency = Queuing Time + Controller time + Xfer Time Highest Bandwidth: Sequential OR Random reads 10/28/15

Kubiatowicz CS162 UCB Fall 2015 Lec 17.23 SSD Architecture Writes (I) Writing data is complex! (~200s 1.7ms s 1.7ms ) Can only write empty pages in a block Erasing a block takes ~1.5ms Controller maintains pool of empty blocks by coalescing used pages (read, erase, write), also reserves some % of capacity Rule of thumb: writes 10x reads, erasure 10x writes https://en.wikipedia.org/wiki/Solid-state_drive 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.24 Amusing calculation: is a full Kindle heavier than an empty one? Actually, Yes, but not by much Flash works by trapping electrons: So, erased state lower energy than written state Assuming that: Kindle has 4GB flash of all bits in full Kindle are in high-energy state High-energy state about 10-15 joules higher Then: Full Kindle is 1 attogram (10-18gram) heavier (Using E = mc2)

Of course, this is less than most sensitive scale (which can measure 10-9grams) Of course, this weight difference overwhelmed by battery discharge, weight from getting warm, . According to John Kubiatowicz, New York Times, Oct 24, 2011 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.25 Storage Performance & Price (jan 13) Bandwidth (Sequential R/W) Cost/GB Size HDD2 50-100 MB/s $0.03-0.07/GB 2-4 TB SSD1,2 200-550 MB/s (SATA)

6 GB/s (read PCI) 4.4 GB/s (write PCI) $0.87-1.13/GB 200GB-1TB DRAM2 10-16 GB/s $4-14*/GB 64GB-256GB *SK Hynix 9/4/13 fire 1 http://www.fastestssd.com/featured/ssd-rankings-the-fastest-solid-state-drives/ http://www.extremetech.com/computing/164677-storage-pricewatch-hard-drive-and-ssd-prices-drop-making-for-a-good-time-to-buy 2 BW: SSD up to x10 than HDD, DRAM > x10 than SSD Price: HDD x20 less than SSD, SSD x5 less than DRAM 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.26 SSD Summary

Pros (vs. hard disk drives): Low latency, high throughput (eliminate seek/rotational delay) No moving parts: Very light weight, low power, silent, very shock insensitive Read at memory speeds (limited by controller and I/O bus) Cons Small storage (0.1-0.5x disk), expensive (20x disk ???) Hybrid alternative: combine small SSD with large HDD Asymmetric block write performance: read pg/erase/write pg Controller garbage collection (GC) algorithms have major effect on performance Limited drive lifetime 1-10K writes/page for MLC NAND Avg failure rate is 6 years, life expectancy is 911 years These are changing rapidly 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.27 What goes into startup cost for I/O? Syscall overhead Operating system processing Controller Overhead

Device Startup Mechanical latency for a disk Media Access + Speed of light + Routing for network Performanceof gbpslinkwith10msstartup 18,000 50 16,000 45 35 12,000 Latency(us) Queuing (next topic) 30 10,000 25 8,000 20 6,000 15 4,000 Bandwidth(mB/s)

40 14,000 10 2,000 5 0 0 0 50,000 100,000 150,000 200,000 250,000 300,000 350,000 400,000 450,000 500,000 Length(b) 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.28 I/O Performance Queue [OS Paths] Controller

User Thread 300 Response Time (ms) I/O device Response Time = Queue + I/O device service time 200 100 0 Performance of I/O subsystem 100% 0% Throughput (Utilization) Metrics: Response Time, Throughput(% total BW) Effective BW per op = transfer size / response time EffBW(n) = n / (S + n/B) = B / (1 + SB/n ) Contributing factors to latency: Software paths (can be loosely modeled by a queue)

Hardware controller I/O device service time Queuing behavior: Can lead to big increases of latency as utilization increases Solutions? 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.29 A Simple Deterministic World Queue arrivals TQ TA Server departures TS TA TA Assume requests arrive at regular intervals, take a

fixed time to process, with plenty of time between Service rate ( = 1/TS) - operations per sec Arrival rate: ( = 1/TA) - requests per second Utilization: U = / , where < Average rate is the complete story 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.30 0 Queue delay 1 Offered Load (TA/TS) time Saturation 1 Empty Queue Unbounded 0 1 Offered Load (TA/TS) Queue delay 1

