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Queueing Analytics: Machine Learning, Causal Queueing, and SiMLQ for Data Driven Simulation

Berkely, Sept 2025

Presenter: Opher Baron¹

Joint work with Shany Azaria¹, Dmitry Krass¹, Mark J. van der Laan², Eliran Scherzer¹, Arik Senderovich³, Yehezkel Reshef¹, Zhenghang Xu¹

¹Rotman School of Management, University of Toronto and SiMLQ, HUIJ

²Department of Statistics, University of California, Berkeley

³School of Information Technology, York University and SiMLQ

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Title: Queueing Analytics: Machine Learning, Causal Queueing, and SiMLQ for Data Driven Simulation

Joint work with: Shany Azaria, Dmitry Krass, Mark van der Laan, Eliran Scherzer, Arik Senderovich, Yehezkel Reshef, Zhenghang Xu.

Abstract: The objective of this talk is to expose researchers to the vast possibilities of using modern machinery and data for implementing effective management analytics for processes that can be modeled as queueing systems. Such process are ubiquitous in modern economies, e.g., customers waiting to service, inventory waiting for processing/transportation, payments and invoices waiting to be generated/cleared, computing tasks waiting for resources. I will thus discuss recent developments in queueing analysis based on several papers.

We will start by defining management analytics along descriptive, predictive, comparative, i.e., comparing performance indicators under different interventions, and prescriptive analytics dimensions. We then shortly discuss ML solution for a G/G/1 based upon [1] and its extension to G(t)/G/1 based on [2]. �Our main focus would be on causal queueing models, based upon [3]. Not many organizations have queueing theorists (QTs) in their staff, but many organizations employ well trained Data Scientist (DS). Can DS use data to provide accurate comparative analytics without expertise in queueing? We suggest a data-driven representation of system building blocks to create a non-queueing simulator without prior knowledge of the system. We show that this approach is effective in comparative analytics, when analyzing expected waits for an GI/M/1 with speed-ups. We first demonstrate that DS can successfully refine the parent sets of queueing variables from data using an off-the-shelf algorithm (even under a moderate sample size). We then use machine learning to estimate the causal structure in this queue, e.g., the Lindley's Recursion and use the G-computation to derive inference results of counterfactual interventions. For the GI/M/1 with speed-ups, we compare the performance of estimates obtained by a QT, who uses data driven estimates for the primitives of the queue, with those made by a DS that uses either parametric (where inter-arrival and service time distributions are known) or nonparametric (where both distributions are unknown) estimators. We find that the errors of the DS that requires no knowledge of the system's dynamic and its features and these of the QT (which requires this knowledge) are comparable. Our results suggest that the DS approach would be effective for practical setting- where even experts QTs cannot provide closed-form results.

We will finish with a short demo of SiMLQ. SiMLQ software uses Machine Learning to automate the visualization, Simulation, and optimization of Queueing processes. SiMLQ automatically constructs data-driven simulation models from event-log data collected by common information systems and enables users to improve processes resource management, increase efficiency, reduce cost, and manage risks. SiMLQ- from data to action.

[1] Sherzer E., Baron O., Krass D., Senderovich A., (2023) Supervised Machine Learning for Solving General Queueing Systems INFORMS Journal on Computing (Forthcoming)

[2] Sherzer E., Baron O., Krass D. Reshef, H., Senderovich A., Approximating G(t)/GI/1 queues with deep learning

[3] Baron, O., Krass, D., van der Laan, M., Senderovich, A,. Xu Z. Queueing Causal Models: Comparative Analytics in Service Systems.

�Bio:

Opher Baron is a Distinguished Professor of Operations Management at the Rotman School of Management, University of Toronto and a cofounder and CEO of SiMLQ. He was a visiting associate Professor at the Industrial engineering and Management faculty of Technion (2009/10) and a visiting Professor at the School of Information Management and Engineering, Shanghai University of Finance and Economics (2016/17). He also served as the Academic Director, MMA Program (2021-2023), and the Operations management and statistics area coordinator (2015-2021). He has a PhD in Operations Management from the Sloan School of Management at the Massachusetts Institute of Technology, and an MBA and BSc in Industrial Engineering and Management from the Technion. On the teaching front, Opher is especially proud of the modeling and analytics courses he introduced and teaches at Rotman. On the application front he launched the Covidppehelp.ca platform with his colleagues. This platform has facilitated the flow of millions of PPE items to end-user customers during the global Covid19 pandemic. In 2024 he cofounded SiMLQ Inc. see WWW.SiMLQ.com. SiMLQ automatically constructs data-driven process Simulators (digital twins) by leveraging event log data, Machine Learning and Queueing theory. His research interests include queueing, business analytics, service operations (such as healthcare), autonomous vehicles, and revenue management. Opher's work is published in leading journals such as Operations Research, and Manufacturing & Service Operations Management, and he has won several research and teaching awards and grants, including the 1000 Talents Plan Scholar from the Shanghai Municipal Government, 2017 and the Rotman 2023 Distinguished Scholarly Contribution Award. Opher is active in the operations research and operations management community. He has given numerous invited keynote lectures and seminars, chaired several conferences, clusters, and sessions, and is currently serving on the advisory board and editorial boards of several leading journals.

