Daniel Stodolsky

Parity logging overcoming the small write problem in redundant disk arrays

Parity encoded redundant disk arrays provide highly reliable, cost effective secondary storage with high performance for read accesses and large write accesses. Their performance on small writes, however, is much worse than mirrored disks—the traditional, highly reliable, but expensive organization for secondary storage. Unfortunately, small writes are a substantial portion of the I/O workload of many important, demanding applications such as on-line transaction processing. This paper presents parity logging, a novel solution to the small write problem for redundant disk arrays. Parity logging applies journalling techniques to substantially reduce the cost of small writes. We provide a detailed analysis of parity logging and competing schemes—mirroring, floating storage, and RAID level 5— and verify these models by simulation. Parity logging provides performance competitive with mirroring, the best of the alternative single failure tolerating disk array organizations. However, its overhead cost is close to the minimum offered by RAID level 5. Finally, parity logging can exploit data caching much more effectively than all three alternative approaches.

The Scotch parallel storage systems

To meet the bandwidth needs of modern computer systems, parallel storage systems are evolving beyond RAID levels 1 through 5. The parallel Data Lab at Carnegie Mellon University has constructed three Scotch parallel storage testbeds to explore and evaluate five directions in RAID evolution: first, the development of new RAID architectures to reduce the cost/performance penalty of maintaining redundant data; second, an extensible software framework for rapid prototyping of new architectures; third, mechanisms to reduce the complexity of and automate error-handling in RAID subsystems; fourth, a file system extension that allows serial programs to exploit parallel storage; and lastly, a parallel file system that extends the RAID advantages to distributed parallel computing environments. This paper describes these five RAID evolutions and the testbeds in which they are being implemented and evaluated.

Parity logging disk arrays

Parity-encoded redundant disk arrays provide highly reliable, cost-effective secondary storage with high performance for reads and large writes. Their performance on small writes, however, is much worse than mirrored disks—the traditional, highly reliable, but expensive organization for secondary storage. Unfortunately, small writes are a substantial portion of the I/O workload of many important, demanding applications such as on-line transaction processing. This paper presents parity logging, a novel solution to the small-write problem for redundant disk arrays. Parity logging applies journalling techniques to reduce substantially the cost of small writes. We provide detailed models of parity logging and competing schemes—mirroring, floating storage, and RAID level 5—and verify these models by simulation. Parity logging provides performance competitive with mirroring, but with capacity overhead close to the minimum offered by RAID level 5. Finally, parity logging can exploit data caching more effectively than all three alternative approaches.

A note on exploiting the Hamiltonian cycle problem substructure of the Asymmetric Traveling Salesman Problem

The assignment problem is a well-known relaxation of the Asymmetric Traveling Salesman Problem (ATSP). Associated with every optimal dual solution to the assignment problem is a directed admissible graph. An ATSP solution is found if the admissible graph is Hamiltonian, otherwise the assignment problem bound may be strengthened. The exploitation of this result requires an exact algorithm for the directed Hamiltonian cycle problem. Computational results are presented for up to 3000 cities to show that determining the Hamiltonicity of admissible graphs improves the performance of an exact ATSP algorithm.