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ContactCenters V. 0.9.9. |
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java.lang.Objectjava.lang.Enum<ArrivalProcessType>
umontreal.iro.lecuyer.contactcenters.app.ArrivalProcessType
public enum ArrivalProcessType
Represents the type of arrival process for a blend/multi-skill call center. This process defines at which times a new call occurs during the simulation. The used arrival process determines how the parameters, usually given using an array of double-precision values, are used. All the arrival processes defined in [3] are supported.
Note that when simulating on an infinite horizon,
only arrival processes capable of generating arrivals
following parameters not evolving with time are allowed.
The recommended arrival processes for such simulations
are POISSON
and PIECEWISECONSTANTPOISSON
.
If the busyness generator for B is undefined, then B is replaced by a deterministic constant = 1.
Enum Constant Summary | |
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CUBICSPLINE
Non-homogenous Poisson arrival process using a cubic spline to model the time-varying arrival rate. |
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DIRICHLET
Dirichlet arrival process. |
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DIRICHLETCOMPOUND
Dirichlet compound arrival process. |
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FIXEDCOUNTS
Uniform arrival process with pre-determined arrival counts Cp in each period. |
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NORTADRIVEN
Represents a NORTA-driven arrival process with negative binomial marginals. |
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PIECEWISECONSTANTPOISSON
Non-homogeneous Poisson arrival process with piecewise-constant arrival rates. |
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PIECEWISECONSTANTPOISSONINT
Non-homogeneous Poisson arrival process with piecewise-constant arrival rates that can change at arbitrary times. |
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POISSON
Poisson arrival process. |
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POISSONGAMMA
Poisson process with piecewise-constant randomized arrival rates [13]. |
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POISSONGAMMANORTARATES
Doubly-stochastic Gamma-Poisson process with piecewise-constant randomized correlated Gamma arrival rates. |
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UNIFORM
Uniform arrival process with piecewise-constant arrival rates. |
Method Summary | |
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String |
toString()
|
static ArrivalProcessType |
valueOf(String name)
Returns the enum constant of this type with the specified name. |
static ArrivalProcessType[] |
values()
Returns an array containing the constants of this enum type, in the order they are declared. |
Methods inherited from class java.lang.Enum |
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clone, compareTo, equals, finalize, getDeclaringClass, hashCode, name, ordinal, valueOf |
Methods inherited from class java.lang.Object |
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getClass, notify, notifyAll, wait, wait, wait |
Enum Constant Detail |
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public static final ArrivalProcessType POISSON
PoissonArrivalProcess
for more
information. Inter-arrival times are
generated independently from the exponential distribution with fixed rate Bλ,
where λ is the base arrival rate given by the first value
of the arrivals element,
and B is a global busyness factor given by
busynessGen element in call center parameters.
The λ parameter can be estimated from data.
public static final ArrivalProcessType PIECEWISECONSTANTPOISSON
PiecewiseConstantPoissonArrivalProcess
for more
information. Inter-arrival times are independent exponential variates with rate
λ(t) = Bλp(t),
where p(t) is the period corresponding to simulation time t,
and λp is the base arrival rate for period p.
The values in arrivals element
give the base arrival rate for each
main period, while the rates for preliminary and wrap-up
periods are always 0.
The λp parameters can be estimated from data
by assuming that the periods are independent, and
the per-period numbers of arrivals follow the
Poisson distribution.
The arrival rates can also be estimated together with
a busyness factor following the gamma
(α0, α0)
distribution. In this case, the number of arrivals
is assumed to follow the negative multinomial distribution
with parameters
α0, ρ1,…, ρP, where
public static final ArrivalProcessType PIECEWISECONSTANTPOISSONINT
PoissonArrivalProcessWithTimeIntervals
for more
information. This process is similar to PIECEWISECONSTANTPOISSON
,
except arrival rates can change at any time, not only at period
boundaries.
More specifically, let
t0 < ... < tL be an increasing
sequence of simulation times, and let
Bλj, for
j = 0,…, L - 1, be the arrival rate
during time interval
[tj, tj+1).
The arrival rate is 0 for t < t0 and t≥tL.
The sequence of times is given using
the times element while the sequence of
rates is given using lambdas.
Of course, the length of the sequence of rates must be
one less than the length of the the sequence of times.
public static final ArrivalProcessType UNIFORM
PoissonUniformArrivalProcess
for more
information. For each main period
p = 1,…, P,
round(Bλp) arrivals are generated
uniformly in the period, and arrival times are
sorted in increasing order.
The values in the arrivals element
give the base arrival rate λp for each
main period, while the rates for preliminary and wrap-up
periods are always 0.
