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QueueWaitScenario

Serving scenarios · Implementation: mlsysim/engine/scenario_definitions/serving.py.

Construct this scenario with keyword inputs. The fields below show the types and defaults declared by this class.

A fleet modeled as one M/G/1 server at offered load utilization.

The mean queue wait, as a multiple of the mean job, is a load factor rho/(1-rho) times a variability factor (1 + C_s^2)/2. The model ignores gang packing and parallel admission; it isolates the effect of load and of spread in job durations.

Notes

Equation: Compose mlsysim.physics.serving.calc_mg1_wait_ratio.

Assumptions: A stable FCFS M/G/1 queue has Poisson arrivals and a supplied service-time coefficient of variation.

Excludes: Multiple-server scheduling, non-Poisson arrivals, and transient overload are absent.

References

Derivation: this scenario binds its input fields to the referenced implementation contracts: mlsysim.physics.serving.calc_mg1_wait_ratio. The methods below identify any additional arithmetic.

Examples

>>> from mlsysim import Scenarios
>>> case = Scenarios.Mg1MixedJobQueueAt80
>>> round(case.load_factor, 4)
4.0

Attributes

Name Description
load_factor Utilization contribution to the M/G/1 waiting-time ratio. Equation: utilization / (1 - | | [service_cv](#mlsysim.engine.scenario_types.QueueWaitScenario.service_cv) | | | [utilization](#mlsysim.engine.scenario_types.QueueWaitScenario.utilization) | | | [variability_factor](#mlsysim.engine.scenario_types.QueueWaitScenario.variability_factor) | Service-time variability contribution to M/G/1 mean waiting. Equation:(1 + service_cv
wait_ratio Mean queue wait divided by mean service duration. Equation:

utilization

Type: float.

Declared default: required.

service_cv

Type: float.

Declared default: required.

load_factor

engine.scenario_types.QueueWaitScenario.load_factor

Utilization contribution to the M/G/1 waiting-time ratio. Equation: utilization / (1 - utilization). Units: dimensionless; requires utilization below one for a stable queue.

variability_factor

engine.scenario_types.QueueWaitScenario.variability_factor

Service-time variability contribution to M/G/1 mean waiting. Equation: (1 + service_cv ** 2) / 2. Units: dimensionless; arrivals are Poisson in this model.

wait_ratio

engine.scenario_types.QueueWaitScenario.wait_ratio

Mean queue wait divided by mean service duration. Equation: mlsysim.physics.serving.calc_mg1_wait_ratio(utilization, service_cv). Units: dimensionless; FCFS single-server assumptions apply.

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