Truck Queue Time
Estimate Erlang-C truck waiting with stable Erlang-B recursion; Poisson arrivals, exponential independent service, infinite queue; not dispatch simulation.
Description
An M/M/c queue models Poisson arrivals and independent exponential service at identical loaders.
An M/M/c queue models Poisson arrivals and independent exponential service at identical loaders. Stability requires arrival demand below total service capacity.
The tool returns loaderUtilizationFraction (loader utilization fraction); probabilityOfWaiting (probability of waiting); meanQueueMinutes (mean queue minutes); meanQueueTruckCount (mean queue truck count). Input measurements and model parameters are supplied by the caller; the tool computes the stated summary rather than acquiring those measurements.
When to use Truck Queue Time
Use Truck Queue Time when you already have truckArrivalsPerHour, serviceRatePerLoaderHour, loaderCount and want loaderUtilizationFraction, probabilityOfWaiting, meanQueueMinutes, meanQueueTruckCount. This is useful for checking a supplied calculation, documenting a measurement convention, or comparing observations prepared on the same basis.
How to use Truck Queue Time and understand its results
- Enter truckArrivalsPerHour, serviceRatePerLoaderHour, loaderCount using the field table below. Match the units, ordering and data boundaries described in the calculation.
- Run the tool after checking the stated bounds and matching paired observations or categories. A malformed request gives a tool error rather than a usable measurement.
- Read loaderUtilizationFraction, probabilityOfWaiting, meanQueueMinutes, meanQueueTruckCount. Use the calculation and interpretation below to distinguish amounts, ratios, signs and decision flags where applicable.
- Review the supplied parameters and assumptions before using the result in a report or comparing it with another observation.
| Input field | Meaning | Value type and bounds | Requirement |
|---|---|---|---|
| truckArrivalsPerHour | Truck arrivals per hour | number | Required |
| serviceRatePerLoaderHour | Service rate per loader hour | number | Required |
| loaderCount | Loader count | integer | Required |
Use 1–1000 loaders, positive per-loader hourly service and nonnegative arrivals below capacity. Compute Erlang B recursively, convert to waiting probability, then obtain queue minutes and queue count.
utilization = arrivals/(loaders×serviceRate); waitHours = ErlangC/(loaders×serviceRate−arrivals) The symbols refer to the supplied quantities or generated values described above; unit conversions and comparison boundaries follow the stated implementation.
{
"input": {
"truckArrivalsPerHour": 1,
"serviceRatePerLoaderHour": 1,
"loaderCount": 2
},
"output": {
"loaderUtilizationFraction": 0.5,
"probabilityOfWaiting": 0.33333333333333337,
"meanQueueMinutes": 20.000000000000004,
"meanQueueTruckCount": 0.33333333333333337
}
}Limitations and assumptions
Real dispatch, finite fleets, correlated arrivals and non-exponential service can violate the model. This returns queue waiting, excluding service time.
Numerical inputs must be finite. The tool checks its declared input shape and calculation constraints; those checks do not verify the quality, calibration or representativeness of the supplied observations.
Alternative or Complementary methods
Truck Productivity: Estimate scheduled truck throughput with utilization conditional on availability; cycle times include operating delays and fleet dispatch interactions are external. Truck Cycle Time: Sum loaded/empty segment travel and service/queue times; speed profiles are inputs, not traction predictions.
Methodological background: Queueing Systems.1
References
-
Queueing Systems — Richard C. Larson, Massachusetts Institute of Technology OpenCourseWare
Similar or alternative tools
- Truck Productivity
Estimate scheduled truck throughput with utilization conditional on availability; cycle times include operating delays and fleet dispatch interactions are external.
- Truck Cycle Time
Sum loaded/empty segment travel and service/queue times; speed profiles are inputs, not traction predictions.