Arrival Count Research Articles

Call center data modeling: a queueing science approach based on Markovian arrival process

ABSTRACT In this paper we analyze the well-known ‘Anonymous bank’ call center dataset from a queueing science viewpoint. For this purpose, fitted distributions for both the inter-arrival and service times as well as for customers patiences are integrated in a simulator to infer quantities of interest related to call centers managerial decisions as waiting times, abandonment rates and queue lengths. In particular, it is shown how a type of Markov renewal process, the Markovian arrival process (MAP), is able to capture some of the characterizing properties of arrivals in a modern call center as overdispersion and positive correlation between arrival counts. The work provides a new inference approach for the MAP based on the count process descriptors and presents new properties concerning the dependence structure of the cumulated number of arrivals in a MAP.

Identifying targets for conservation: the arrival and loss of Common Eider Somateria mollissima ducklings in an estuarine nursery

ABSTRACTCapsuleThe arrival of Common Eider Somateria mollissima ducklings into a reception and nursery area is a measure of breeding success and phenology but reveals gaps in knowledge for effective conservation.AimsEstuarine habitats are important wildlife areas but are continually under threat from human activities. Common Eiders may be an indicator species for monitoring the impacts of development in estuaries used by them as nursery areas. The aim of this study was to understand the arrival and distribution of ducklings in a commercial and recreational estuarine environment.MethodsCoquet Island, Northumberland, is a breeding site for Common Eiders at the southern limit of their range on the east coast of the UK. Numbers of ducklings arriving in the adjacent Coquet Estuary nursery area were monitored daily during the breeding season over a 27-year period from 1995 to 2021 inclusive.ResultsCounts of ducklings were higher overall in less disturbed parts of the estuary, but there were no consistent patterns of habitat use. First-arrival dates varied annually by up to 23 days. Daily arrival counts were affected by tide and, to a lesser extent, rain and wind direction. Observed arrivals each season correlated with counts of breeding females on Coquet Island. There was evidence for links between broader-scale weather conditions (North Atlantic Oscillation indices) and yearly variation in rates of duckling arrival. Arrivals were more synchronous in years when ducklings were late in arriving and supported theoretical predictions from modelling studies. There were high daily rates of duckling loss from the estuary which may have been a consequence of brood movements out of the estuary and loss to predation. There was a positive correlation between counts of ducklings and attendant females.ConclusionsAnnual duckling counts show the value of estuaries for monitoring phenological variation in the breeding of Common Eiders. A better understanding of environmental factors influencing duckling retention or loss in estuaries is needed. Enabling human and wildlife activities to exist together within estuarine environments may promote effective conservation.

Using ADS-B Trajectories to Measure How Rapid Exit Taxiways Affect Airport Capacity

The capacity of an airport can be specified with a so-called capacity envelope, which indicates how many take-offs and landings an aerodrome is capable of handling per unit time. In this study, the capacity envelope of an airport is determined on the basis of Automatic Dependent Surveillance-Broadcast aircraft trajectories obtained via the Opensky Network. Trajectories are classified as departures and arrivals by using rule-based algorithms. Subsequently, the time of landing or take-off is determined for all these flight movements. Since some of the trajectories used in this study are not entirely covered near the ground, an XGboost model is used to improve the determination of the take-off and landing times. In a final step, the capacity envelope is determined. To this end, the number of take-offs and landings operated at an airport within 15-minute intervals are counted first. Then, the 92.5th percentile of departures is computed for all observed arrival counts. Finally, a concave, non-increasing piecewise-linear function is fitted to these quantile values. The method introduced in this study is subsequently applied to Lisbon Airport in order to evaluate if and how the construction of an additional rapid exit taxiway has affected its capacity. The results suggest that Lisbon Airport benefits from this rapid exit taxiway. Indeed, especially when the airport handles a high number of landings, the additional rapid exit taxiway appears to allow for a slightly higher number of departures.

