complexType "ccmsk:ArrivalProcessParams"

Namespace: | http://www.iro.umontreal.ca/lecuyer/contactcenters/msk
Content: | complex, 15 attributes, 16 elements
Defined: | globally in ccmsk.xsd, see XML source
Includes: | definitions of 12 attributes and 13 elements
Used: | at 2 locations

XML Representation Summary
<...
| arrivalsMult | = | xsd:double : "1"
| checkAgentsForCall | = | xsd:boolean : "false"
| correlationFit | = | ("FULLCORRELATION" | "MARKOVLINEARFIT" | "MARKOVSINGLERHO") : "MARKOVLINEARFIT"
| estimateBusyness | = | xsd:boolean : "false"
| gammaShapeEstimatorType | = | ("SINGLESHAPE" | "SPLINESHAPE") : "SINGLESHAPE"
| gammaShapeSmoothingFactor | = | xsd:double : "0.95"
| maxIter | = | xsd:int : "200"
| movingWindowSize | = | xsd:int : "5"
| name | = | xsd:string
| normalize | = | xsd:boolean : "false"
| numMonteCarlo | = | xsd:int : "200"
| sourceEnabled | = | xsd:boolean : "true"
| splineSmoothingFactor | = | xsd:double : "1"
| type | = | xsd:string
| varianceEpsilon | = | xsd:double : "1.0e-4"
| >
Content: | properties?, sourceToggleTime*, call*, busyGen?, (data | (arvGen?, arrivals) | (poissonGammaShape, poissonGammaRate, copulaSigma?) | arrivalRates | (nortaSigma, nortaGamma, nortaP) | (times, lambdas))
</...>

Content Elements (16):

  arrivalRates (type cc:MultiPeriodGenParams), arrivals (type ssj:nonNegativeDoubleList), arvGen (type ssj:RandomVariateGenParams), busyGen (type ssj:RandomVariateGenParams), call (type ccmsk:ProducedCallTypeParams), copulaSigma (type ssj:DoubleArray), data (type ssj:IntArray), lambdas (type ssj:nonNegativeDoubleList), | nortaGamma (type ssj:positiveDoubleList), nortaP (type ssj:double01iList), nortaSigma (type ssj:DoubleArray), poissonGammaRate (type ssj:nonNegativeDoubleList), poissonGammaShape (type ssj:nonNegativeDoubleList), properties (type ssj:PropertiesParams), sourceToggleTime (type ccmsk:TimeIntervalParams), times (type ssj:nonNegativeDurationList)

All Direct / Indirect Based Elements (2):

  arrivalProcess (type ccmsk:ArrivalProcessParams), | defaultArrivalProcess (type ccmsk:ArrivalProcessParams)

Known Usage Locations

- As direct type of elements (2):

  arrivalProcess (type ccmsk:ArrivalProcessParams), | defaultArrivalProcess (type ccmsk:ArrivalProcessParams)

Annotation
Represents the parameters for an arrival process producing inbound calls. This includes the type of the arrival process set by the `type` attribute as well as additional parameters specific to the chosen type. The most commonly used element is `arrivals` which assign arrival rates or expected number of arrivals to each main period.

Most arrival processes are influenced by a busyness factor which change the arrival rates. In particular, for Poisson-based arrival processes, the busyness factor simply multiplies the arrival rates. For other arrival processes, the generated number of arrivals is multiplied by the factor, and the result is rounded to the nearest integer. This factor is the product of a random variate common to all inbound call types, a multiplier specific to the arrival process and given by the `arrivalsMult` attribute, and a global multiplier given by the `arrivalsMult` attribute in `MSKCCParams.` The random busyness factor follows the distribution given by the `busynessGen` element in `MSKCCParams.` By default, all the multipliers are 1, and the random variate follows a degenerate distribution assigning probability 1 to the constant 1.

Type Definition Detail

Type Derivation Tree ssj:Named ccmsk:CallSourceParams (extension) ccmsk:ArrivalProcessParams (extension)

XML Source (w/o annotations (26); see schema source)

