Queueing System Simulation

Poisson arrivals, configurable server pool c, finite total system capacity K, and switchable service-time distributions.

Controls

Arrival rate λ (customers/sec) Mean service time E[S] (sec) Service distribution

Service variability (CV) 0.8

System capacity K Servers c Warm-up time (sec) Measurement window (sec)

Simulation speed 10×

Model Notes

K is total system capacity, including the 2 customers in service. If the system already has K customers, a new arrival is dropped.

The reported averages are based only on the measurement window after warm-up. Wait/system times are conditional on served customers, not dropped arrivals.

Replications

Base seed

Runs

Batch mode re-runs the same scenario with deterministic seeds seed, seed+1, ... and reports 95% confidence intervals.

Arrivals

Queue

Departures

Sim time: 0.0s Phase: Warm-up Measured time: 0.0s In system: 0 In queue: 0 Busy servers: 0 ρ: 0.00

Measured Metrics

Measured arrivals0

Served0

Dropped0

Throughput0.00/s

Avg wait0.00s

Avg system0.00s

Mean util0%

Server utilizations-

Avg queue len0.00

Avg system len0.00

Drop rate0.0%

DistributionGamma

Theoretical Reference

Only available for exponential service, i.e. M/M/c/K.

Modeln/a

Blocking probability-

Expected system size E[N]-

Expected queue size E[Nq]-

Effective arrival rate-

Expected sojourn E[T]-

Replication Summary

Runs0

Seed range-

Mean throughput-

95% CI throughput-

Mean avg wait-

95% CI avg wait-

Mean drop rate-

95% CI drop rate-

Mean avg queue len-

95% CI avg queue len-

Little's Law gap-

Mean util-

History

Queue length System size Drops