The λp parameters can be estimated from data
by assuming that the periods are independent, and
the per-period numbers of arrivals follow the
Poisson distribution.
public static final ArrivalProcessType FIXEDCOUNTS
FixedCountsArrivalProcess
for more information.
public static final ArrivalProcessType POISSONGAMMA
PoissonGammaArrivalProcess
for more
information. As with PIECEWISECONSTANTPOISSON
,
the arrival rate is given by
λ(t) = Bλp(t).
The base arrival rates λp are constant during each main period,
but they are not deterministic:
for main period p, the base rate of the Poisson
process is defined as a gamma random variable with
shape parameter
αG, p, and
scale parameter
λG, p (mean
αG, p/λG, p).
Shape parameters are stored in
element
poissonGammaShape
while scale parameters are stored in
poissonGammaScale.
As with the Poisson process with deterministic arrival rates,
the generated base arrival rates are multiplied
by a busyness factor B to get
the arrival rates, and the arrival rate is 0
during preliminary and wrap-up periods.
The
αG, p and
λG, p
parameters can be estimated from data by considering
that the number of arrivals during period p follow
the negative binomial distribution with parameters
(αG, p, λG, p/(αG, p + λG, p)),
independently of the other periods.
However, the parameters of the distribution of the
busyness factor cannot be estimated at the
same time as the gamma parameters.
public static final ArrivalProcessType POISSONGAMMANORTARATES
PoissonGammaNortaRatesArrivalProcess
for more
information.
The base arrival rates λp are constant during each period,
but they are not deterministic:
for period p, the base rate of the Poisson
process is defined as a correlated gamma random variable. The marginal
distribution of the rate is gamma with
shape parameter
αG, p, and
scale parameter
λG, p
(and mean
αG, p/λG, p). The correlation structure
is modelled using the normal copula model with positive definite correlation matrix
having elements in [- 1, 1].
If
αG, p or
λG, p
are 0, the resulting arrival rate during period p is always 0.
The Gamma shape parameters are stored in
element poissonGammaShape
while the Gamma scale parameters are stored in
poissonGammaScale. A correlation matrix must be given
by copulaSigma.
As with the Poisson process with deterministic arrival rates,
the generated base arrival rates are multiplied
by a busyness factor B to get
the arrival rates, and the arrival rate is 0
during preliminary and wrap-up periods.
The parameters of the distribution of the
busyness factor cannot be estimated at the
same time as the gamma parameters.
public static final ArrivalProcessType DIRICHLETCOMPOUND
DirichletCompoundArrivalProcess
for more
information.
public static final ArrivalProcessType DIRICHLET
DirichletArrivalProcess
for more information.
The values in arrivals element are used for the αp parameters. If a busyness factor B is generated for the day, the generated Ap's are multiplied by B and rounded to the nearest integer to get the modified number of arrivals. The parameters αp can be estimated from data, but one needs to specify a distribution for A to estimate parameters from. This arrival process cannot estimate parameters of the busyness factor.
public static final ArrivalProcessType NORTADRIVEN
NORTADrivenArrivalProcess
for more information.
To use this process, a correlation matrix must be given by nortaSigma, and parameters for the negative binomials must be supplied by nortaGamma and nortaP. If a busyness factor B is generated for the day, the generated Ap's are multiplied by B and rounded to the nearest integer to get the modified number of arrivals. This arrival process does not support parameter estimation from data.
public static final ArrivalProcessType CUBICSPLINE
Interpolating splines are forced to pass through every point, i.e., si(ti) = λ(ti) for i = 0,…, n - 2, and sn-2(tn-1) = λ(tn-1). On the other hand, smoothing splines tolerate some error, i.e., the spline minimizes
Both kinds of splines enforce the three following continuity
constraints:
si(ti+1) | = | si+1(ti+1), | |
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= | ![]() |
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and ![]() |
= | ![]() |
To use this arrival process, one must specify the ti's with the times element, the λ(ti)'s with lambdas element, and the smoothing factor with smoothingFactor attribute. For this arrival process, times and lambdas must share the same length.
Method Detail |
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public static ArrivalProcessType[] values()
for (ArrivalProcessType c : ArrivalProcessType.values()) System.out.println(c);
public static ArrivalProcessType valueOf(String name)
name
- the name of the enum constant to be returned.
IllegalArgumentException
- if this enum type has no constant
with the specified name
NullPointerException
- if the argument is nullpublic String toString()
toString
in class Enum<ArrivalProcessType>
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ContactCenters V. 0.9.9. |
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