<xsd:complexType name="ArrivalProcessParams"> <xsd:complexContent> <xsd:extension base="ccmsk:CallSourceParams"> <xsd:sequence> <xsd:element maxOccurs="1" minOccurs="0" name="busyGen" type="ssj:RandomVariateGenParams"> </xsd:element> <xsd:choice> <xsd:element name="data" type="ssj:IntArray"> </xsd:element> <xsd:sequence> <xsd:element maxOccurs="1" minOccurs="0" name="arvGen" type="ssj:RandomVariateGenParams"> </xsd:element> <xsd:element name="arrivals" type="ssj:nonNegativeDoubleList"> </xsd:element> </xsd:sequence> <xsd:sequence> <xsd:element name="poissonGammaShape" type="ssj:nonNegativeDoubleList"> </xsd:element> <xsd:element name="poissonGammaRate" type="ssj:nonNegativeDoubleList"> </xsd:element> <xsd:element maxOccurs="1" minOccurs="0" name="copulaSigma" type="ssj:DoubleArray"> </xsd:element> </xsd:sequence> <xsd:element name="arrivalRates" type="cc:MultiPeriodGenParams"> </xsd:element> <xsd:sequence> <xsd:element name="nortaSigma" type="ssj:DoubleArray"> </xsd:element> <xsd:element name="nortaGamma" type="ssj:positiveDoubleList"> </xsd:element> <xsd:element name="nortaP" type="ssj:double01iList"> </xsd:element> </xsd:sequence> <xsd:sequence> <xsd:element name="times" type="ssj:nonNegativeDurationList"> </xsd:element> <xsd:element name="lambdas" type="ssj:nonNegativeDoubleList"> </xsd:element> </xsd:sequence> </xsd:choice> </xsd:sequence> <xsd:attribute name="type" type="xsd:string"> </xsd:attribute> <xsd:attribute default="false" name="normalize" type="xsd:boolean"> </xsd:attribute> <xsd:attribute default="false" name="estimateBusyness" type="xsd:boolean"> </xsd:attribute> <xsd:attribute default="1" name="splineSmoothingFactor" type="ssj:double01i"> </xsd:attribute> <xsd:attribute default="MARKOVLINEARFIT" name="correlationFit" type="ccmsk:CorrelationFit"> </xsd:attribute> <xsd:attribute default="SINGLESHAPE" name="gammaShapeEstimatorType" type="ccmsk:GammaShapeEstimatorType"> </xsd:attribute> <xsd:attribute default="0.95" name="gammaShapeSmoothingFactor" type="ssj:double01i"> </xsd:attribute> <xsd:attribute default="200" name="maxIter" type="ssj:nonNegativeInt"> </xsd:attribute> <xsd:attribute default="5" name="movingWindowSize" type="ssj:nonNegativeInt"> </xsd:attribute> <xsd:attribute default="200" name="numMonteCarlo" type="ssj:nonNegativeInt"> </xsd:attribute> <xsd:attribute default="1.0e-4" name="varianceEpsilon" type="ssj:nonNegativeDouble"> </xsd:attribute> <xsd:attribute default="1" name="arrivalsMult" type="ssj:nonNegativeDouble"> </xsd:attribute> </xsd:extension> </xsd:complexContent> </xsd:complexType>

Attribute Detail (defined in this component only)
arrivalsMult

  Determines the local multiplier of the arrival process. Any arrival process can be represented as a counting process {A(t), t>0} where A(t) gives the number of arrivals during time interval [0, t]. If multipliers are used, the arrival process becomes { round (MA(t)), t>0}, where round(.) rounds its argument to the nearest integer. The multiplier M is determined by multiplying this parameter with the global arrivalsMult attribute. This can be used to alter the call volume without modifying the detailed parameters of the arrival processes.

  Type: | ssj:nonNegativeDouble
  Use: | optional
  Default: | "1"
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:attribute default="1" name="arrivalsMult" type="ssj:nonNegativeDouble"> </xsd:attribute>

correlationFit

  Determines how to compute the sigma correlation matrix for the gamma norta rate arrival process.

  Type: | ccmsk:CorrelationFit
  Use: | optional
  Default: | "MARKOVLINEARFIT"
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:attribute default="MARKOVLINEARFIT" name="correlationFit" type="ccmsk:CorrelationFit"> </xsd:attribute>

estimateBusyness

  Determines if the parameters for the distribution of the busyness factor must be estimated with the parameters of the arrival process. If this attribute is set to `true,` the probability distribution of the busyness factor is set with the estimated parameters. This estimation affects how the arrivals are modeled and is not supported for all arrival processes. The busyness factor generated from the estimated distribution also affects the arrival processes for all other inbound calls. If the attribute is `false` (the default), only the parameters of the arrival process are estimated. This option has no effect if the `data` child element is not specified, and it can be set only for a single arrival process in the parameter file.

  Type: | xsd:boolean
  Use: | optional
  Default: | "false"
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:attribute default="false" name="estimateBusyness" type="xsd:boolean"> </xsd:attribute>

gammaShapeEstimatorType

  This option allows to select between estimators of the shape parameter in case of the Poisson gamma arrival process.

