In [12_del] workflow scheduling algorithms have classified into

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In 12_del workflow scheduling algorithms have
classified into two main categories:QoS constrained and QoS optimization. The
QoS constrained algorithms try to optimize some QoS parameters while meeting
other user-defined QoS constraints. For instance, some
studies have considered budget constraint while minimizing makespan. In 19kargahi, a primitive
scheduling that minimizes the makespan is constructed. If the cost is within
the budget, the schedule will be finalized. Otherwise, tasks are remapped to
the cheaper processorswhich can meet the budget constraint. The QoS
optimization algorithm attempts to optimize all QoS parameters. In this
category, some research has been conducted to provide a balance between QoS
parameters such as time and cost in 13–16 del. In the mentioned works, it is
supposed that the processors are always available. However, in real world, the
failure of processors and networks is inevitable. The resources may become unavailable
due to reasons such as link failure, power variation and software/hard ware failures
23,24kargahi. Thus, considering reliability is essential for efficient
workflow scheduling to reduce the failure of workflow execution. Based on the
common Exponential distribution assumption in the reliability research 31
rel2017, for each processor, the arrival of failures follows a Poisson
distribution with

, which is a positive real number, and equal to
the expected number of occurrences of failures in unit time

.And the reliability during the interval of time

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. 10rel2010 MCMS and PRMS are developed to
achieve the maximum system reliability while satisfying a given time
constraint. Obviously, the reliability achieved by these research is limited
and special schemas, such as active replication, are necessary. The primary and
backup scheduling algorithm can tolerate one failure in the systems. Main
representative methods include efficient fault-tolerant reliability cost driven
(eFRCD) 33,rel 2017_2, efficient fault-tolerant reliability driven (eFRD) 34rel
2017-2, and minimum completion time with less replication cost (MCT-LRC) 35rel
2017-2 et al. Regarding their limitations, first, these approaches assume that
no more than one failure happens at one moment; they are too ideal to tolerate
potential multiple failures.In 2 rel2017_1, Benoit et al. presented the FTSA
algorithm which uses ? +1 replicas for each task to guarantee the system
reliability. In 21, Benoit et al. further designed a new scheduling algorithm
to minimize schedule length under both throughput and reliability constraints
for a parallel application on heterogeneous systems based on the active
replication scheme. The main problem in 2 rel 2017 1, 21rel2017_2 is that
they need ? backups for each task with high redundancy to satisfy application’s
reliability requirement. This will lead to large resource redundancy which has
an adverse impact for the system performance and causes high resource cost.Recent
studies begun to explore active redundancy for each task approach to satisfy
application’s reliability requirement 14rel2017-2, 15rel2017-2. Active
redundancy means different tasks have different numbers of replicas, and this
approach has lower resource cost than the fixed ? backups for each task based
on active replication 14 rel2017-2. In 14rel2017-2 and 15rel2017-2, the
authors proposed fault-tolerant scheduling algorithms MaxRe and RR; both MaxRe
and RR incorporate reliability analysis into the active replication and exploit
a dynamic number of backups for different tasks by considering each task’s sub-reliability
requirement. MaxRe and RR have limitations in calculating the sub-reliability
requirements of tasks. In 15rel2017-2, the authors also presented the DRR
algorithm that extends RR by further considering the deadline requirement of a
parallel application; also, we are interested in satisfying reliability and
deadline requirement in this study. However, some of these algorithms do not
consider communication between tasks as well as failure of the links in a

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