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Foundations of Waiting Line Theory for Operations Leaders

Course Orientation and Operational Framing of Queuing Problems

Stochastic Building Blocks: Random Variables, Poisson Arrivals, and Exponential Service

Core Single-Server Models: M/M/1, M/M/1/K, and M/M/1 with Balking and Reneging

Parallel Capacity and Quality of Service: M/M/c and M/M/c/K Systems

General Service and Arrival Distributions: M/G/1, G/G/1, and Variability Impacts

Networks of Queues and Flow in Operations

Little’s Law, Conservation Laws, and Performance Diagnostics

Designing Control Policies and Queue Disciplines for Business Objectives

Simulation for Validation and Decision Support: Discrete-Event Methods

End-to-End Case Practicum: From Problem Framing to Governance

Knowledge Checks and Applied Quizzes

Quiz 1: Foundations and Notation

Quiz 2: Arrival and Service Processes

Quiz 3: M/M/1 Models and Stability

Quiz 4: Multi-Server Systems and Erlang Formulas

Quiz 5: Variability Effects in M/G/1 and G/G/1

Quiz 6: Queue Disciplines and Priorities

Quiz 7: Networks of Queues

Quiz 8: Little’s Law and Diagnostics

Quiz 9: Control Policies and Staffing under Variability

Quiz 10: Simulation and End-to-End Design

Master the science and practice of waiting lines to unlock throughput, service levels, and cost efficiency across your operations. End-to-End Queuing Systems: Modeling, Simulation, and Operational Design is a practitioner-focused course for supply chain and operations leaders who need to diagnose congestion, right-size capacity, and design reliable service experiences. You’ll progress from foundational probability concepts and classic M/M/1 models to multi-server systems, general interarrival/service distributions, and networks of queues. Along the way, you will connect every concept to business KPIs—utilization, wait times, abandonment, service-level targets, and total cost of ownership. The course blends analytic formulas (Erlang B/C, Pollaczek–Khinchine, Kingman’s approximation) with hands-on discrete-event simulation to validate assumptions, quantify risk, and guide decisions under variability and seasonality. You will learn to set staffing using square-root safety, implement priority disciplines aligned to SLAs, and design controls such as WIP caps, admission policies, reservations, and dynamic pricing. The capstone practicum takes you from strategy to governance, building an implementation roadmap with data, diagnostics, and monitoring. Whether you run call centers, warehouses, clinics, or transportation hubs, this course equips you to model, simulate, and operationalize queues end-to-end—turning variability into a competitive advantage.

End-to-End Queuing Systems: Modeling, Simulation, and Operational Design

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            <p>Queuing systems sit at the heart of operational performance, translating variability in arrivals and service into the realities of throughput, service level, cost, and risk. This course equips supply chain and operations managers to model, analyze, simulate, and design end-to-end waiting line systems across warehouses, call centers, hospitals, retail, transportation, and manufacturing. We begin with a pragmatic framing of queuing problems and the KPIs executives care about, then build the stochastic foundations—Poisson arrivals, service-time modeling, renewal processes, and diagnostics for the memoryless assumption—grounded in real data practices such as stationarity checks, overdispersion assessment, time-of-day effects, and parameter estimation for λ and μ with confidence intervals and goodness-of-fit.</p>
<p>Analytical competence progresses from single-server models (M/M/1 variants with finite capacity, balking, and reneging) to multi-server systems (M/M/c, M/M/c/K) where Erlang B and C inform delay and blocking, staffing to targets, and the pooling benefits and limits of parallel capacity. We generalize to M/G/1 and G/G/1 to quantify the impact of variability via SCV, Pollaczek–Khinchine, and Kingman’s approximation, and study queue disciplines and priorities—FCFS, LCFS, preemption—to align with SLAs and risk profiles. The course then extends to networks of queues—Jackson and Gordon–Newell product-form models, bottleneck analysis, visit ratios, WIP controls such as Kanban and CONWIP—and leverages Little’s Law and conservation principles for system-wide diagnostics. Design-centric modules translate analytics into operational policy: architecture choices (single pooled vs dedicated lines), admission control, dynamic pricing, and time-varying staffing (including SIPP), all under explicit cost models for capacity, waiting, abandonment, and penalties.</p>
<p>Because managerial decisions must be validated under real-world variability, a dedicated simulation block develops discrete-event methods: event scheduling, resource modeling, input modeling and calibration, warm-up detection, run-length selection, variance reduction, and design of experiments for sensitivity and what-if analysis. The capstone practicum integrates strategy, model selection, data governance, and stakeholder communication into an implementable roadmap with monitoring, control charts, and continuous improvement. Knowledge checks throughout solidify foundations—from notation and arrival/service processes to multi-server Erlang formulas, variability effects, network behavior, diagnostics, control policies, and simulation—ensuring participants can move from conceptual models to defendable, KPI-linked operational designs.</p>
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