What is the difference between M/M/1 and M/M/c queues?

M/M/1 has a single server; M/M/c has c parallel servers. Both assume Poisson arrivals and exponential service times. The calculator reports utilization, Lq, L, Wq, and W for each.

What does utilization (ρ) mean in queuing?

Utilization is the fraction of time servers are busy (ρ = λ/μ for M/M/1). The system is only stable when ρ < 1; otherwise the queue grows without bound.

Queue Problem Solver

Analyze queuing systems using M/M/1 and M/M/c models

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Queue Model

Arrival Rate (λ)

Customers per unit time

Service Rate (μ)

Customers per unit time per server

Utilization Preview: ρ = λ / (c × μ) = 10 / (1 × 15) = 0.6667

Import CSVCSV: parameter,value — arrivalRate, serviceRate, numServers, queueModel (M/M/1 or M/M/c). After Solve, also Export results CSV.

Queue Problem Solver

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Theory of Queuing Systems

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