Review Magnetic Disk Characteristic Cylinder all the tracks under the head at a given point on all surface Head Read write data is a three stage process CS162 Operating Systems and Systems Programming Lecture 18 File Systems Naming and Directories Track Sector Cylinder 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 Queueing Time Controller time Seek Time Rotation Time Xfer Time Result Software Queue Device Driver Hardware Controller Request November 2 2005 Prof John Kubiatowicz http inst eecs berkeley edu cs162 Media Time Seek Rot Xfer Highest Bandwidth transfer large group of blocks sequentially from one track 11 02 05 Kubiatowicz CS162 UCB Fall 2005 Review Introduction to Queuing Theory Queue Controller Arrivals Disk Lec 18 2 Goals for Today Finishing Disk Performance Hardware performance parameters Queuing Theory Departures Queuing System File Systems What about queuing time Structure Naming Directories Let s apply some queuing theory Queuing Theory applies to long term steady state behavior Arrival rate Departure rate Little s Law Mean tasks in system arrival rate x mean response 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 Typical queuing theory doesn t deal with transient behavior only steady state behavior 11 02 05 Kubiatowicz CS162 UCB Fall 2005 Lec 18 3 Note Some slides and or pictures in the following are adapted from slides 2005 Silberschatz Galvin and Gagne 11 02 05 Kubiatowicz CS162 UCB Fall 2005 Lec 18 4 Background 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 m1 Arrival Rate Distribution of service times Squared coefficient of variance C 2 m12 Aggregate description of the distribution Important values of C No variance or deterministic C 0 memoryless or exponential C 1 Past tells nothing about future Many complex systems or aggregates well described as memoryless mean Disk response times C 1 5 majority seeks avg Mean time must wait for server to complete current task Can derive m1 z m1 1 C Not just m1 because doesn t capture variance Lec 18 5 A Little Queuing Theory M G 1 and M M 1 Computation of wait time in queue Tq Tq Lq Tser u m1 z Little s Law Tq Tq Tq Tq Tq Tser u m1 z Defn of utilization u u Tq u m1 z 1 u m1 z u Tq m1 z u 1 u Tser 1 C u 1 u Notice that as u 1 Tq Assumptions so far General service distribution no restrictions 1 server Called M G 1 queue Tq Tser 1 C u 1 u Memoryless service distribution C 1 Called M M 1 queue Tq Tser u 1 u Kubiatowicz CS162 UCB Fall 2005 Server Parameters that describe our system Tser C u mean number of arriving customers second mean time to service a customer m1 squared coefficient of variance 2 m12 service rate 1 Tser server utilization 0 u 1 u Tser Tq Lq Time spent in queue Length of queue Tq by Little s law Basic Approach Customers before us must finish mean time Lq Tser If something at server takes m1 z to complete on avg m1 z mean residual wait time at server Tser 1 C Chance something at server u mean time is u m1 z Tq Lq Tser u m1 z 11 02 05 Kubiatowicz CS162 UCB Fall 2005 Lec 18 6 A Little Queuing Theory An Example Example Usage Statistics User requests 10 8KB disk I Os per second Requests service exponentially distributed C 1 0 Avg service 20 ms controller seek rot Xfertime Questions How utilized is the disk Ans server utilization u Tser What is the average time spent in the queue Ans Tq System in equilibrium No limit to the queue works First In First Out Time between two successive arrivals in line are random and memoryless M for C 1 exponentially random Server can start on next customer immediately after prior finishes 11 02 05 Service Rate 1 Tser Computation of wait time in queue Tq C 0 m1 z m1 C 1 m1 z m1 Kubiatowicz CS162 UCB Fall 2005 Queue Parameters we wish to compute Memoryless Mean Residual Wait Time m1 z 11 02 05 A Little Queuing Theory Mean Wait Time Mean m1 Lec 18 7 What is the number of requests in the queue Ans Lq Tq What is the avg response time for disk request Ans Tsys Tq Tser Wait in queue then get served Computation avg arriving customers s 10 s Tser avg time to service customer 20 ms 0 02s u server utilization Tser 10 s 02s 0 2 Tq avg time customer in queue Tser u 1 u 20 x 0 2 1 0 2 20 0 25 5 ms 0 005s Lq avg length of queue Tq 10 s 005s 0 05 Tsys avg time customer in system Tq Tser 25 ms 11 02 05 Kubiatowicz CS162 UCB Fall 2005 Lec 18 8 Disk Scheduling Disk can do only one request at a time What order do you choose to do queued requests FIFO Order 2 3 2 1 3 10 7 2 5 2 2 2 User Requests Head My office hours How many people would like me to have an office hour on Tuesday or Thursday Better get started on Project 3 SSTF Shortest seek time first 3 2 1 Design is due on Monday Disk Head Fair among requesters but order of arrival may be to random spots on the disk Very long seeks Pick the request that s closest on the disk Although called SSTF today must include rotational delay in calculation since rotation can be as long as seek Con SSTF good at reducing seeks but may lead to starvation Administrivia 4 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 11 02 05 Kubiatowicz CS162 UCB Fall 2005 Lec 18 9 11 02 05 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 User s view System s view system call interface Collection of Bytes UNIX Doesn t matter to system what kind of data structures you want to store on disk System s view inside …
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