EventBasedTimestampWeightedTally

class pydsol.core.statistics.EventBasedTimestampWeightedTally(name: str)

Bases: EventProducer, EventListener, TimestampWeightedTally

The EventBasedTimestampWeightedTally can receive its observations by subscribing (listening) to one or more EventProducers that provides the values for the statistic using the EventProducer’s fire(…) method. This way, the statistic gathering and processing is decoupled from the process in the simulation that generates the data: there can be zero, one, or many statistics listeners for each data producing object in the simulation.

This event-based statistic object also fire events with the values of the calculated statistics values, so a GUI-element such as a graph or table can subscribe to this event-based statistics object and be automatically updated when values of the statistic change. Again, this provides decoupling and flexibility where on beforehand it is not known whether zero, one, or many (graphics or simulation) objects are interested in the values that this statistics object calculates.

The EventBasedTimestampWeightedTally is a statistics object that calculates descriptive statistics for piecewise constant observations, such as weighted mean, weighted variance, minimum observation, maximum observation, etc. Contrary to the WeightedTally, the weights are implicitly calculated based on timestamps that are provided with each observation.

The initialize() method resets the statistics object. The initialize method can, for instance, be called when the warmup period of the simulation experiment has completed.

In order to properly ‘close’ the series of observations, a virtual observation has to be provided at the end of the observation period, to count the value and duration of the last interval into the statistics. The end_observations method takes care of ending the observation period. After calling end_observations(timestamp), further calls to the register method will be silently ignored.

In a sense, the EventBasedTimestampWeightedTally can be seen as a normal Tally where the observations are multiplied by the duration (interval between two successive timestamps) when the observation had that particular value. But instead of dividing by the number of observations to calculate the mean of the ordinary Tally, the sum of durations times observation values is divided by the total duration of the observation period till the last registered timestamp.

Example

In discrete-event simulation, the EventBasedTimestampWeightedTally is often used to calculate statistics for (average) queue length, or (average) utilization of a server. Every time the actual queue length or utilization changes, the new value is registered with the timestamp, and the previous observation value is counted towards the statistic with the time interval between the previous timestamp and the new timestamp as the weight.

Attributes:

• _name (str) – the name by which the statistics object can be identified

• _n (int) – the number of observations

• _n_nonzero (int) – the number of non-zero weights

• _sum_of_weights (float) – the sum of the weights

• _weighted_sum (float) – the sum of the observation values times their weights

• _weight_times_variance (float) – the weighted variant of the second moment of the statistic

• _min (float) – the lowest value in the current observations

• _max (float) – the highest value in the current observations

• _start_time (float) – timestamp of the first registered observation

• _last_timestamp (float) – timestamp when the currently valid observation value was set

• _last_value – currently valid observation value

• _active – true after initializations until end_observations has been called

__init__(name: str)

Construct a new EventBasedTimestampWeightedTally statistics object. The EventBasedTimestampWeightedTally can receive its observations by subscribing (listening) to one or more EventProducers that provides the values for the statistic using the EventProducer’s fire(…) method. This way, the statistic gathering and processing is decoupled from the process in the simulation that generates the data: there can be zero, one, or many statistics listeners for each data producing object in the simulation.

This event-based statistic object also fire events with the values of the calculated statistics values, so a GUI-element such as a graph or table can subscribe to this event-based statistics object and be automatically updated when values of the statistic change. Again, this provides decoupling and flexibility where on beforehand it is not known whether zero, one, or many (graphics or simulation) objects are interested in the values that this statistics object calculates.

The EventBasedTimestampWeightedTally is a statistics object that calculates descriptive statistics for weighted observations, such as weighted mean, weighted variance, minimum, and maximum, where the weights are implicitly calculated based on successive timestamps. The intervals between the timestamp are used as the weights.

Parameters:

name (str) – The name by which the statistics object can be identified.

Raises:

TypeError – when name is not a string

initialize()

Initialize the statistics object, resetting all values to the state where no observations have been made. This method can, for instance, be called when the warmup period of the simulation experiment has completed.

notify(event: TimedEvent)

The notify method is the method that is called by the EventProducer to register an observation. The event should be a TimedEvent that has a timestamp as one of its attributes. The EventType for the observation should be the StatEvents.TIMESTAMP_DATA_EVENT and the payload should be a float with the observation value.

Parameters:

event (TimedEvent) – The timed event fired by the EventProducer to provide data to the statistic. The content of the event has to be a float with the observation value.

Raises:

• TypeError – when event is not of the type TimedEvent

• ValueError – when the event’s event_type is not a TIMESTAMP_DATA_EVENT

• TypeError – when the event’s payload is not a float

• ValueError – when timestamp or value is NaN

• ValueError – when the provided timestamp is before the last registered timestamp

register(timestamp: float, value: float)

The event-based classes still have a register method. This method is called by the notify method, but can also be called separately. The method processes one timestamped observation.

