CS162Operating Systems andSystems ProgrammingLecture 18File Systems, Naming, and DirectoriesNovember 2, 2005Prof. John Kubiatowiczhttp://inst.eecs.berkeley.edu/~cs162Lec 18.211/02/05Kubiatowicz CS162 ©UCB Fall 2005Review: Magnetic Disk Characteristic• Cylinder: all the tracks under the head at a given point on all surface• Read/write data is a three-stage process:– Seek time: position the head/arm over the proper track (into proper cylinder)– Rotational latency: wait for the desired sectorto 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• Highest Bandwidth: – transfer large group of blocks sequentially from one trackSectorTrackCylinderHeadPlatterSoftwareQueue(Device Driver)HardwareControllerMedia Time(Seek+Rot+Xfer)RequestResultLec 18.311/02/05Kubiatowicz CS162 ©UCB Fall 2005DeparturesArrivalsQueuing SystemReview: Introduction to Queuing Theory• What about queuing time??– 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 behaviorQueueControllerDiskLec 18.411/02/05Kubiatowicz CS162 ©UCB Fall 2005Goals for Today• Finishing Disk Performance– Hardware performance parameters– Queuing Theory• File Systems– Structure, Naming, DirectoriesNote: Some slides and/or pictures in the following areadapted from slides ©2005 Silberschatz, Galvin, and GagneLec 18.511/02/05Kubiatowicz CS162 ©UCB Fall 2005Background: Use of random distributions• Server spends variable time with customers– Mean (Average) m1 = Σp(T)×T– Variance σ2= Σp(T)×(T-m1)2= Σp(T)×T2-m1– Squared coefficient of variance: C = σ2/m12Aggregate 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– Disk response times C ≈ 1.5 (majority seeks < avg)• Mean Residual Wait Time, m1(z):– Mean time must wait for server to complete current task– Can derive m1(z) = ½m1×(1 + C)» Not just ½m1 because doesn’t capture variance– C = 0 ⇒ m1(z) = ½m1; C = 1 ⇒ m1(z) = m1Mean (m1)meanMemorylessDistributionof service timesσLec 18.611/02/05Kubiatowicz CS162 ©UCB Fall 2005A Little Queuing Theory: Mean Wait Time• Parameters that describe our system:– λ: mean number of arriving customers/second– Tser: mean time to service a customer (“m1”)– C: squared coefficient of variance = σ2/m12– μ: service rate = 1/Tser– u: server utilization (0≤u≤1): u = λ/μ = λ×Tser• Parameters we wish to compute:– Tq: Time spent in queue– Lq: Length of queue = λ×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× ½(1+C)» Chance something at server = u ⇒ mean time is u × m1(z)• Computation of wait time in queue (Tq):– Tq= Lq× Tser+ u × m1(z)Arrival Rate λQueueServerService Rate μ=1/TserLec 18.711/02/05Kubiatowicz CS162 ©UCB Fall 2005A Little Queuing Theory: M/G/1 and M/M/1• Computation of wait time in queue (Tq):Tq= Lq× Tser+ u × m1(z) Tq= λ×Tq× Tser+ u × m1(z) Tq= u × Tq+ u × m1(z)Tq× (1 – u) = m1(z) × u ⇒ Tq= m1(z) × u/(1-u) ⇒Tq= Tser× ½(1+C) × u/(1 – u)• Notice that as u→1, Tq→∞ !• Assumptions so far:– 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• General service distribution (no restrictions), 1 server:– Called M/G/1 queue: Tq= Tser× ½(1+C) × u/(1 – u))• Memoryless service distribution (C = 1):– Called M/M/1 queue: Tq= Tser× u/(1 – u)Little’s LawDefn of utilization (u)Lec 18.811/02/05Kubiatowicz CS162 ©UCB Fall 2005A 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 = λTser– What is the average time spent in the queue? » Ans: Tq– What is the number of requests in the queue? » Ans: Lq= λTq– What is the avg response time for disk request? » Ans: Tsys= Tq+ Tser(Wait in queue, then get served)• Computation:λ (avg # arriving customers/s) = 10/sTser(avg time to service customer) = 20 ms (0.02s)u (server utilization) = λ×Tser= 10/s × .02s = 0.2Tq(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) = λ×Tq=10/s × .005s = 0.05Tsys(avg time/customer in system) =Tq+ Tser= 25 msLec 18.911/02/05Kubiatowicz CS162 ©UCB Fall 2005Disk Scheduling• Disk can do only one request at a time; What order do you choose to do queued requests?• FIFO Order– Fair among requesters, but order of arrival may be to random spots on the disk ⇒ Very long seeks• SSTF: Shortest seek time first– 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• 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 middle2,32,13,107,25,22,2HeadUserRequests142Disk Head3Lec 18.1011/02/05Kubiatowicz CS162 ©UCB Fall 2005Administrivia• My office hours– How many people would like me to have an office hour on Tuesday or Thursday?• Better get
View Full Document
Unlocking...