Delivered Throughput Delivered Throughput A Ideal Linear World time What does the queue wait time look like? Grows unbounded at a rate ~ (Ts/TA) till request rate subsides 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.31 A Bursty World arrivals Queue T Q Server T departures S

Arrivals Q depth Server Requests arrive in a burst, must queue up till served Same average arrival time, but almost all of the requests experience large queue delays Even though average utilization is low 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.32 So how do we model the burstiness of arrival? Elegant mathematical framework if you start with exponential distribution Probability density function of a continuous random variable with a mean of 1/ f(x) = e-x Memoryless 1 0.9 Likelihood of an event occuring is independent of how long weve been waiting Lots of short arrival intervals (i.e., high

instantaneous rate) Few long gaps (i.e., low instantaneous rate) 10/28/15 0.8 0.7 mean arrival interval (1/) 0.6 0.5 0.4 0.3 0.2 0.1 0 0 1 2 3 Kubiatowicz CS162 UCB Fall 2015 4 5 6

x () 7 8 9 10 Lec 17.33 Background: General Use of random distributions Server spends variable time with customers Mean (Average) m1 = p(T)T Variance 2 = p(T)(T-m1)2 = p(T)T2-m12 Mean (m1) Squared coefficient of variance: C = 2Distribution /m12 Aggregate description of the distribution. of service times Important values of C: No variance or deterministic C=0 memoryless or exponential C=1

mean Past tells nothing about future Many complex systems (or aggregates) Memoryless well described as memoryless Disk response times C 1.5 (majority seeks < avg) 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.34 Introduction to Queuing Theory Queue Controller Arrivals Disk Departures Queuing System What about queuing time?? Lets apply some queuing theory Queuing Theory applies to long term, steady state

behavior Arrival rate = Departure rate Arrivals characterized by some probabilistic distribution Departures characterized by some probabilistic distribution 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.35 Littles Law N arrivals departures B L In any stable system Average arrival rate = Average departure rate the average number of tasks in the system (N) is equal to the throughput (B) times the response time (L) N (ops) = B (ops/s) x L (s) Regardless of structure, bursts of requests, variation in service instantaneous variations, but it washes out in the average

Overall requests match departures 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.36 A Little Queuing Theory: Some Results Assumptions: System in equilibrium; No limit to the queue Time between successive arrivals is random and memoryless Arrival Rate Queue Service Rate =1/Tser Server Parameters that describe our system: : mean number of arriving customers/second Tser: mean time to service a customer (m1) C: squared coefficient of variance = 2/m12 : service rate = 1/Tser u: server utilization (0u1): u = / = Tser

Parameters we wish to compute: Tq: Time spent in queue Lq: Length of queue = Tq (by Littles law) Results: Memoryless service distribution (C = 1): Called M/M/1 queue: Tq = Tser x u/(1 u) General service distribution (no restrictions), 1 server: 10/28/15 Called M/G/1 queue: TCS162 x (1+C) x u/(1 u)) Kubiatowicz UCB Fall 2015 q = Tser Lec 17.37 A Little Queuing Theory: An Example Example Usage Statistics: User requests 10 x 8KB disk I/Os per second Requests & service exponentially distributed (C=1.0) Avg. service = 20 ms (From controller+seek+rot+trans) Questions: How utilized is the disk?

Ans: server utilization, u = Tser What is the average time spent in the queue? Ans: Tq What is the number of requests in the queue? Ans: Lq What is the avg response time for disk request? Ans: Tsys = Tq + Tser Computation: (avg # arriving customers/s) = 10/s Tser (avg time to service customer) = 20 ms (0.02s) u (server utilization) = x Tser= 10/s x .02s = 0.2 10/28/15 Kubiatowicz CS162 Fall 2015 T (avg time/customer in UCB queue) = T x u/(1Lec 17.38 u) Queuing Theory Resources Handouts page contains Queueing Theory Resources: Scanned pages from Patterson and Hennesey book that gives further discussion and simple proof for general eq.