The method processes one observation value and a timestamp that indicates from which time the observation is valid, and calculate all statistics up to and including the previous registered value for the duration between the last timestamp and the timestamp provided in this method. Successive timestamps can be the same, but a later timestamp cannot be before an earlier one.

Note

When two successive timestamps are the same, the observation value is counted towards the number of observations, and for the minimum and maximum observation value, but it does not contribute to the other statistics.

Parameters:

• timestamp (float) – The timestamp from which the observation value is valid.

• value (float) – The observation value.

Raises:

• TypeError – when timestamp or value is not a number

• ValueError – when weight or value is NaN

• ValueError – when the provided timestamp is before the last registered timestamp

add_listener(event_type: EventType, listener: EventListener)

Add an EventListener to this EventProducer for a given EventType. If the listener already is registered for this EventType, this will be ignored.

Parameters:

• event_type (EventType) – the EventType for which this listener subscribes

• listener (EventListener) – the subscriber to register for the provided Eventtype

Raises:

EventError – if any of the arguments is of the wrong type

end_observations(timestamp: float)

In order to properly ‘close’ the series of observations, a virtual observation has to be provided at the end of the observation period, to count the value and duration of the last interval into the statistics. The end_observations method takes care of ending the observation period. After calling end_observations(timestamp), further calls to the register method will be silently ignored.

Parameters:

timestamp (float) – The timestamp of the final interval before the observations end. The last registered value will be counted into the statistics for the duration of (timestamp - last_timestamp).

Raises:

• ValueError – when the provided timestamp is nan

• ValueError – when the provided timestamp is before the last registered timestamp

has_listeners() → bool

indicate whether this producer has any listeners or not

isactive() → bool

Indicate whether the statistic is active and can register observations. After calling end_observations(timestamp) _active will be set to False and further calls to the register method will be silently ignored.

Returns:

Whether the statistic is active and can register observations.

Return type:

bool

last_value() → float

Return the last registered value (this value has not yet been counted into the statistics, unless end_observations() has been called).

Returns:

The last registered value.

Return type:

float

max() → float

Return the (unweighted) observation with the highest value. When no observations were registered, NaN is returned.

Returns:

The observation with the highest value, or NaN when no observations were registered.

Return type:

float

min() → float

Return the (unweighted) observation with the lowest value. When no observations were registered, NaN is returned.

Returns:

The observation with the lowest value, or NaN when no observations were registered.

Return type:

float

n() → int

Return the number of observations.

Returns:

The number of observations.

Return type:

int

property name: str

Return the name of this statistics object.

Returns:

The name of this statistics object.

Return type:

str

remove_all_listeners(event_type: EventType | None = None, listener: EventListener | None = None)

Remove an EventListener (if given) for a provided EventType (if given) for this EventProducer. It is no problem if there are no matches. There are four situations:

event_type == None and listener == None

all listeners for all event types are removed

event_type == None and listener is specified

the listener is removed for any event for which it was registered

event_type is specified and listener == None

all listeners are removed for the given event_type

event_type and listener are both specified

the listener for the given event type is removed, if it was registered; in essence this is the same as remove_listener

Parameters:

• event_type (EventType, optional) – the EventType for which this listener unsubscribes

• listener (EventListener, optional) – the subscriber to remove for the provided EventType

Raises:

EventError – if any of the arguments is of the wrong type

remove_listener(event_type: EventType, listener: EventListener)

Remove an EventListener of this EventProducer for a given EventType. If the listener is not registered for this EventType, this will be ignored.

Parameters:

• event_type (EventType) – the EventType for which this listener unsubscribes

• listener (EventListener) – the subscriber to remove for the provided Eventtype

Raises:

EventError – if any of the arguments is of the wrong type

classmethod report_footer() → str

Return a string representing a footer for a textual table with a monospaced font that can contain multiple tallies.

classmethod report_header() → str

Return a string representing a header for a textual table with a monospaced font that can contain multiple weighted tallies.

report_line() → str

Return a string representing a line with important statistics values for this tally, for a textual table with a monospaced font that can contain multiple tallies.

weighted_mean() → float

Return the weighted mean. When no observations were registered, NaN is returned.

The weighted mean of the WeightedTally is calculated with the formula:

\[\mu_{W} = \frac{\sum_{i=1}^{n} w_{i}.x_{i}}{\sum_{i=1}^{n} w_{i}}\]

where n is the number of observations, \(w_{i}\) are the weights, and \(x_{i}\) are the observations.

