Queuing Model Examples

Mathematical Modeling · Axiom Academy

EXAMPLE Queuing Model Examples Master queuing theory through worked examples: bank tellers, call centers, wait times, and utilization Problem: Single Bank Teller Queue Scenario: A small bank branch has one teller window. Customers arrive randomly throughout the day, and each customer requires a variable amount of time to be served. Given: Customers arrive at an average rate of 12 per hour (Poisson process). The average service time is 4 minutes per customer (exponentially distributed). Find: The utilization, average wait time in queue, average total time in system, and average number of customers waiting. What do these results tell us? At 80% utilization, the teller is busy most of the time, but customers experience significant waits (16 minutes on average). The high wait time relative to service time is characteristic of queuing systems - even moderate utilization leads to congestion. If arrival rate increased to 14/hour (rho = 0.93), wait times would nearly triple! Step 1: Understanding Utilization The utilization rho = 0.8 means the teller is busy 80% of the time. Why does this relatively moderate utilization still lead to such long wait times? Scenario: A call center needs to determine how many agents to staff. Callers expect quick answers, and the company has a service level agreement (SLA) requiring 80% of calls to be answered within 20 seconds.

This is the written version of the interactive lesson above. See the full Mathematical Modeling course.