Police staffing and workload assignment in law enforcement using multi-server queueing models

Liu, Zhongyi; Liu, Jingchen; Zhai, Xiaofeng; Wang, Guanying

doi:10.1016/j.ejor.2019.01.004

Cited by 9 publications

(4 citation statements)

References 34 publications

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“…The formulas for the load factors of the system as a part of the input flow of requirements ( 16), for the nonordinary functions f k (17) and for the probabilities p k (12) remain unchanged. The analytical description of the final probabilities for the states in the M L /M/n/m QS with the presence of requirements in the queue takes the form:…”

Section: Methodsmentioning

confidence: 99%

“…Currently, queuing system models are being actively used for analysis, for predicting efficiency and for optimizing decisions made in various areas. These include the following areas: telecommunication networks [5,6,7,8,9,10], socio-economic systems [11,12], production systems [13,14,15,16] and logistic systems [17,18,19], computing systems [20,21], traffic management systems [22,23,24,25] and others.…”

Section: Review Of the Literaturementioning

confidence: 99%

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The States Final Probabilities Analytical Description in Queuing System With an Entrance Flow of Requirements Groups, With Waiting and Leaving the Queue

Городнов

Kyrylenko

Repilo

2020

RIC

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Context. The problem of predicting the efficiency of real queuing systems in the event of a possible arrival of requirements groups and leaving of "impatient" requirements from the queue. The aim of the study was to model the operation of such systems to create opportunities to control their operation in real time.Objective. The aim of the research is to obtain an analytical description of the state's final probabilities in a Markov queuing system with an input flow of requirements groups, with individual service of requirements, with a limited number of waiting places and with individual leaving of "impatient" requirements from the queue that is necessary to predict the values of the queuing system performance indicators.Method. The probabilities of queuing systems states with an input flow of requirements groups with a random composition and with leaving of "impatient" requirements from the queue are described by the Kolmogorov differential equations. In a stationary state, these equations are transformed into a linearly dependent homogeneous system of algebraic equations. The structure of the equations depends on the numerical values of the input flow requirements group's parameters and the controlled service system. Therefore, an attempt to predict the efficiency of a system is faced with the need to write down and numerically solve a countable set of algebraic equations systems that is quite difficult. The key idea of the proposed method for finding an analytical description of the final probabilities for the specified queuing system was the desire to localize the influence of requirements groups in the input flow on the operation of the queuing system in multiplicative non-ordinary functions. Such functions allow obtaining the required analytical description and assessing the degree of the final probabilities transformation, in comparison with known systems, as well as assessing the predicted values of the noted queuing system efficiency indicators when choosing the parameters for controlling its operation.Results. For the first time analytical expressions are obtained for the final probabilities of the queuing system states with an input flow of random composition requirements groups, with a limited number of waiting places, with individual service and leaving "impatient" requirements from the queue, which makes it possible to evaluate all known indicators of the system's performance.Conclusions. The resulting description turned out to be a general case for well-known types of Markov queuing systems with non-ordinary and with the simplest input flow of requirements. The results of the numerical experiment testify in favor of the correctness of the obtained analytical expressions for the final probabilities and in favor of the possibility of their practical application in real queuing systems when solving problems of forecasting efficiency, as well as analyzing and synthesizing the parameters of real queuing systems.

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Section: Methodsmentioning

confidence: 99%

Section: Review Of the Literaturementioning

confidence: 99%

The States Final Probabilities Analytical Description in Queuing System With an Entrance Flow of Requirements Groups, With Waiting and Leaving the Queue

Городнов

Kyrylenko

Repilo

2020

RIC

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“…Traditionally, Linear programming, Objective programming, Mixed integer linear programming, Dynamic programming, and Data envelopment analysis are used for optimization. Alternatively, the literature mentions applications of Computational intelligence (e.g., Fuzzy logic and Evolutionary computing), Queuing modeling, Stochastic programming, and Robust optimization (Souto Anido et al, 2018;Turan et al, 2021;Liu et al, 2019;Bastian et al, 2020).…”

Section: Quantitative Techniquesmentioning

confidence: 99%

A workload measurement framework for determining staffing needs

Salimgereyev

2023

Materials of the International Scientific-Practical Conference “The Paradigm of Sustainable Economic Development in the Context

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Determining workforce demand is an integral part of the workforce planning process -determining workforce size, composition, organization, and deployment. It analyzes the current and forecasts the future levels of workload required to fulfill the organization's mission and the factors that influence the workload. But the lack of reliable sources of actual task durations is the most significant difficulty in determining the workload. This paper proposes a workload measurement framework. Its purpose is to measure the workloads of tasks managerial, professional, and technical employees perform at the workplace.Our approach suggests a detailed description of work processes and an elementwise time study using a specially designed web application.The proposed workload measurement framework was successfully implemented in the study to determine staffing needs for local government employees. More than 1800 state employees responded to the time study. The proposed workload measurement framework provided quality data for workload analytics.The proposed workload measurement framework has two benefits. Firstly, it provides the workload model developers with the actual task duration data, thus making the workload models more accurate and less dependent on subjective inputs. Secondly, it decreases the labor-intensity of the data collection and analysis processes, thus reducing the workload model development lead times.

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“…Despite its importance, the overstaffing issue (staff use efficiency) has received relatively scant attention in the hospitality literature. The empirical literature on staff scheduling in service industries and those facing stochastic demand is dominated by applications in healthcare, specifically nursing and emergency units (Arisha and Abo-Hamad, 2013;Gul and Guneri, 2012;Maier-Rothe and Wolfe, 1973) and call centers (Chevalier and Van den Schrieck, 2008;Defraeye and Van Nieuwenhuyse, 2016;Gurvich et al, 2010;Koçaga et al, 2015) and police departments (Kaplan, 2013;Liu et al, 2019). Rocha et al(2012) show a clear need for more research in this area given the small amount of empirical research in hospitality compared to transport and nursing.…”

Section: Introductionmentioning

confidence: 99%