  Type: | ccmsk:GammaShapeEstimatorType
  Use: | optional
  Default: | "SINGLESHAPE"
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:attribute default="SINGLESHAPE" name="gammaShapeEstimatorType" type="ccmsk:GammaShapeEstimatorType"> </xsd:attribute>

gammaShapeSmoothingFactor

  Regulates the smoothness of the solution in the estimation of the gamma shape parameters for the Poisson gamma arrival process. When it is 1 there is no smoothing and shape parameters are assumed to be independent across sub-periods. This parameter is used only when `gammaShapeEstimatorType` is `SPLINESHAPE`.

  Type: | ssj:double01i
  Use: | optional
  Default: | "0.95"
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:attribute default="0.95" name="gammaShapeSmoothingFactor" type="ssj:double01i"> </xsd:attribute>

maxIter

  The number of iterations in the optimization routine that estimate the gamma shape parameters in the Poisson gamma arrival process. The value recommended is 200 when `gammaShapeEstimatorType` is `SINGLESHAPE`, and 1000 when `gammaShapeEstimatorType` is `SPLINESHAPE`.

  Type: | ssj:nonNegativeInt
  Use: | optional
  Default: | "200"
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:attribute default="200" name="maxIter" type="ssj:nonNegativeInt"> </xsd:attribute>

movingWindowSize

  Sets the number of subperiods that are used to average the MME estimate in the Poisson gamma arrival process. Without averaging, the MME estimates are too noisy. If we want no averaging, we can set `movingWindowSize` = 1. The parameter is used only when `gammaShapeEstimatorType` is `SPLINESHAPE`.

  Type: | ssj:nonNegativeInt
  Use: | optional
  Default: | "5"
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:attribute default="5" name="movingWindowSize" type="ssj:nonNegativeInt"> </xsd:attribute>

normalize

  Determines how base arrival rates are interpreted for arrival processes arising as Poisson processes. More specifically, if this attribute is set to `true,` arrival rates are interpreted as the expected number of arrivals during a time interval. In this case, the arrival rates given by the user or generated randomly are internally divided by the length of interval. This gives normalized arrival rates relative to the default simulation time unit. Most of the times, the intervals correspond to main periods, but they are user-defined if the `type` attribute is set to `PIECEWISECONSTANTPOISSONINT.` On the other hand, if this attribute is set to `false,` the simulator assumes that the arrival rates are relative to one simulation time unit so no normalization is performed. For example, when a Poisson process with piecewise-constant arrival rates has normalized parameters, `lambda p` indicates the average number of arrivals during simulation period `p` instead of the average number of arrivals per simulation time unit.

  Type: | xsd:boolean
  Use: | optional
  Default: | "false"
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:attribute default="false" name="normalize" type="xsd:boolean"> </xsd:attribute>

numMonteCarlo

  This is the number of Monte Carlo samples used in the estimation of the parameters by the maximum likelihood method for the gamma distribution of the busyness factors.

  Type: | ssj:nonNegativeInt
  Use: | optional
  Default: | "200"
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:attribute default="200" name="numMonteCarlo" type="ssj:nonNegativeInt"> </xsd:attribute>

splineSmoothingFactor

  Determines the smoothing factor for the spline representing the arrival rate. If this double-precision parameter is unspecified, it defaults to 1, which results in an interpolating spline. See the description of the `CUBICSPLINE` arrival process for more information on the role of this factor.

  Type: | ssj:double01i
  Use: | optional
  Default: | "1"
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:attribute default="1" name="splineSmoothingFactor" type="ssj:double01i"> </xsd:attribute>

type

  Determines the type of arrival process to generate calls from. Any enum constant in the Java class `ArrivalProcessType` from package `umontreal.iro.lecuyer.contactcenters.app` is accepted as a value for this attribute. Moreover, custom simulation programs or Java archives may define additional types of arrival processes; see the `ArrivalProcessFactory` class from package `umontreal.iro.lecuyer.contactcenters.msk.spi` for more information about this.

  Type: | xsd:string
  Use: | optional
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:attribute name="type" type="xsd:string"> </xsd:attribute>

varianceEpsilon

  Determines the lower bound for the variance of busyness obtained from the gamma distribution. When the variance obtained from the estimated parameters is smaller than this bound, then the distribution is set to a constant and the variance is 0. See the description of the `estimateBusyness` for related information on the role of this factor.

  Type: | ssj:nonNegativeDouble
  Use: | optional
  Default: | "1.0e-4"
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:attribute default="1.0e-4" name="varianceEpsilon" type="ssj:nonNegativeDouble"> </xsd:attribute>

Content Element Detail (defined in this component only)
arrivalRates

  Determines the probability distribution for the arrival rate of each period of the horizon. This is used only for the Poisson arrival process with randomized arrival rates.