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Research Team

Opher Baron �Distinguished Professor of Operations Management�University of Toronto

Prev.: Consulting

Dmitry Krass �Sydney Cooper Chair in Business & Technology

University of Toronto

Prev.: Consulting, Custometrics Inc. (co- founder)

Arik Senderovich�Ast. Professor School of Information Technologies �York University

Prev.: Mindzie (academic advisor)

Dr. Shany Azaria

Dr. Yehezkel Reshef

SⁱML^Q // From Data to Action!

Dr. Eliran Sherzer

Mr. Zhengheng Xu

Prof. Mark J. Van der Laan

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Spheres of Business Analytics: �Two Dimensions (Extending Baron, 2021)

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Future

Past

Existing System Alternative Systems Better Systems

Predictive analytics

Prescriptive

Analytics

Descriptive analytics

Comp-

arative

Analytics

How long would customers wait if we adopt policies that we have not observed?

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How Should We Study & Teach Queueing?

They are everywhere:

Service: banks, buses
Manufacturing: WIP is inventory in a queue
Traffic jams…

After analysis their performances can be improved

But:

Can we develop analytics to improve congested systems?
Would today’s simulations suffice?
From Process Mining to QueueMiner

Queueing: why do I care?

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Queueing: What do we need to learn?

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A/B/C/X/Y/Z:

A - Arrivals (Poisson/appointment based/empirical …)
B - Service times (Exponential/lognormal/empirical/ML…)
C - Servers’ capacity (static/dynamic/∞/ML)
X - Queue capacity (finite/infinite)
Y - Service policy (FCFS, LCFS, Processor Sharing/…)
Z - Routing scheme in queueing networks (Markovian/empirical…)

All of these may be state dependent

∞

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Management Analytics in Queueing

Descriptive analytics: How long did customers wait at 11:00am?
Predictive analytics: How long will customers wait at 1:00pm?
Comparative analytics: How long would customers wait if service speed changed at 11:00am (by changing staff, etc.)?
Prescriptive analytics: What is the optimal staffing level?

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Topics of the day ☺

Management Analytics
Causal Queueing Models
SiMLQ From Data to Action! www.SiMLQ.com

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SⁱML^Q // From Data to Action!

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Use Data for Comparative Analytics of Queues

Queueing theorist:

Known arrival / service process and queueing dynamics
Exact analysis (or approximations)
Parameters Estimation
E.g., Pollaczek-Khinchine formula for E(wait) in M/G/1

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Data scientist:

Unknown arrival / service process / queueing dynamics
Causal models
Statistics and ML

Can data be used for comparative analytics of queues �– with limited domain and queueing knowledge?

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Structural Causal Queueing Models (SCQM)

Develop structural causal queueing models (SCQM)
Establish a data-driven estimation roadmap for using SCQM
Numerically test performance

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Knowledge of system and queueing theory does not help much in performing data-driven comparative analytics

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Using Data (Event Logs) in Queueing

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	Queueing �Theorist	Data �Scientist
General solution	Estimate queueing primitives Use the estimation with QT solution methods	Define the default parent set Refine the parent set Estimate structural assignment functions Monte-Carlo simulation
Example (M/M/1 with speed-ups)	Estimate arrival rates, service rates Use Pollaczek-Khinchine	Define the default parent set Refine the parent set Estimate structural assignment functions: Estimate likelihood functions Estimate Lindely’s recursion Monte-Carlo simulation

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Related Works

Queueing theory�Pollaczek (1930), Khinchin(1967), Wang et al. (2015), Yom-Tov and Mandelbaum (2014)
Learning in queues�Palomo and Pender (2020, 2021), Baron et al. (2022), Pender and Zhang (2021)

