Highly Available and Heterogeneous ContinuousMedia Storage Systems

Roger Zimmermann and Shahram Ghandeharizadeh, Member, IEEE

IEEE TRANSACTIONS ON MULTIMEDIA DECEMBER 2004

Outline

Introduction Three alternative techniques

Independent subservers Dependent subservers Disk merging

Reliability modeling Simulation results Conclusion

Introduction

Problems (heterogeneous disks) Magnetic disks might fail. Storage requires are ever increasing.

Requirements Parity-based data protection. High throughput. Low cost. Long lifetime.

Mean time to service loss (MTTSL)

Three alternative techniques

Video X

:

:

:

Block 2

Block 1

Block 0

Fragment 1Fragment 0 Fragment 2

Parity

X0,0 X0,1 X0,2

X1,0 X1,1 X1,2

X2,0 X2,1 X2,2

X0,p

X1,p

X2,p

•4 disks; can be repaired if a disk is failed.

Independent subservers (1/2)

Technique 1: independent subservers. Objects X, Y, etc., are assigned to only one parity group.

Independent subservers (2/2)

Advantage Easy Reliable

Disadvantage Load 集中於存 hot video 的 parity group( 有 hot s

pot) Low throughput

Dependent subservers (1/2)

Technique 2: dependent subservers. Objects X, Y, etc., are assigned to all parity group.

Dependent subservers (2/2)

Advantage Load distribution High throughput

Disadvantage The same object 的各區域保護不一致 Low availability (MTTSL is short)

Disk merging (1/2)Technique 3: physical (heterogeneous) and logical (homogeneous) view of a multidisk storage server employing disk merging. Six physical disks are mapped to 12 logical disks.

Disk merging (2/2)

Advantage The same of dependent subservers Low memory 、 low cost 容易擴充，對 heterogeneous 的適應較佳

Disadvantage MTTSL is short ( 但也夠長了 )

Constraint includes A physical disk drive should not form multiple logical

disks of a single parity group.

Reliability Modeling

Analytical of reliability modeling Reliability of a single disk. Multiple disks; a single parity group. Logical disks; a single parity group. Logical disks; multiple parity groups.

Reliability of a single disk.

MTTR : mean time to repair. μ: The repair rate. MTTR=(1/μ) .

Ref:D. P. Siewiorek and R. S. Swarz, The Theory and Practice of Reliable Systems Design. Bedford, MA: Digital Press, 1982.

R(t): The reliability function of a system.MTTF: mean time to failure.λ: The failure rate

Multiple disks; a single parity group. (1/4)

Figure : Markov model for a heterogeneous disk array (one parity group). The labels in each state denote the number of disk failures encountered by the array.

λi: the failure rate of disk i.

μi: the repair rate of disk i.

G: independent physical disk drives.

Multiple disks; a single parity group. (2/4)

Simplified Markov model for a heterogeneous disk array.

We can be solved MTTSL using a set of linear equations and Laplace transforms.

Multiple disks; a single parity group. (3/4)

Example: compute the MTTSL of state 0 to state 2

Multiple disks; a single parity group. (4/4)

MTTR: mean time to repair.

MTTF: mean time to failure.

Let μ=1/MTTRdisk ,λi=1/MTTFdiski

Logical disks; a single parity group.

Disk merging can not guaranteed for all the disks are independent.

Two case of logical disk are possible: A logical disk maps to exactly one physical disk

The MTTF of logical disk is equal to physical disk. A logical disk maps to multiple physical disks.

The MTTF of logical disk is harmonic sum for failure of independent components.

Logical disks; multiple parity groups.

Large storage systems Many logical disks. Many parity groups.

If the groups are assumed to be independent, then the reliability is

The MTTSL is harmonic sum of series of groups.

R: reliability

D: the number of physical disk

G: the parity group size

D/G: the number of parity group

Simulation model

simulation 作法為 每一個時間點在每一個 disk 都有一個機率會發生 d

isk failure 的 event. (disk failure != service loss) 累積了 100000 次的 service loss event 後 , 再求每

一個 service loss 的平均時間，就等於 MTTSL.

Simulation results (1/4)

Simulation results (2/4)

The advantages of disk merging over technique 2 includes A single block size is used across the complete

storage system. (easy to cache & management) In disk merging , a single disk can form a parity

group. But Technique 2 can not.

Simulation results (3/4)

(a) Two heterogeneous test storage systems. (b) Configuration parameters.

Case1: comparison of analytical versus simulation results

Simulation results (4/4)Case2:Impact of Logical-to-physical disk mapping and comparison with RAID 5.

Conclusion

It uses a parity-base fault tolerance techniques for heterogeneous storage systems to allow a mix of physical disk drives to be protected from data and service loss.