Robust heavy-traffic approximations for service systems facing overdispersed demand.

Area of Science:

• Operations Research
• Applied Probability
• Stochastic Modeling

Background:

• Service systems often exhibit arrival rate variability exceeding Poisson process assumptions, a phenomenon known as overdispersion.
• Overdispersion can lead to inaccurate performance predictions and inefficient capacity planning in traditional models.
• Accurate modeling of arrival processes is crucial for optimizing service system design and operation.

Purpose of the Study:

• To develop scalable heavy-traffic approximations for discrete-time stochastic models exhibiting overdispersion.
• To introduce novel capacity sizing rules that explicitly account for overdispersion.
• To provide robust performance approximations for moderately sized systems and those not operating in heavy traffic.

Main Methods:

• Analysis of a class of discrete-time stochastic models.
• Derivation of heavy-traffic approximations scalable with system size.
• Development of capacity sizing rules incorporating overdispersion.
• Validation of approximations for performance characteristics.

Main Results:

• Scalable heavy-traffic approximations were derived for systems with overdispersed arrival processes.
• Novel capacity sizing rules were established, effectively managing overdispersion.
• Robust performance approximations were achieved for moderate and non-heavy traffic conditions.
• The proposed methods demonstrated improved accuracy over traditional approaches.

Conclusions:

• The developed models and methods effectively address overdispersion in service system arrivals.
• The novel capacity sizing rules enhance system robustness and efficiency.
• This research provides valuable tools for designing and managing service systems with complex arrival patterns.