CS152 Computer Architecture and Engineering Lecture 24 I O and Storage Systems April 29 2004 John Kubiatowicz www cs berkeley edu kubitron lecture slides http inst eecs berkeley edu cs152 Recap Nano layered Disk Heads Special sensitivity of Disk head comes from Giant Magneto Resistive effect or GMR IBM is leader in this technology Same technology as TMJ RAM breakthrough we described in earlier class Coil for writing 4 28 04 UCB Spring 2004 CS152 Kubiatowicz Recap Disk Device Terminology Disk Latency Queueing Time Controller time Seek Time Rotation Time Xfer Time Order of magnitude times for 4K byte transfers Average Seek 8 ms or less Rotate 4 2 ms 7200 rpm Xfer 1 ms 7200 rpm 4 28 04 UCB Spring 2004 CS152 Kubiatowicz Disk I O Performance 300 Metrics Response Time Throughput Response Time ms 200 100 latency goes as Tser u 1 u u utilization 0 100 0 Throughput Utilization total BW Queue Proc IOC Device Response time Queue Device Service time 4 28 04 UCB Spring 2004 CS152 Kubiatowicz Introduction to Queueing Theory Arrivals Black Box Departures Queueing System Queueing Theory applies to long term steady state behavior Arrival rate Departure rate Little s Law Mean number tasks in system arrival rate x mean reponse time Observed by many Little was first to prove Simple interpretation you should see the same number of tasks in queue when entering as when leaving Applies to any system in equilibrium as long as nothing in black box is creating or destroying tasks 4 28 04 UCB Spring 2004 CS152 Kubiatowicz A Little Queuing Theory Use of random distributions System Queue Proc server IOC Avg Device Server spends a variable amount of time with customers Weighted mean m1 f1 x T1 f2 x T2 fn x Tn F p T xT 2 f1 x T12 f2 x T22 fn x Tn2 F m12 p T xT2 m12 Squared coefficient of variance C 2 m12 Unitless measure 100 ms2 vs 0 1 s2 Exponential distribution C 1 most short relative to average few others long 90 2 3 x average 63 average Avg Hypoexponential distribution C 1 most close to average C 0 5 90 2 0 x average only 57 average Hyperexponential distribution C 1 further from average C 2 0 90 2 8 x average 69 average 0 4 28 04 UCB Spring 2004 CS152 Kubiatowicz A Little Queuing Theory Variable Service Time System Queue Proc server IOC Device Disk response times C 1 5 majority seeks average Yet usually pick C 1 0 for simplicity Avg Memoryless exponential dist Many complex systems well described by memoryless distribution 0 Time Another useful value is average time must wait for server to complete current task m1 z Called Average Residual Wait Time Not just 1 2 x m1 because doesn t capture variance Can derive m1 z 1 2 x m1 x 1 C No variance C 0 m1 z 1 2 x m1 Exponential C 1 m1 z m1 4 28 04 UCB Spring 2004 CS152 Kubiatowicz A Little Queuing Theory Average Wait Time Calculating average wait time in queue Tq All customers in line must complete avg time m1 Tser 1 If something at server it takes to complete on average m1 z Chance server is busy u average delay is u x m1 z Tq u x m1 z Lq x Tser Little s Law Tq u x m1 z x Tq x Tser Tq u x m1 z u x Tq Defn of utilization u Tq x 1 u m1 z x u Tq m1 z x u 1 u Tser x 1 2 x 1 C x u 1 u Notation average number of arriving customers second Tser average time to service a customer u server utilization 0 1 u x Tser Tq average time customer in queue Lq average length of queue Lq x Tq m1 z average residual wait time Tser x 1 2 x 1 C 4 28 04 UCB Spring 2004 CS152 Kubiatowicz A Little Queuing Theory M G 1 and M M 1 Assumptions so far System in equilibrium Time between two successive arrivals in line are random Server can start on next customer immediately after prior finishes No limit to the queue works First In First Out Afterward all customers in line must complete each avg Tser Described memoryless or Markovian request arrival M for C 1 exponentially random General service distribution no restrictions 1 server M G 1 queue When Service times have C 1 M M 1 queue Tq Tser x u 1 u Tser u Tq 4 28 04 average time to service a customer server utilization 0 1 u x Tser average time customer in queue UCB Spring 2004 CS152 Kubiatowicz A Little Queuing Theory An Example Processor sends 10 x 8KB disk I Os per second requests service exponentially distrib avg disk service 20 ms This number comes from disk equation Service time Ave seek ave rot delay transfer time ctrl overhead On average how utilized is the disk What is the number of requests in the queue What is the average time spent in the queue What is the average response time for a disk request Notation average number of arriving customers second 10 Tser average time to service a customer 20 ms 0 02s u server utilization 0 1 u x Tser 10 s x 02s 0 2 Tq average time customer in queue Tser x u 1 u 20 x 0 2 1 0 2 20 x 0 25 5 ms 0 005s Tsys average time customer in system Tsys Tq Tser 25 ms Lq average length of queue Lq x Tq 10 s x 005s 0 05 requests in queue Lsys average tasks in system Lsys x Tsys 10 s x 025s 0 25 4 28 04 UCB Spring 2004 CS152 Kubiatowicz Memory System I O Performance Processor Request Rate Service Rate Pipelined Bus with queue at controller Time to transfer request Queue Memory DRAM Controller Tqueue Queueing Delay service time Time to transfer data DRAM has DETERMINISTIC service time Tser tRAC n 1 tPC tprecharge Tq m1 z x u 1 u Tser x 1 2 x 1 C x u 1 u with C 0 4 28 04 UCB Spring 2004 CS152 Kubiatowicz Administrivi Goato the Projects link and describe your project By Friday Thursday Sections in lab again 119 Cory Discuss your design document Send draft to TA tonight Midterm II next Wednesday 5 30 8 30 in 306 Soda Hall Pizza afterwards Topics Pipelining Caches Memory systems Buses and I O Disk equation Queueing theory Can bring 1 page of notes and calculator Handwitten double sided CLOSED BOOK Oral Report Powerpoint 15 minute presentation 5 minutes for questions 4 28 04 UCB Spring 2004 CS152 Kubiatowicz Giving Commands to I O Devices Two methods are used to address the device Special I O instructions Memory mapped I O Special I O instructions specify Both the device number and the command word Device number the processor communicates this via a set of wires normally included as part of the I O bus Command word this is usually …
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