Real-time scheduling with resource sharing on heterogeneous multiprocessors

Consider the problem of scheduling a task set τ of implicit-deadline sporadic tasks to meet all deadlines on a t-type heterogeneous multiprocessor platform where tasks may access multiple shared resources. The multiprocessor platform has mk processors of type-k, where k∈{1,2,…,t}. The execution time of a task depends on the type of processor on which it executes. The set of shared resources is denoted by R. For each task τi, there is a resource set Ri⊆R such that for each job of τi, during one phase of its execution, the job requests to hold the resource set Ri exclusively with the interpretation that (i) the job makes a single request to hold all the resources in the resource set Ri and (ii) at all times, when a job of τi holds Ri, no other job holds any resource in Ri. Each job of task τi may request the resource set Ri at most once during its execution. A job is allowed to migrate when it requests a resource set and when it releases the resource set but a job is not allowed to migrate at other times. Our goal is to design a scheduling algorithm for this problem and prove its performance.