An Online Learning Approach to Dynamic Pricing and Capacity Sizing in Service Systems

Online Learning in Queueing Systems Most queueing models have no analytic solutions, so previous research often resorts to heavy-traffic analysis for performance analysis and optimization, which requires the system scale (e.g., arrival and service rate) to grow to infinity. In “An Online Learning Approach to Dynamic Pricing and Capacity Sizing in Service Systems,” X. Chen, Y. Liu, and G. Hong develop a new “scale-free” online learning framework designed for optimizing a queueing system, called gradient-based online learning in queue (GOLiQ). GOLiQ prescribes an efficient procedure to obtain improved decisions in successive cycles using newly collected queueing data (e.g., arrival counts, waiting times, and busy times). Besides its robustness in the system scale, GOLiQ is advantageous when focusing on performance optimization in the long run because its data-driven nature enables it to constantly produce improved solutions which will eventually reach optimality. Effectiveness of GOLiQ is substantiated by theoretical regret analysis (with a logarithmic regret bound) and simulation experiments.

An Online Learning Approach to Dynamic Pricing and Capacity Sizing in Service Systems

Online Learning in Queueing Systems Most queueing models have no analytic solutions, so previous research often resorts to heavy-traffic analysis for performance analysis and optimization, which requires the system scale (e.g., arrival and service rate) to grow to infinity. In “An Online Learning Approach to Dynamic Pricing and Capacity Sizing in Service Systems,” X. Chen, Y. Liu, and G. Hong develop a new “scale-free” online learning framework designed for optimizing a queueing system, called gradient-based online learning in queue (GOLiQ). GOLiQ prescribes an efficient procedure to obtain improved decisions in successive cycles using newly collected queueing data (e.g., arrival counts, waiting times, and busy times). Besides its robustness in the system scale, GOLiQ is advantageous when focusing on performance optimization in the long run because its data-driven nature enables it to constantly produce improved solutions which will eventually reach optimality. Effectiveness of GOLiQ is substantiated by theoretical regret analysis (with a logarithmic regret bound) and simulation experiments.

Use of Real-Time Information to Predict Future Arrivals in the Emergency Department.

We aimed to build prediction models for shift-level emergency department (ED) patient volume that could be used to facilitate prediction-driven staffing. We sought to evaluate the predictive power of rich real-time information and understand 1) which real-time information had predictive power and 2) what prediction techniques were appropriate for forecasting ED demand. We conducted a retrospective study in an ED site in a large academic hospital in New York City. We examined various prediction techniques, including linear regression, regression trees, extreme gradient boosting, and time series models. By comparing models with and without real-time predictors, we assessed the potential gain in prediction accuracy from real-time information. Real-time predictors improved prediction accuracy on models without contemporary information from 5% to 11%. Among extensive real-time predictors examined, recent patient arrival counts, weather, Google trends, and concurrent patient comorbidity information had significant predictive power. Out of all the forecasting techniques explored, SARIMAX (Seasonal Autoregressive Integrated Moving Average with eXogenous factors) achieved the smallest out-of-sample the root mean square error (RMSE) of 14.656 and mean absolute prediction error (MAPE) of 8.703%. Linear regression was the second best, with out-of-sample RMSE and MAPE equal to 15.366 and 9.109%, respectively. Real-time information was effective in improving the prediction accuracy of ED demand. Practice and policy implications for designing staffing paradigms with real-time demand forecasts to reduce ED congestion were discussed.

A Study Of Predicting Arrival Patterns Of Airport Passengers To The Counters On The Basis Of International Terminal

AI-based passenger arrival predictions to the processing points are essential to ensure efficient management of many intertwined operational processes in the airport ecosystem. For example, to be able to analyze the number of ground service personnel that will be required in the following hours, days in different parts of the airport and for different types of operations, it is essential to predict how many passengers will come to the airport in the following time zones. Moreover, density-driven intelligent energy management and dynamic price offering options in different services could only be generated with accurate passenger arrival predictions. Passenger arrivals can be detected with various technologies such as computer vision, IoT, lidar, and radar. However, passenger boarding pass printing event messages from the CUPPS solution, which is implemented in İzmir Adnan Menderes Airport International Terminal, is used as the data source in this study. Also, Linear regression, FEDOT, LSTM, and hybrid methods are configured and compared to predict passenger arrival counts to the counters of the international terminal in the specified time slots.

