In overload conditions

the QoS of applications with weakly hard real-time constraint is degraded diversely.To deal with the unfairness case caused by only considering an infinite interval or a fixed finite window loss-rate

this paper brings up a concept with a (

p

k

)constraint

which is based on variable interval.Based on the (p

k)constraint

an algorithm is proposed

named as AWCS(Any Window Constraint Scheduling).A simple version of AWCS is put forward

which is called KWCS(K-Window Constraint Schedule).Extensive experiments show that KWCS can supersede AWCS

and not only achieve comparative performance but also get lower complexity.The properties of two algorithms are addressed

and a general representation of delay bound of the scheduling algorithms is brought forward.Results show

that both AWCS and KWCS can provide better performance than other weakly hard real-time schedule algorithms in heavily overload circumstances.