Issues and Challenges in the Performance Analysis

of Real Disk ArraysElizabeth Varki, Arif Merchant,

Jianzhang Xu and Xiaozhou QiuPresented by:Soumya Eachempati

RAID

• Redundant Array of Inexpensive Disks• Redundancy and Striping

– Capacity– Speed (Parallelism)– Availability of storage systems

• Multiple disks, large caches, array controllers - implement load-balancing, request coalescing, adaptive prefetching.

Why - Performance Modeling

• Storage systems are slow.• Any improvement in the performance would

escalate the system performance for I/O intensive applications.

• Metrics used:– Response time– Throughput– Queue length

Approaches

• Analytic - quick and dirty, less expensive

• Simulation - more accurate, lot of effort• So which method will you choose?• Authors develop analytic model that

includes array controller optimizations

Previous Work• Disk array performance• Efficient Caching algorithms• This paper models the parallelism of disk arrays

and effects of caching on performance.• Presents a Baseline model with known parameter

values.• Extraction of array controller optimizations using

the baseline model and workloads that isolate specific optimizations.

Disk Array Architecture

RAID 1/0 configuration

Key Components

Some Assumptions• M jobs generate synchronous requests.• At-most one request from each stream at the

disk array.• Each job spends some time at the CPU

before submitting request to the disk array.• Read only and write only requests stream.• No queueing at the CPU/terminal.

Read Model

Write Model

Response time• Array_response_time[m] =

cache_response_time[m] + disks_response_time[m]

• Array_throughput[m] = m / (CPU_delay + array_response_time[m])

• Cache_queue[m] = cache_response_time[m] * array_throughput[m] (Little’s law)

Response time• Arrival theorem states that the number of jobs

“seen” by a job upon arrival at a subsystem is equal to the mean queue length at the subsystem computed when the network has one less job.

• The response time of the arriving job is equal to the sum of the arriving job’s service time plus the time required to service the jobs seen ahead.

Baseline model parameters

• Disk Service time• Parallelism Overhead• Disk access probability• Cache parameters• Write model input parameters.

Disk Service time

• Very important to get an accurate estimate.

• Seek distance - disk scheduling policy and location of disk IO requests.

€

disk _ service_ time = seek _ time + rotational_ latency + transfer_ time

transfer_ time = diskIO_ sizedisk _ transfer_ rate

Mean _ rotational_ latency = constan t = 0.5* disk _ rotation _ time

Seek _ time =α + β seek _ distance →α + β full_ stroke _ distance (1+ disk _queue)

Disk positioning time

Degree of sequentiality has minimal effect for disk_queue > 3Disk positioning time linear function of disk_queue length for disk_queue < 3 for simplicity.

Cyclic dependancy

• Disk service time depends on disk queue length which again depends on disk service time.

• Assume disk queue length is an input parameter.

• If CPU_delay = 0 then disk_queue = M * disk_access_probability.

Parameters• Parallel_overhead = max_position_time -

disk_position_time• Disk_access_probability = cache_miss_probability *

num_diskIOs_per_request / stripe_width• Cache_hit = 1 - (read_ahead_miss *

re_reference_miss)• Cache_service_time = request_size /

cache_transfer_rate.• Once destage_threshold is reached, writes data to all

the disks at a time.– µ = stripe_width / 2 * disk_service_time

Array controller Optimizations

• Access coalescing policy• Redundancy based load balancing

policy• Adaptive prefetching• Simplest baseline model - small random

read requests with CPU_delay = 0.

Workload Characterization

Setup

• Trace of all IO activity at the device driver level.

• Trace contains– I/O submission and completion times.– Logical addresses– Sizes of requests

Optimizations• Disk I/O accesses to contiguous data on the

same disk coalesced into a single disk IO.• Example : 96KB striped across 3 disks with

stripe unit size = 16KB.• Redundancy load balancing

– Single request distributed to both the disk and its mirror. (transfer time reduction)

– 2 different requests to the disks and its mirrors.(queue length reduction)

Policy effects• Access coalescing and load balancing effect

number of disk IO requests per request.• Large request sizes > stripe_width *

stripe_unit_size• Num_diskIOs_per_request = stripe_width

(transfer time reduction) = stripe_width / 2 for disk_queue_length

reduction.

Access Coalescing• Random workloads - caching is eliminated.• Using large request sizes both the policies

can be evaluated > stripe_width / 2• Adaptive prefetching: Sequential read

requests - workload.• Explicit read-ahead is turned off.• Re-reference hit is zero.

Modeling Adaptive prefetching and load balancing

• Num_disIOs_per_request = stripe_width for request_size > stripe_width * stripe_unit_size

• Ceiling(requests_size / stripe_unit_size)

Load Balancing

• Workload consists of same-sized requests.

Write-back caching• Size at-most 2 stripes.• Large requests - bypass the cache.

Validation• Model performs better for random than

sequential Ios• Random Reads - 3.7%• Random writes - 5.5%• Sequential reads - 8.8%• Sequential writes - 8.0%• Adaptive prefetching works well for disk queue

length < 4.• Disk writes and disk reads similar performance.

Challenges• Disk parameters disk queue length affects the

caching policies as well.• Paucity of data.(Bus transfer rate 35% higher)• Performance as a function of disk array

controller optimizations, array caching policies, workload distributions along with disk service time, the stripe unit size and stripe width.

• Better Approximation of disk queue length.

THANK YOU

Questions?