BASE SHEAR COEFFICIENT OF MEDIUM AND LOW-RISE STEEL STRUCTURE BASED ON ENERGY BALANCE FOR CONTINUOUS USE AFTER EARTHQUAKE

In recent years, regarding buildings that serve as bases for disaster relief work and as living spaces, the social desire is for continued use of and less repair work for such buildings after earthquakes. To meet that kind of wish, post-quake building damage must be kept to the slightest minimum. With the aim of continues use of buildings after earthquakes, this report deals with medium and low-rise steel structure buildings, giving consideration to practical guidelines for base shear coefficients in order to minimize building damage to the slightest possible after foreshocks, main shocks and aftershocks. The first priority was to theoretically speculate based on energy balance to derive a calculation formula for cumulative plastic deformation ratio corresponding to level of damage, the speed conversion value equivalent to total energy input and the natural period parameterized base shear coefficient (α1). Also, the application of this calculation formula to foreshocks, main shocks and aftershocks was made possible by introducing a cumulative energy spectrum. The derivation processes for the above are explained in Chapters 2 and 3. Next, from analysis results of α1 applied to seismic waves widely used in actual design, consideration was given to base shear coefficients that meet the current seismic code together with guidelines for base shear coefficients that would make it possible for continued use of buildings after earthquakes. By setting base shear coefficient guidelines in which a building’s Ds value is 0.4 or more with the 1st natural period at less than 1s, or where the Ds value is 0.25 or more with a natural period of 1s to 2s, the degree of damage is less than moderate even for earthquakes that very rarely occur, which fulfills the required performance in the seismic code. If a design is oriented to continuous use of the building after foreshocks, main shocks and aftershocks, then the pragmatic assessment would be to aim for a natural period of 1s or more and a base shear coefficient of 0.45 or greater as the Ds value. These analytical considerations are explained in Chapter 4. Finally, Chapter 5 explores the observation waves for the Pacific Coast of Tohoku Earthquake (2011) and Kumamoto Earthquake (2016), considering base shear coefficients that will make continued use of buildings possible after earthquakes. Regarding a building with first natural period of less than 1s, a short period region (greatly exceeding the energy input of an earthquake that very rarely occurs [a wave arrival count of 2]) existed in the energy input of observation waves of accumulated foreshocks, main shocks and aftershocks. Thus, this research confirmed that a natural period of 1s or more and a Ds value of 0.45 or more as the base shear coefficient will, generally speaking, minimize damage to less than slight for the abovementioned accumulated observations waves.

A Machine Learning Framework for Profitability Profiling and Dynamic Price Prediction for the New York City Taxi Trips

The New York City Taxi & Limousine Commission’s (NYC TLC) Yellow cabs are facing increased competition from app-based car services such as Ola, Uber, Didi, Lyft and Grab which is rapidly eating away its revenue and market share. Research work: In response to this, the study proposes to do profitability profiling of the taxi trips to focus on various key aspects that generate more revenue in future, visualization to assess the departure and arrival counts of the trips in various locations based on time of the day to maintain demand and supply equilibrium and also build a dynamic price prediction model to balance both margins as well as conversion rates. Methodology/Techniques used: The NYC TLC yellow taxi trip data is analysed through a cross-industry standard process for data mining (CRISP-DM) methodology. Firstly, the taxi trips are grouped into two profitability segments according to the fare amount, trip duration and trip distance by applying K means clustering. Secondly, spatiotemporal data analysis is carried to assess the demand for taxi trips at various locations at various times of the day. Thirdly, multiple linear regression, decision tree, and random forest models are adopted for dynamic price prediction. The findings of the study are as follows, high profitable segments are characterized by airport pickup and drop trips, Count of trip arrivals to airports are more compared to departures from airports at any time of the day, and further analysis revealed that drivers making only a few numbers of airport trips can earn more revenue compared to making more number of trips in local destinations. Compared to multiple linear regression and decision tree, the random forest regression model is considered to be most reliable for dynamic pricing prediction with an accuracy of 91%. Application of research work: The practical implication of the study is the deployment of a dynamic pricing model that can increase the revenue of the NYC TLC cabs along with balancing margin and conversion rates.

A neural-network-based approach for diagnosing hardware faults in cloud systems

In this article, we propose a novel scheme for diagnosing intermittent faults for cloud systems. We have investigated the characteristic of high-level symptomatic behavior on top of a cloud system and identified that (1) arrival counts of high-level symptoms go up with the number of fault injections at different speeds, which may help us to differentiate one fault model from another; (2) the nested level of fatal traps is found to be an indicative of fault duration, which is helpful for fault model diagnosis; (3) fatal traps triggered by certain faulty units is explored, providing useful information for locating faults. Based on these features, an n-dimensional space taking symptom’s arrival rate (grown up skew of the arrival count) as each dimension, which formulates the diagnosis problem as a pattern recognition problem is defined. Then, a backpropagation neural-network-based online hardware fault diagnosis scheme is proposed. Experimental results show that diagnosis accuracy of fault location is 99.2%, the accuracy of fault model is 96.7%, and the latency is affordable. This scheme has been implemented in firmware so that it covers cloud software stacks (virtual machine monitor, virtual machines, and user applications) and incurs zero hardware overhead.

