Abstract
The reliability of modular (n-out-of-m)-systems can not only be improved by an increase in the number of replicates, but also by the provision of additional facilities for backward recovery. The latter approach combines static and dynamic redundancy, resulting in two main advantages: Firstly, more fault types are tolerated, even particular propagating faults which cause loss of the majority. Secondly, the expense of joint application of voting and backward recovery can be significantly reduced to be lower than the sum of expenses of separate implementation of the two techniques.
In this paper, we present a concept of an efficient recoverable (n-out-of-m)-system. Its efficiency is achieved by novel solutions in the particular design space induced by the combination of different techniques: • The establishment of recovery points is shifted into idle phases of any of the m redundant processors as far as possible. • The necessary synchronization is implemented by a special agreement protocol which only consists of the messages needed for fault masking anyway, provided that the communication system enables multicast (no reliable multicast required!). • Both relative and absolute tests contribute to fault detection. • Depending on the actual fault situation, the state information for recovery can be obtained from the established recovery points or a faultless replicate, if there is any. Moreover, the replicates may be rolled back independently or in common. These choices enable compromises between fault encapsulation and performance.
A brief evaluation turns out that our concept of recovery in (n-out-of-m)-systems can be more efficient than an increased number of replicates, because during normal operation the overhead of establishing recovery points can be reduced, and in the presence of faults additional fault types can be tolerated.
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Abbreviations
- A:
-
application process to be implemented in a fault-tolerant way
- A1, …, Am :
-
replicates of the application process A (The replicates form static redundancy)
- APS:
-
agreement protocol with signatures
- fL :
-
maximum number of faulty links
- fN :
-
maximum number of faulty nodes
- fNL :
-
maximum number of faulty fault regions, consisting of one node and one link
- fS :
-
maximum number of faulty storage locations for recovery points
- fT :
-
maximum number of wrong absolute tests which do not detect a local fault
- FSP:
-
fault masking and synchronization protocol
- IL policy:
-
individual link for each node sending messages during protocol execution
- λ:
-
load caused by other processes
- λ1, …, λm :
-
load of nodes N1,…, Nm
- L1, …, Lm :
-
links, providing a multicast property
- M1, …, Mm :
-
multicast messages of FSP in an (n-out-of-m)-system
- m:
-
number of replicates to form a statically redundant (n-out-of-m)-system
- MVS:
-
majority-violating syndrome
- MPS:
-
majority-preserving syndrome
- n:
-
minimum number of faultless replicates in an (n-out-of-m)-system to enable majority voting
- N1,…, Nm :
-
nodes where the replicates A1, …, Am of the application process A are allocated
- Nm+1, …, N2·m :
-
nodes where the voters V1, …, Vm are allocated
- r:
-
number of recovery points available at a single time point
- rmin :
-
minimum number of recovery points, a node is excluded from establishment of recovery points after it has kept the token for the maximum time period tsingle
- R1, …, Rr :
-
recovery points to provide dynamic redundancy for backward recovery
- S1,…, Sr :
-
storage locations for the recovery points R1, …, Rr
- SP:
-
synchonization protocol to determine the node which must establish a recovery point
- τ:
-
additional portion of the execution time required for the establishment of recovery points
- T1, …, Tm :
-
local absolute tests at nodes N1, …, Nm
- token:
-
indication which node must establish the next recovery point
- tmax :
-
maximum message delay
- tsingle :
-
maximum time interval a single node is allowed to keep the token for establishment of recovery points
- V1, …, Vm :
-
voters
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Echtle, K., Niedermaier, A. (1991). Efficient Recovery of Statically Redundant Systems. In: Cin, M.D., Hohl, W. (eds) Fault-Tolerant Computing Systems. Informatik-Fachberichte, vol 283. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-76930-6_3
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