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Capacity planning and scheduling for jobs with uncertainty in resource usage and duration

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Abstract

Organizations around the world schedule jobs (programs) regularly to perform various tasks dictated by their end users. With the major movement toward using a cloud computing infrastructure, our organization follows a hybrid approach with both cloud and on-prem servers. The objective of this work is to perform capacity planning, i.e., estimate resource requirements, and job scheduling for on-prem grid computing environments. A key contribution of our approach is handling uncertainty in both resource usage and duration of the jobs, a critical aspect in the finance industry where stochastic market conditions significantly influence job characteristics. For capacity planning and scheduling, we simultaneously balance two conflicting objectives: (a) minimize resource usage and (b) provide high quality of service to the end users by completing jobs by their requested deadlines. We propose approximate approaches using deterministic estimators and pair sampling-based constraint programming. Our best approach (pair sampling-based) achieves up to 41.6% estimated peak reduction in resource usage compared to manual scheduling without compromising on the quality of service.

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Notes

  1. Refer to Sect. 3 for definitions of D and R.

  2. Unless mentioned otherwise, the unit of time is in seconds throughout the paper.

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Acknowledgements

The authors would like to acknowledge Alberto Pozanco, Rui Silva, and Daniel Borrajo for their helpful suggestions and comments on this work. This paper was prepared for informational purposes in part by the Artificial Intelligence Research Group of JPMorgan Chase & Co and its affiliates ("J.P. Morgan") and is not a product of the Research Department of J.P. Morgan. J.P. Morgan makes no representation and warranty whatsoever and disclaims all liability, for the completeness, accuracy or reliability of the information contained herein. This document is not intended as investment research or investment advice, or a recommendation, offer or solicitation for the purchase or sale of any security, financial instrument, financial product or service, or to be used in any way for evaluating the merits of participating in any transaction, and shall not constitute a solicitation under any jurisdiction or to any person, if such solicitation under such jurisdiction or to such person would be unlawful.

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The authors have no relevant financial or non-financial interests to disclose.

Author information

Authors and Affiliations

  1. AI Research, J. P. Morgan, New York, USA

    Sunandita Patra & Manuela Veloso

  2. CIB Athena Applied Intelligence, J. P. Morgan, London, UK

    Mehtab Pathan & Wided Ouaja

  3. AI Research, J. P. Morgan, London, UK

    Mahmoud Mahfouz, Parisa Zehtabi & Daniele Magazzeni

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  1. Sunandita Patra
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  2. Mehtab Pathan
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  3. Mahmoud Mahfouz
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  4. Parisa Zehtabi
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  5. Wided Ouaja
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  6. Daniele Magazzeni
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  7. Manuela Veloso
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Correspondence to Sunandita Patra.

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Appendix: Table of symbols

Appendix: Table of symbols

Symbol

Description

COS

Capacity optimization and scheduling

COSPiS

Capacity optimization and scheduling via paired sampling

Det

Deterministic estimator-based constraint programming approach

MILP

Mixed integer linear programming

b

A job represented as a tuple (q, f, u, D, J, R).

q

The requested start time of job b.

f

Flexibility measure indicating the maximum delay allowed for the start of job b after its requested start time q.

u

The latest completion time (deadline) of job b.

D

A list of recorded durations or running times from historic data of job b’s previous executions.

J

The set of jobs that job b depends on; job b can only start once all jobs in J have been completed.

R

The history of the number of CPU cores utilized by job b.

\(B_n\)

The set of n jobs, each represented as \(b_j\).

\(S_n\)

A schedule for n jobs, represented as \((s_1, s_2, \dots , s_n)\), where \(s_j\) is the scheduled start time of job \(b_j\).

T

The maximum timespan (makespan) within which all jobs need to run.

\(S^*_n\)

The optimal start-time schedule for \(B_n\) within a makespan of T.

\(\{s_j\}^n_{j=1}\)

A set of integer variables where \(s_j\) indicates the start time of job \(b_j \in B_n\).

p

An integer variable indicating the maximum (peak) number of CPU cores used across all jobs at any time \(t \in T\).

\({\hat{b}}_j\)

A job \(b_j\) mapped using a deterministic estimator function \(\varvec{{f^{est}}}\).

\({\hat{d}}_j\), \({\hat{r}}_j\)

Estimations of the duration and CPU usage of job \(b_j\), respectively.

\({\textbf{X}}\), \({\textbf{Y}}\)

Sets of job runtime intervals and resource usages for n jobs, used in the cumulative constraint.

\(f^{est}\)

Estimator function

K

Hyperparameter of COSPiS (number of pair samples)

\(\alpha\)

Hyperparameter of COSPiS (tolerance of job deadline violations)

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Patra, S., Pathan, M., Mahfouz, M. et al. Capacity planning and scheduling for jobs with uncertainty in resource usage and duration. J Supercomput 80, 22428–22461 (2024). https://doi.org/10.1007/s11227-024-06282-8

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