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Granger Causality�Maziarz (2015), Shojaie and Fox (2022), Tank et al. (2021), Song et al. (2023)
Causal inference under interference�Tchetgen and Van der Weele (2012), Farias et al. (2022), Li et al. (2023), Ding (2024)
G-computation, causal inference with longitudinal data�Robins (1986), Neugebauer and van der Laan (2007), Stitelman and van der Laan (2010), Rytgaard et al. (2022)

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Event Log from an M/M/1 w. Speed-up

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Arrival

Last Arrival

Service End

time

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Queueing Theorist Approach

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This is the gold standard

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Using Data (Event Logs) in Queueing

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	Queueing �Theorist	Data �Scientist
General solution		Define the default parent set Refine the parent set Estimate structural assignment functions Monte-Carlo simulation
Example (M/M/1 with speed-ups)

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SCQM: Event Logs

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Arrival

Last Arrival

Service End

time

Observed variables (so far):

Service Start

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SCQM: Parents Set and Its Refinement

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SCQM: Assignment Function

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Using Data (Event Logs) in Queueing

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	Queueing �Theorist	Data �Scientist
General solution
Example (M/M/1 with speed-ups)		Define the default parent set Refine the parent set Estimate structural assignment functions: Estimate likelihood functions Estimate Lindely’s recursion Monte-Carlo simulation

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SCQM in M/M/1 with Speed-ups

Parent set: Causal graph
Assignment functions: Known
Evaluate:

Likelihood function
Lindley’s recursion
W. intervention: G-comp.

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Lindley’s recursion:

This is the �gold standard

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Causal Model Learning

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Numerical Results: M/M/1 with speed-ups

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Numerical Results: G/M/1 with speed-ups

Uniform inter-arrival time
Queueing theorists: no exact solution -> use approximations

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No-closed form => ML solution

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Generalizing the SCQM

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Structural Causal Queueing Models (SCQM)

Develop structural causal queueing models (SCQM)
Establish a data-driven estimation roadmap for using SCQM
Numerically test performance (G/G/k, Tandem…)
An important tool for modern QT!

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Knowledge of system and queueing theory does not help much in performing data-driven comparative analytics

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Topics of the day ☺

Management Analytics
ML for queueing

Can machines solve general queueing systems? (GI/G/1)
Approximating G(t)/G/1 queues with deep learning

Causal Queueing Models
SiMLQ From Data to Action! www.SiMLQ.com

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SⁱML^Q // From Data to Action!

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From Data to Action!

Automating data-driven

process management using:

Simulation and

Machine

Learning for

Queues

www.SiMLQ-emrgency.com

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Digital Twin Processes

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07

06

04

02

03

01

05

1. Data collection (IT)

5. What if analysis

6. Action Selection

7. Action!

4. Simulation & ML

3. Process map and dashboard

2. Event Log

#	Activity	Time
1	A	8:00
2	A	8:10
1	B	8:11

www.SiMLQ-emrgency.com

www.SiMLQ.com

// From Data to Action!

The process for digital twin creation using SiMLQ starts with existing data in current IT Systems (EPIC in AHS).

The analytical team transforms these data to an event log that enables the creation of process maps (bottom left screenshot) and dashboards (bottom middle, simulation & ML, screenshot) to improve visibility into the process in the data. The team then train a simulation model that can be used to support what if analysis (top right screenshot).

The medical team compare the effectiveness of different actions and a select actions to be implemented. This action then changes the system- leading to new data collected in the system.

A key advantage of SiMLQ is that in contrast to traditional simulation models that take months to develop and calibrate, SiMLQ’s goes from data to simulation in seconds! This allows (i) real time usage of the resulting simulation and (ii) immediate start of the next cycle of “from data to action” using an up-to-date simulation model. This interaction between the data to the simulation model that causes the process, data, and the digital twin to impact each other is the essence of the digital twin process. The quickness of SiMLQ’s simulation model generation facilitates this and allows data driven actions, such as changes of patient routing, in real time.

Another key advantage is the learning from different applications that improve SiMLQ’s automating modeling. The more data SiMLQ has- the better its ED simulation model.

The digital twin process based upon data from several EDS is where the value of SiMLQ gets BIG!

