Operations research application: Queuing theory is applied to which of the following problem domains?

Introduction / Context:
Queuing theory studies waiting lines where entities arrive, wait for service, are served, and depart. It is an operations research tool for designing and controlling service systems, manufacturing flows, and transportation networks.

Given Data / Assumptions:

• Stochastic arrivals (often Poisson) and service times (e.g., exponential) are common assumptions.
• Performance measures include average queue length, waiting time, server utilization, and probability of delay.
• Goal is to balance service capacity against waiting costs.

Concept / Approach:
Queuing models (e.g., M/M/1, M/M/c, M/G/1) capture the dynamics of systems with variability. They apply to machine repair, call centers, hospital triage, traffic intersections, and even production scheduling when stations and buffers behave as queues.

Step-by-Step Solution:

Verification / Alternative check:
Simulation of arrival/service variability confirms analytical predictions and aids complex, non-Markovian cases.

Why Other Options Are Wrong:
Each single domain alone underrepresents the breadth of queuing theory; it is relevant across all listed areas.

Common Pitfalls:
Assuming deterministic flow; neglecting variability leads to undersized capacity and long waits.

Final Answer:
All of these