  Type: | cc:MultiPeriodGenParams, complex content
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:element name="arrivalRates" type="cc:MultiPeriodGenParams"> </xsd:element>

arrivals

  Determines the parameters specific to the arrival process being used. The effect of this array of double-precision values depends on the chosen arrival process type. For the Poisson process with piecewise-constant arrival rates, it contains lambda p while for Dirichlet, it contains alpha p .

  Type: | ssj:nonNegativeDoubleList, simple content
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:element name="arrivals" type="ssj:nonNegativeDoubleList"> </xsd:element>

arvGen

  Determines the random variate generator used to generate the total number of arrivals for each replication, when the `type` attribute is set to `DIRICHLET.`

  Type: | ssj:RandomVariateGenParams, simple content
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:element maxOccurs="1" minOccurs="0" name="arvGen" type="ssj:RandomVariateGenParams"> </xsd:element>

busyGen

  Determines the parameters of the random variate generator used to generate the busyness factor for increased variability of this arrival process. If this element is present, a new busyness factor is generated from the given distribution, and corresponds to the busyness factor for the day. If the generated factor is smaller than 1, the day is less busy than usual for this type of arrivals. If it is greater than 1, it is more busy than usual. The base arrival rate of this type of inbound calls is multiplied by this busyness factor to obtain the rates being used. If this element is omitted, the busyness factor is deterministic and always equals 1.

  Type: | ssj:RandomVariateGenParams, simple content
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:element maxOccurs="1" minOccurs="0" name="busyGen" type="ssj:RandomVariateGenParams"> </xsd:element>

copulaSigma

  Determines the correlation matrix used by the Gamma-Poisson doubly stochastic arrival process with correlared Gamma rates. This parameter requires a P x P symmetric and positive-definite matrix, if it is used.

  Type: | ssj:DoubleArray, complex content
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:element maxOccurs="1" minOccurs="0" name="copulaSigma" type="ssj:DoubleArray"> </xsd:element>

data

  Determines the data used to estimate the parameters of the arrival process. This matrix of integers must contain one row for each observation and one column for each main period. Each element of the matrix represents the number of arrivals observed on a specific day during a given period. Parameter estimation is used automatically if this element is given. Note that only some arrival processes support parameter estimation.

  Type: | ssj:IntArray, complex content
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:element name="data" type="ssj:IntArray"> </xsd:element>

lambdas

  Determines the values of the arrival rate at each time given by `times,` when the arrival process is based on a time-varying arrival rate. Depending on the arrival process, this array must have the same length L as `times,` or contain L-1 values.

  Type: | ssj:nonNegativeDoubleList, simple content
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:element name="lambdas" type="ssj:nonNegativeDoubleList"> </xsd:element>

nortaGamma

  Determines the first parameters used for the marginal negative binomials, for the NORTA-driven arrival process. If the arrival process is NORTA-driven, this array is required to contain P elements.

  Type: | ssj:positiveDoubleList, simple content
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:element name="nortaGamma" type="ssj:positiveDoubleList"> </xsd:element>

nortaP

  Determines the second parameters used for the marginal negative binomials, for the NORTA-driven arrival process. If the arrival process is NORTA-driven, this array is required to contain P elements.

  Type: | ssj:double01iList, simple content
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:element name="nortaP" type="ssj:double01iList"> </xsd:element>

nortaSigma

  Determines the correlation matrix used by the NORTA-driven arrival process. This parameter requires a P x P symmetric and positive-definite matrix, if NORTA is used.

  Type: | ssj:DoubleArray, complex content
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:element name="nortaSigma" type="ssj:DoubleArray"> </xsd:element>

poissonGammaRate

  Determines the arrival rate parameters for the Poisson-gamma arrival process. This array must contain one parameter per main period, or a single value to be used for all periods.

  Type: | ssj:nonNegativeDoubleList, simple content
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:element name="poissonGammaRate" type="ssj:nonNegativeDoubleList"> </xsd:element>

poissonGammaShape

  Determines the shape parameters for the Poisson-gamma arrival process. This array must contain one parameter per main period, or a single value which is used for all periods.

  Type: | ssj:nonNegativeDoubleList, simple content
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:element name="poissonGammaShape" type="ssj:nonNegativeDoubleList"> </xsd:element>

times

  Determines the times at which the arrival rate is specified, for some Poisson process with a time-varying arrival rate.

  Type: | ssj:nonNegativeDurationList, simple content
  Defined: | locally, within (this) ccmsk:ArrivalProcessParams complexType

  XML Source (w/o annotations (1); see schema source)

  <xsd:element name="times" type="ssj:nonNegativeDurationList"> </xsd:element>

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