Returns:

The weighted mean, or NaN when no observations were registered.

Return type:

float

weighted_stdev(biased: bool = True) → float

Return the (biased) weighted population standard deviation of all observations since the statistic initialization. The biased version needs at least one observation. For the unbiased version, two observations are needed. When too few observations were registered, NaN is returned.

The formula for the biased (population) weighted standard deviation is:

\[\sigma_{W} = \sqrt{ \frac{\sum_{i=1}^{n}{w_i (x_i - \mu_{W})^2}} {\sum_{i=1}^{n}{w_i}} }\]

where \(w_i\) are the weights, \(x_i\) are the observations, \(n\) is the number of observations, and \(\mu_W\) is the weighted mean of the observations.

For the unbiased (sample) weighted variance (and, hence, for the standard deviation), different algorithms are suggested by the literature. As an example, R and MATLAB calculate weighted sample variance differently. SPSS rounds the sum of weights to the nearest integer and counts that as the ‘sample size’ in the unbiased formula. When weights are used as so-called reliability weights (non-integer) rather than as frequency weights (integer), rounding to the nearest integer and using that to calculate a ‘sample size’ is obviously incorrect. See the discussion at https://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Weighted_sample_variance and at https://stats.stackexchange.com/questions/51442/weighted-variance-one-more-time. Here we have chosen to implement the version that uses reliability weights. The reason is that the weights in simulation study are most usually time intervals that can be on any (non-integer) scale.

The formula used for the unbiased (sample) weighted standard deviation is:

\[S_{W} = \sqrt{ \frac{M}{M - 1} . \sigma^2_{W} }\]

or as a complete formula:

\[S_{W} = \sqrt{ \frac{M}{M - 1} . \frac{\sum_{i=1}^{n}{w_i (x_i - \mu_{W})^2}} {\sum_{i=1}^{n}{w_i}} }\]

where \(w_i\) are the weights, \(x_i\) are the observations, \(n\) is the number of observations, \(M\) is the number of non-zero observations, and \(\mu_W\) is the weighted mean of the observations.

Parameters:

biased (bool) – Whether to return the biased (population) standard deviation or the unbiased (sample) standard deviation. By default, biased is True and the population standard deviation is returned.

Returns:

The weighted standard deviation of all observations since the initialization, or NaN when too few (non-zero) observations were registered.

Return type:

float

weighted_sum() → float

Return the sum of all observations times their weights since the statistic initialization.

Returns:

The sum of the observations times their weights.

Return type:

float

weighted_variance(biased: bool = True) → float

Return the weighted population variance of all observations since the statistic initialization. The biased version needs at least one observation. For the unbiased version, two observations with non-zero weights are needed. When too few observations were registered, NaN is returned.

The formula for the biased (population) weighted variance is:

\[\sigma^{2}_{W} = \frac{\sum_{i=1}^{n}{w_i (x_i - \mu_{W})^2}} {\sum_{i=1}^{n}{w_i}}\]

where \(w_i\) are the weights, \(x_i\) are the observations, \(n\) is the number of observations, and \(\mu_W\) is the weighted mean of the observations.

For the unbiased (sample) weighted variance, different algorithms are suggested by the literature. As an example, R and MATLAB calculate weighted sample variance differently. SPSS rounds the sum of weights to the nearest integer and counts that as the ‘sample size’ in the unbiased formula. When weights are used as so-called reliability weights (non-integer) rather than as frequency weights (integer), rounding to the nearest integer and using that to calculate a ‘sample size’ is obviously incorrect. See the discussion at https://en.wikipedia.org/wiki/Weighted_arithmetic_mean#Weighted_sample_variance and at https://stats.stackexchange.com/questions/51442/weighted-variance-one-more-time. Here we have chosen to implement the version that uses reliability weights. The reason is that the weights in simulation study are most usually time intervals that can be on any (non-integer) scale.

The formula used for the unbiased (sample) weighted variance is:

\[S^{2}_{W} = \frac{M}{M - 1} . \sigma^2_{W}\]

or as a complete formula:

\[S^{2}_{W} = \frac{M}{M - 1} . \frac{\sum_{i=1}^{n}{w_i (x_i-\mu_{W})^2}} {\sum_{i=1}^{n}{w_i}}\]

where \(w_i\) are the weights, \(x_i\) are the observations, \(n\) is the number of observations, \(M\) is the number of non-zero observations, and \(\mu_W\) is the weighted mean of the observations.

Parameters:

biased (bool) – Whether to return the biased (population) variance or the unbiased (sample) variance. By default, biased is True and the population variance is returned.

Returns:

The weighted variance of all observations since the initialization, or NaN when too few (non-zero) observations were registered.

Return type:

float