[Paper Review] Opportunistic Scheduling for Optimal Spot Instance Savings in the Cloud

Neelkamal Bhuyan, Randeep Bhatia+2 more|arXiv (Cornell University)|Jan 18, 2026

Advanced Queuing Theory Analysis0 citations

TL;DR

This paper develops a queuing-theoretic framework for scheduling delay-sensitive jobs over spot and on-demand cloud instances to minimize average cost under a delay constraint, deriving optimal policies for tight and relaxed delay regimes and proposing a learning-augmented adaptive admission policy.

ABSTRACT

We study the problem of scheduling delay-sensitive jobs over spot and on-demand cloud instances to minimize average cost while meeting an average delay constraint. Jobs arrive as a general stochastic process, and incur different costs based on the instance type. This work provides the first analytical treatment of this problem using tools from queuing theory, stochastic processes, and optimization. We derive cost expressions for general policies, prove queue length one is optimal for low target delays, and characterize the optimal wait-time distribution. For high target delays, we identify a knapsack structure and design a scheduling policy that exploits it. An adaptive algorithm is proposed to fully utilize the allowed delay, and empirical results confirm its near-optimality.

Motivation & Objective

• Formalize delay-constrained scheduling of delay-sensitive jobs on spot and on-demand cloud instances as a G/G/1 queuing problem.
• Characterize optimal policies under two delay regimes: tight (low delta) and relaxed (high delta).
• Derive closed-form cost expressions and optimal wait-time distributions; identify a knapsack structure in the relaxed regime.
• Propose an adaptive admission control policy that learns the optimal fractional admission while scheduling on spot instances.
• Validate the approach with empirical results showing near-optimal performance across varying spot availabilities.

Proposed method

• Model the system as a G/G/1 queue with spot and on-demand services and a decision policy that selects joining probability q_n and maximal wait time X_n for each arriving job.
• Derive E[C] = k - (k-1) * (E[A]/E[S_μ]) * (1 - π_0) as the cost per job for general policies.
• Prove optimal queue length of one for delta in a tight regime (δ ≤ P(A ≤ S_μ)/λ) and derive the corresponding E[C] = k - (k-1) μ δ.
• Characterize the optimal maximal wait-time distribution via a linear program that maximizes P(X > S_μ) under the delay constraint (Theorem 3).
• Identify a knapsack structure in the relaxed delay regime and develop a 3-phase greedy policy (Theorem 4) for near-optimal scheduling.
• Introduce Algorithm 1 (Adaptive Admission Control Policy) to learn the optimal fractional admission while scheduling on spot instances.
• Provide learning-augmented policy that empirically converges to optimal behavior under various spot availability patterns.

Experimental results

Research questions

• RQ1 How to minimize average cost per job while ensuring the average delay does not exceed δ when scheduling on spot and on-demand instances?
• RQ2 What queue-length and wait-time policies are optimal in the tight delay regime?
• RQ3 What is the optimal wait-time distribution for the single-slot (queue length ≤ 1) policy under tight delay constraints?
• RQ4 How can a knapsack-like structure be exploited to achieve near-optimality in the relaxed delay regime?
• RQ5 Can an adaptive admission control policy learn and approach the optimal policy in practice across different spot availability patterns?

Key findings

• The cost per job in a general G/G/1 setting is E[C] = k - (k-1) * (E[A]/E[S_μ]) * (1 - π_0).
• In the tight delay regime, the optimal queue length is one, with E[C] = k - (k-1) μ δ for appropriate X distribution.
• The optimal maximal wait-time distribution for the single-slot policy is obtained by solving a linear program that maximizes P(X > S_μ) under the delay constraint.
• In the relaxed delay regime, a knapsack structure emerges, enabling a near-optimal 3-phase greedy policy.
• An adaptive admission control policy (Algorithm 1) learns the optimal fractional admission r* and achieves near-optimal cost with convergence evidence from experiments.
• Empirical results show fast convergence of the adaptive policy across different spot availability patterns and arrival processes.