A complete website full of resources Midterms with queueing theory questions: Midterm IIs from previous years that Ive taught Assume that Queueing theory is fair game for Midterm II and/or the final! 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.39 Optimize I/O Performance Queue [OS Paths] Controller User Thread 300 Response I/O device Response Time = Queue + I/O device service time Howto improve performance?

Time (ms) 200 100 0 0% 100% Throughput (Utilization) Make everything faster (% total BW) More Decoupled (Parallelism) systems multiple independent buses or controllers Optimize the bottleneck to increase service rate Use the queue to optimize the service Do other useful work while waiting Queues absorb bursts and smooth the flow Admissions control (finite queues) Limits delays, but may introduce unfairness and livelock 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.40 When is the disk performance highest

When there are big sequential reads, or When there is so much work to do that they can be piggy backed (c-scan) OK, to be inefficient when things are mostly idle Bursts are both a threat and an opportunity Waste space for speed? 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.41 Disk Scheduling Disk can do only one request at a time; What order do you choose to do queued requests? 2,3 2,1 3,10 7,2 5,2 2,2 User Requests Head FIFO Order

SSTF: Shortest seek time first Pick the request thats closest on the disk3 Although called SSTF, today must include rotational delay in calculation, since 2 1 rotation can be as long as seek Con: SSTF good at reducing seeks, but 4 may lead to starvation Disk Head Fair among requesters, but order of arrival may be to random spots on the disk Very long seeks SCAN: Implements an Elevator Algorithm: take the closest request in the direction of travel No starvation, but retains flavor of SSTF C-SCAN: Circular-Scan: only goes in one direction Skips any requests on the way back Fairer than SCAN, not biased towards pages in middle 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.42 Building a File System File System: Layer of OS that transforms block interface of disks (or other block devices) into

Files, Directories, etc. File System Components Disk Management: collecting disk blocks into files Naming: Interface to find files by name, not by blocks Protection: Layers to keep data secure Reliability/Durability: Keeping of files durable despite crashes, media failures, attacks, etc User vs. System View of a File Users view: Durable Data Structures Systems view (system call interface): Collection of Bytes (UNIX) Doesnt matter to system what kind of data structures you want to store on disk! Systems view (inside OS): Collection of blocks (a block is a logical transfer unit, while a sector is the physical transfer unit) Block size sector size; in UNIX, block size is 4KB 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.43

Translating from User to System View File System What happens if user says: give me bytes 2 12? Fetch block corresponding to those bytes Return just the correct portion of the block What about: write bytes 212? Fetch block Modify portion Write out Block Everything inside File System is in whole size blocks For example, getc(), putc() buffers something like 4096 bytes, even if interface is one byte at a 10/28/15 time Kubiatowicz CS162 UCB Fall 2015 Lec 17.44 Disk Management Policies Basic entities on a disk: File: user-visible group of blocks arranged sequentially in logical space Directory: user-visible index mapping names to files (next lecture) Access disk as linear array of sectors. Two Options:

Identify sectors as vectors [cylinder, surface, sector]. Sort in cylinder-major order. Not used much anymore. Logical Block Addressing (LBA). Every sector has integer address from zero up to max number of sectors. Controller translates from address physical position First case: OS/BIOS must deal with bad sectors Second case: hardware shields OS from structure of disk Need way to track free disk blocks Link free blocks together too slow today Use bitmap to represent free space on disk Need way to structure files: File Header 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.45 Summary Devices have complex protocols for interaction and performance characteristics Response time (Latency) = Queue + Overhead + Transfer Effective BW = BW * T/(S+T)

HDD: controller + seek + rotation + transfer SDD: controller + transfer (erasure & wear) Bursts & High Utilization introduce queuing delays Systems (e.g., file system) designed to optimize performance and reliability Relative to performance characteristics of underlying device Disk Performance: Queuing time + Controller + Seek + Rotational + Transfer Rotational latency: on average rotation Transfer time: spec of disk depends on rotation speed and bit storage density Queuing Latency: M/M/1 and M/G/1 queues: simplest to analyze As utilization approaches 100%, latency Tq = Tser x (1+C) x u/(1 u)) 10/28/15 Kubiatowicz CS162 UCB Fall 2015 Lec 17.46

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