Useful Parameters

Basic Definition of Service Rate

πœ‡= Number of customers served / Total service time
Or simply: πœ‡=1/Average service time
If average service time = 5 minutes per customer:
πœ‡=1/5 =0.2 customers per minute

Arrival Rate vs Service Rate

Arrival Rate vs Service Rate
Ξ» (lambda) = arrival rate (customers per unit time)
ΞΌ (mu) = service rate

Utilization Factor

Traffic Intensity (Utilization Factor)
𝜌=πœ†/πœ‡
If ρ < 1 β†’ system is stable
If ρ β‰₯ 1 β†’ queue will grow indefinitely

Little’s Law

Relationship Between Time and Number
𝐿 =πœ†π‘Š πΏπ‘ž=πœ†π‘Šπ‘ž

Quick Summary

Service rate (ΞΌ) = speed of serving customers
ΞΌ = 1 / service time
Always ensure that: πœ‡>πœ†

Simple Example

If: Arrival rate (Ξ») = 4 customers/hour Service rate (ΞΌ) = 6 customers/hour
Then: 𝜌=4/6 =0.67
πŸ‘‰ System is stable.

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