Efficiently calculate key metrics for your queueing systems with our free online Queueing Theory Calculator. Analyze customer waiting times, server utilization, and system stability using M/M/1 model principles. Optimize service delivery and resource allocation for better customer experience and operational efficiency.
Formula:
For an M/M/1 queueing system (single server, Poisson arrivals, exponential service times):
- Utilization (ρ): ρ = λ / μ
- Average Customers in System (L): L = λ / (μ - λ)
- Average Customers in Queue (Lq): Lq = λ2 / (μ * (μ - λ))
- Average Time in System (W): W = 1 / (μ - λ)
- Average Time in Queue (Wq): Wq = λ / (μ * (μ - λ))
- Probability of Empty System (P0): P0 = 1 - ρ
- λ (Lambda): Arrival Rate (e.g., customers per hour)
- μ (Mu): Service Rate (e.g., customers per hour)