Generally,aparallelapplicationconsistsofprecedenceconstrainedstochastictasks,wheretaskprocessingtimesandintertaskcommunicationtimesarerandomvariablesfollowingcertainprobabilitydistributions.Schedulingsuchprecedenceconstrainedstochastictaskswithcommunicationtimesonaheterogeneousclustersystemwith