M/G/1 Queue Calculator

About this calculator

The M/G/1 queue calculator models a single-server queue with Poisson (memoryless, “M”) arrivals but a general (“G”) service-time distribution — meaning service times don't have to be exponential, unlike the simpler M/M/1 model. It applies the Pollaczek–Khinchine formula, Wq = ρ(1 + Cs²) / (2μ(1 − ρ)), where ρ = λ/μ is utilization, λ is the arrival rate, μ is the service rate, and Cs² is the squared coefficient of variation of service time, to compute expected waiting time, queue length, and utilization.

The key insight the P–K formula captures is that variability in service time — not just its average — drives congestion: for a fixed utilization, a highly variable service process (Cs² > 1) produces much longer queues than a consistent one (Cs² close to 0), which is why call centers and computer networks with unpredictable job sizes need this model rather than the simpler M/M/1. Operations researchers, network engineers, and call-center capacity planners use this calculator to predict wait times from real, non-exponential service-time data.