Optimality of an affine intensity policy for maximizing the probability of an arrival count in point-process intensity control

This paper considers the problem of maximizing the probability of attaining a prescribed count of arrivals generated by a point process, by controlling its intensity. Our analysis shows the existence of optimal intensity switching times that are affine in the arrival count, thereby contributing to the literature on the optimality of affine policies. The optimal intensity control law is established, along with closed-form expressions for its numerical parameters. Several properties of the value function are listed as well.

Forecasting online user activeness for behavioural targeting: the effect of data sampling

Probability models have been built to model online ad click and conversion, but few studies have examined user activeness, which is the start of any further online behaviour. Using a discrete-time setting, this study builds a three-parameter Bayesian model to forecast user activeness. Users with the same arrival count in the training period are grouped into a segment and their activeness in the test period is forecasted accordingly. The forecasting results are affected by data sparsity and history, while the first factor impacts how to sample the users and the second decides how much historic data should be used in forecasting. Using data from a major ecommerce website, we find that the model performs well when the training period is short while the users are active.

Forecasting online user activeness for behavioural targeting: the effect of data sampling

Probability models have been built to model online ad click and conversion, but few studies have examined user activeness, which is the start of any further online behaviour. Using a discrete-time setting, this study builds a three-parameter Bayesian model to forecast user activeness. Users with the same arrival count in the training period are grouped into a segment and their activeness in the test period is forecasted accordingly. The forecasting results are affected by data sparsity and history, while the first factor impacts how to sample the users and the second decides how much historic data should be used in forecasting. Using data from a major ecommerce website, we find that the model performs well when the training period is short while the users are active.

Heavy-traffic limits for queues with periodic arrival processes

We establish conventional heavy-traffic limits for the number of customers in a Gt/GI/s queue with a periodic arrival process. We assume that the arrival counting process can be represented as the composition of a cumulative stochastic process that satisfies an FCLT and a deterministic cumulative rate function that is the integral of a periodic function. We establish three different heavy-traffic limits for three different scalings of the deterministic arrival rate function. The different scalings capture the three cases in which the predictable deterministic variability (i) dominates, (ii) is of the same order as, or (iii) is dominated by the stochastic variability in the arrival and service processes.

Predicting the continuation of a function with applications to call center data

We show how to construct the best linear unbiased predictor (BLUP) for the continuation of a curve, and apply the proposed estimator to real-world call center data. Using the BLUP, we demonstrate prediction of the workload process, both directly and based on prediction of the arrival counts. The Matlab code and all data sets in the presented examples are available in the supplementary material.

Análise de frequência de máximos anuais baseada em séries de duração parcial. Combinação das distribuições de Poisson inflacionada de zeros e generalizada de Pareto, modelo ZIP-GP

In frequency analysis of hydrological extremes under a peaks-over-threshold (PoT) approach, the model with Poisson arrival counts and Generalized Pareto (GP) distributed exceedances – Poisson-GP model is widely used. Such model requires the validation of the hypothesis that the distribution of the annual number of extreme events may be described by a Poisson distribution (Poisson hypothesis), which is not always verifiable in practical terms. The present study concerns the use of an alternative distribution for modeling the annual number of hydrological extremes the Zero-Inflated Poisson (ZIP) distribution with two parameters. A ZIP-GP model for extreme frequency analysis is proposed. This model is less restrictive than the Poisson-GP model since it allows for a more accurate description of the occurrence process in a PoT framework if the fraction of years with no exceedances is significantly higher than the theoretical mass at zero of the Poisson distribution. An application of the ZIP-GP model to flood data from Northern Portugal and the evaluation of its performance relative to the Poisson-GP model is presented. The results show that the ZIP-GP model outperforms the Poisson-GP model, especially for lower quantiles, hence the ZIP distribution is a valid alternative to the Poisson distribution for modeling the annual occurrence counts of peaks in a PoT approach for flood frequency analysis.