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A More ‘Real’ Process

Shift Effect and Its Impact in Emergency Departments

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Malekzadeh, Parvin

RAZ

NON RAZ

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The SiMLQ team

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Vladislav Nagovitsyn

Ali Jandaghi Alaee

Dr. Shany Azaria

Dr. Parvin Malekzadeh

Arik Senderovich, CTO�

Dmitry Krass, CSO

Opher Baron, CEO

Amirmohammad Naeini

www.SiMLQ-emrgency.com

www.SiMLQ.com

// From Data to Action!

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Demo: https://www.simlq-emergency.com/

RESEARCH AGENDA ON COURT CONGESTION

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July 2024

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Main takeaways:

Management Analytics

Comparative and prescriptive analytics

ML for queueing

Quick accurate solutions for single server queues

Causal Queueing Models

Introduced SCQM that uses data to express PI without domain and queueing knowledge

SiMLQ From Data to Action! www.SiMLQ.com

Scalable Software from Data to Action!

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SⁱML^Q // From Data to Action!

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Thanks!�QNA?

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Presenter: Opher Baron¹
Joint work with Shany Azaria¹, Dmitry Krass¹, Mark J. van der Laan², Eliran Scherzer¹, Arik Senderovich³, Yehezkel Reshef¹, Zhenghang Xu¹

¹Rotman School of Management, University of Toronto and SiMLQ
²Department of Statistics, University of California, Berkeley
³School of Information Technology, York University and SiMLQ

SⁱML^Q // From Data to Action!

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Special Issue on Service Engineering: Data Driven Service Design and Optimization Guest Editors: Opher Baron, Arik Senderovich, Desheng (Dash) Wu

Submission deadline: October 1, 2025
Service design: Data and its processing facilitate modern business models such as sharing or platform operations. How can data improve resource usage and welfare in these businesses?
Service optimization: Using data to set optimal capacity or design systems that maximize efficiency, reduce wait times, and improve resource allocation across various service industries. How can data be used to set optimal service capacity and design systems that maximize efficiency, reduce wait times, and improve resource allocation across various touchpoints?
Enhanced customer experience: Analytics can help service businesses to better understand their customers’ needs and preferences, leading to more personalized and effective ongoing and new services and improved tailored service recommendations.
Information technology in support of service: Data can support the automatic creation, monitoring, and management of business processes, for example, via highlighting automation opportunities or enhancing the usage of digital twins.
Adoption of advanced information technology in services: Modern information technology and algorithms can support services, for example, in high-frequency trading, and AI in support of diagnostics in healthcare, but their adoption often faces difficulties. How can these difficulties be overcome?
Usage of on-line data: Access to real-time data provides businesses with insights into their performance, allowing them to make informed decisions on their operational, tactical, and strategic initiatives.
Applications of AI&ML: Recent algorithms, such as LLM, can overhaul business management, for example, by improving customer support. How could service business use AI&ML to improve productivity?
Improved risk management in services: By analyzing historical data and identifying potential risks, service businesses can make informed decisions about lending, investing, credit rating, and other financial activities.

// From Data to Action!

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Related Works

Queueing theory�Pollaczek (1930), Khinchin(1967), Wang et al. (2015), Yom-Tov and Mandelbaum (2014)
Learning in queues�Palomo and Pender (2020, 2021), Baron et al. (2022), Pender and Zhang (2021)
Granger Causality�Maziarz (2015), Shojaie and Fox (2022), Tank et al. (2021), Song et al. (2023),
Causal inference under interference�Hudgens and Halloran (2008), Tchetgen and VanderWeele (2012), Farias et al. (2022), Li et al. (2023), Ding (2024)
G-computation, causal inference with longitudinal data�Robins (1986), Neugebauer and van der Laan (2007), Stitelman and van der Laan (2010), Petersen et al. (2014), Rytgaard et al. (2022)

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Parent Set Refinement

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L1 regularization

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Team

Software development and implementation

Opher Baron �Distinguished Professor of Operations Management�University of Toronto

Prev.: Consulting

Dmitry Krass �Sydney Cooper Chair in Business & Technology

University of Toronto

Prev.: Consulting, Custometrics Inc. (co- founder)

Arik Senderovich�Ast. Professor School of Information Technologies �York University

Prev.: Mindzie (academic advisor)

Dev. Team

Research Team

Vladislav Nagovitsyn

Seyedsepehr Fazely Petrodi

Dr. Shany Azaria

Dr. Yehezkel Reshef

Data Sci.

Ali Jandaghi Alaee

75+ years of innovative research, teaching, and consulting

Data + AI, simulation, optimization, queueing, process management, business analytics for strategic decisions

SⁱML^Q // From Data to Action!