Towards Optimality in Parallel Job Scheduling

Elastic Job Scheduling with Unknown Utility Functions

“…the target region (by setting 𝑟 𝜏 to 𝑥 𝑟 ) and proceed to the next epoch. (e) Otherwise, increment 𝑖 and repeat step (2). Note that in step 2(a), each point 𝑥 𝑙 , 𝑥 𝑐 , 𝑥 𝑟 is queried multiple times but each time counts as one query, i.e., the sequence of queries output by the algorithm will have multiple copies of 𝑥 𝑙 , 𝑥 𝑐 , 𝑥 𝑟 .…”

“…The links between job schedulers and servers are randomly generated with each scheduler having expected degree 6 (i.e., connected to 6 servers). At every time slot, the arrival rate of each class is a uniform random variable in {2, 3, 4, 5} while the service rate of each server is a uniform random variable in [2,4]. We assign an underlying utility function to each class of one of the four types:…”

“…Job scheduling is a class of problems that study schedule construction and resource allocation to jobs over a set of machines to optimize for performance objectives such as mean completion time [1,2], makespan [3,5], utility [4,5], and system stability [6,7]. Due to the flexibility and versatility in its modeling and formulation, job scheduling has found a wide range of applications such as supply chain management [1], operating system optimization [2], and cloud computing [6,7,10].…”

“…2 independent samples8 of 𝑓 𝑘 (𝒙 𝑘 ), by Hoeffding's inequality, the lower and upper estimates used by Algorithm 1 satisfies P{𝑓 𝑘 (𝑥 𝑘 ) ∈ [𝑓 𝐿 𝑘 (𝑥 𝑘 ), 𝑓 𝑈 𝑘 (𝑥 𝑘 )]} ≥ 1 − 𝛿/(2𝐾 + 𝑀). The same holds for {𝜆 𝑘 } and {𝜇 𝑚 }.…”