KingmanQueueScenario
Economics scenarios · Implementation: mlsysim/engine/scenario_definitions/economics.py.
Construct this scenario with keyword inputs. The fields below show the types and defaults declared by this class.
One server under Kingman’s approximation at two utilizations, with a holding price.
Notes
Equation: The result property delegates to the named solver documented below; it converts declared scenario units before passing the inputs.
Assumptions: The queue has one server with stable utilization and supplied arrival/service squared coefficients of variation.
Excludes: Tail guarantees, transient overload, and exact waiting-time distributions.
References
Derivation: the scenario composes mlsysim.physics.serving.calc_kingman_wait_ratio, mlsysim.solvers.KingmanQueueModel. Their contracts supply the underlying equations; property equations show the remaining unit conversions and accounting.
Examples
>>> from mlsysim import Scenarios
>>> scenario = Scenarios.BurstyModelServerQueuePrice
>>> value = scenario.result
>>> type(value).__name__
'KingmanQueueResult'Attributes
| Name | Description |
|---|---|
| arrival_scv | |
| high_utilization | |
| holding_rate | |
| low_utilization | |
| result | Return the typed accounting result from KingmanQueueModel using this scenario’s |
| service | |
| service_scv |
Methods
| Name | Description |
|---|---|
| wait_at | Mean queue wait at stable utilization from Kingman’s variability factor times mean |
wait_at
engine.scenario_types.KingmanQueueScenario.wait_at(utilization)Mean queue wait at stable utilization from Kingman’s variability factor times mean service duration.
Equation: calc_kingman_wait_ratio(utilization, arrival_scv, service_scv) * service.
service
Type: Quantity.
Declared default: required.
arrival_scv
Type: float.
Declared default: required.
service_scv
Type: float.
Declared default: required.
low_utilization
Type: float.
Declared default: required.
high_utilization
Type: float.
Declared default: required.
holding_rate
Type: Quantity.
Declared default: required.
result
engine.scenario_types.KingmanQueueScenario.result
Return the typed accounting result from KingmanQueueModel using this scenario’s declared inputs; units and exclusions follow that solver contract.
Equation: KingmanQueueModel().solve(service, arrival_scv, service_scv, low_utilization, high_utilization, float(holding_rate.to('USD / second').magnitude)).