Forecasting Call Center Arrivals: Fixed-Effects, Mixed-Effects, and Bivariate Models

We consider different statistical models for the call arrival process in telephone call centers. We evaluate the forecasting accuracy of those models by describing results from an empirical study analyzing real-life call center data. We test forecasting accuracy using different lead times, ranging from weeks to hours in advance, to mimic real-life challenges faced by call center managers. The models considered are (i) a benchmark fixed-effects model that does not exploit any dependence structures in the data; (ii) a mixed-effects model that takes into account both interday (day-to-day) and intraday (within-day) correlations; and (iii) two new bivariate mixed-effects models, for the joint distribution of the arrival counts to two separate queues, that exploit correlations between different call types. Our study shows the importance of accounting for different correlation structures in the data.

A normal copula model for the arrival process in a call center

AbstractWe propose and examine a probabilistic model for the multivariate distribution of the number of calls in each period of the day (e.g., 15 or 30 min) in a call center, where the marginal distribution of the number of calls in any given period is arbitrary, and the dependence between the periods is modeled via a normal copula. Conditional on the number of calls in a period, their arrival times are independent and uniformly distributed over the period. This type of model has the advantage of being simple and reasonably flexible, and can match the correlations between the arrival counts in different periods much better than previously proposed models. For the situation where the number of periods is large, so the number of correlations to estimate can be excessive, we propose simple parametric forms for the correlations, defined as functions of the time lag between the periods. We test our proposed models on three data sets taken from real‐life call centers and compare their goodness of fit to the best previously proposed methods that we know. In the three cases, the new models provide a much better match of the correlations and coefficients of variation of the arrival counts in individual periods.

Workload forecasting for a call center: Methodology and a case study

Today's call center managers face multiple operational decision-making tasks. One of the most common is determining the weekly staffing levels to ensure customer satisfaction and meeting their needs while minimizing service costs. An initial step for producing the weekly schedule is forecasting the future system loads which involves predicting both arrival counts and average service times. We introduce an arrival count model which is based on a mixed Poisson process approach. The model is applied to data from an Israeli Telecom company call center. In our model, we also consider the effect of events such as billing on the arrival process and we demonstrate how to incorporate them as exogenous variables in the model. After obtaining the forecasted system load, in large call centers, a manager can choose to apply the QED (Quality-Efficiency Driven) regime's "square-root staffing" rule in order to balance the offered-load per server with the quality of service. Implementing this staffing rule requires that the forecasted values of the arrival counts and average service times maintain certain levels of precision. We develop different goodness of fit criteria that help determine our model's practical performance under the QED regime. These show that during most hours of the day the model can reach desired precision levels.

Relative Abundance and Distribution of Mariana Swiftlets (Aves: Apodidae) in the Northern Mariana Islands1

The endangered Mariana Swiftlet, Aerodramus bartschi (Mearns, 1909), occurs in its native habitat on only three islands worldwide—Guam, Saipan, and Aguiguan. It is locally extinct on the islands of Rota and Tinian, and numbers have declined on Guam. On Saipan and Aguiguan, the bird remains common. We present previously unpublished data from reports lodged with the Commonwealth of the Northern Mariana Islands Division of Fish and Wildlife combined with an analysis of arrival count data from surveys conducted regularly on Saipan (1985–2005) and opportunistically on Aguiguan (1985–2002). Direct counts of swiftlets arriving at nesting caves did not permit island-wide population estimates but provided an index useful for assessing relative abundance. On Aguiguan, swiftlets occurred in only a few of the available caves; the population was small, more densely concentrated than on the other islands, and relatively stable. On Saipan, swiftlet numbers declined for the first part of the monitoring period (1985–1992), then increased significantly (1998–2005), and now stand at their highest level (>5,000 birds) since 1985. Large between-year fluctuations, high variation in colony attendance patterns, and occasional abandonment and recolonization of some caves were evident during the 20-yr monitoring period. Of the potential constraints to the population, pesticide use, typhoons and supertyphoons, habitat alteration by feral animals, human disturbance in the nesting caves, and predation remain areas of concern. Conservation measures may have lessened some disturbance events and nest damage by cockroaches, while other measures, such as translocation, may improve the species' chances of persistence.