Translating Empirical State-Dependent Service Times Into Queueing Models.

Area of Science:

• Operations Research
• Queueing Theory
• Behavioral Economics

Background:

• Empirical studies indicate human behavior influences service times in queues, leading to workload dependency.
• Existing queueing models often simplify or ignore these behavioral impacts on service times.

Purpose of the Study:

• To investigate the translation of empirical, workload-dependent service times into state-dependent queueing models.
• To differentiate between static and dynamic behavioral mechanisms influencing service times.
• To provide analytical guidelines for selecting appropriate queueing models based on service time data.

Main Methods:

• Identification and categorization of static and dynamic state-dependent queueing models.
• Analysis of behavioral mechanisms (e.g., early task initiation, social pressure) within these models.
• Translation of empirical service time data into model input parameters for static and dynamic models.
• Derivation of closed-form equations for converting service times to service rates and vice versa.

Main Results:

• Translating service times into dynamic models can yield invalid service rates, challenging dynamic behavioral mechanisms.
• For dynamic models, mean service times are not always the inverse of service rates.
• Workload measurement timing significantly impacts observed mean service time patterns in dynamic models.
• Conditions for monotonic relationships between mean service times and service rates were identified.

Conclusions:

• The study provides evidence against certain dynamic behavioral mechanisms in queueing systems.
• Guidelines are offered for researchers to select and specify state-dependent queueing models using empirical service time data.
• The analytical scope of queueing theory is expanded by incorporating empirical service time dynamics.