scholarly journals Queue Management Benchmark for Modelling Patients' Flow in Nigerian Public Hospitals

2021 ◽  
pp. 17-27
Author(s):  
Akpan, Anietie Peter ◽  
John, Efiok Nsikan
Keyword(s):  
Queuing Theory ◽  
Arrival Rate ◽  
General Purpose ◽  
Optimal Number ◽  
Public Hospitals ◽  
Service Rate ◽  
Queue Management ◽  
Managerial Implications ◽  
Performance Benchmark ◽  
The Mean

Although queue management in hospitals is widely researched, little is known about the benchmark for modelling patients flow in terms of the optimal number of servers required for effective service delivery. This study applied the queuing theory to the Nigerian public hospitals by setting a benchmark for modelling patients flow. A mixture of survey and observation was adopted to garner data for 30 days from patients in six public hospitals in Nigeria. Data were subjected to performance analysis via the Temporary Ordered Routine Algorithm. The computed performance values were further compared with their acceptable benchmarks for multi-server queues through the General Purpose System Simulator. We found the queuing system in the select hospitals not in congruence with the system performance benchmark; the mean service rate in each facility was low compared to the mean arrival rate; and the simulated number of doctors for were below the modelled benchmark. Managerial implications of findings were discussed.

scholarly journals Performance Modelling of Health-care Service Delivery in Adekunle Ajasin University, Akungba-Akoko, Nigeria Using Queuing Theory

2020 ◽  
pp. 119-127
Author(s):  
Orimoloye Segun Michael
Keyword(s):  
Health Care ◽  
Service Delivery ◽  
Queuing Theory ◽  
Health Care Service ◽  
Health Centre ◽  
Arrival Rate ◽  
Queuing System ◽  
Service Rate ◽  
Suitable Model ◽  
The Mean

The queuing theory is the mathematical approach to the analysis of waiting lines in any setting where arrivals rate of the subject is faster than the system can handle. It is applicable to the health care setting where the systems have excess capacity to accommodate random variation. Therefore, the purpose of this study was to determine the waiting, arrival and service times of patients at AAUA Health- setting and to model a suitable queuing system by using simulation technique to validate the model. This study was conducted at AAUA Health- Centre Akungba Akoko. It employed analytical and simulation methods to develop a suitable model. The collection of waiting time for this study was based on the arrival rate and service rate of patients at the Outpatient Centre. The data was calculated and analyzed using Microsoft Excel. Based on the analyzed data, the queuing system of the patient current situation was modelled and simulated using the PYTHON software. The result obtained from the simulation model showed that the mean arrival rate of patients on Friday week1 was lesser than the mean service rate of patients (i.e. 5.33> 5.625 (λ > µ). What this means is that the waiting line would be formed which would increase indefinitely; the service facility would always be busy. The analysis of the entire system of the AAUA health centre showed that queue length increases when the system is very busy. This work therefore evaluated and predicted the system performance of AAUA Health-Centre in terms of service delivery and propose solutions on needed resources to improve the quality of service offered to the patients visiting this health centre.

scholarly journals PERBAIKAN SISTEM PENGUMPULAN SAMPAH PADA PERUMAHAN DI KOTA BATAM

2019 ◽  
Vol 13 (2) ◽  
pp. 117
Author(s):  
Welly Sugianto
Keyword(s):  
Queuing Theory ◽  
Garbage Collection ◽  
Finite Population ◽  
Arrival Rate ◽  
Optimal Number ◽  
Service Rate ◽  
Optimum Number ◽  
Total Cost ◽  
Operational Costs

AbstrakProses pengangkutan sampah di kota Batam dilakukan oleh truk pengangkut sampah. Truk pengangkut sampah masuk ke perumahan dan mengambil sampah yang ada di depan setiap rumah warga. Jumlah truk sampah tidak memadai sehingga sampah menumpuk di depan rumah warga. Warga mengambil inisiatif untuk membuang sampah tersebut di sembarang tempat sehingga tercipta TPS liar. Penelitian ini bertujuan untuk mencari jumlah truk pengangkut sampah yang optimum agar tidak terjadi timbunan sampah di depan rumah warga dan mencegah timbulnya TPS liar. Pendekatan yang digunakan adalah teori antrian dengan populasi terbatas. Truk sampah melayani sejumlah rumah dalam satu wilayah. Jumlah rumah dalam satu wilayah bersifat terbatas dan tetap. Rumah ditetapkan sebagai pelanggan jika jumlah sampah yang ada di depan rumah lebih dari 5 kantong atau lebih dari 20 kg. Beberapa data yang akan diobservasi adalah tingkat kedatangan dan kecepatan pelayanan. Berdasarkan data tersebut dapat dihitung beberapa parameter seperti tingkat antrian, waktu objek dalam antrian, probabilitas objek dalam sistem antrian, probabilitas sejumlah objek dalam antrian, dan biaya total yang merupakan penggabungan antara biaya antrian dan biaya operasional. Penelitian ini dilakukan di Kota Batam. Hasil penelitian menunjukkan bahwa teori antrian dengan populasi terbatas dapat diterapkan untuk menghitung jumlah truk pengangkut sampah yang optimum. Implementasi usulan perbaikan berdampak pada peningkatan kecepatan pelayanan dari 267,2 rumah per hari menjadi 480,8 rumah per hari. Jumlah truk yang optimum untuk satu wilayah perumahan setelah implementasi perbaikan adalah 2. Abstract[Determination of the Optimal Number of Trucks in the Garbage Transport Process] The garbage collection process in Batam city is carried out by garbage truck. Trucks must enter the housing and take out the garbage that is in front of each house. the number of garbage trucks is not enough so that the garbage overflows in front of the house. Residents took the initiative to dispose of the garbage in any place so as to create illegal polling stations. The objective of this research are to find the optimum garbage truck to avoid garbage pile in front of the residents' house and to prevent the occurrence of illegal polling stations. The approach used is queuing theory with limited population. Garbage trucks serve a number of houses in one area. The number of houses in one area is limited and fixed. The house is designated as a customer if the amount of garbage in front of the house is more than 5 bags or more than 20 kg. Some data to be observed is the arrival rate and speed of service. Some parameters to be calculated are the queue level, the time of the object in the queue, the probability of the object in the queue sistem, the probability of a number of objects in the queue, and the total cost which is a combination of queuing costs and operational costs. This research was conducted in Batam City. The results show that queuing theory with limited population can be applied to calculate the number of optimum garbage trucks. Implementation of the proposed improvements has an impact on the increase of speed of service rate  from 267.2 houses per day to 480.8 houses per day. The optimum number of trucks in region  after the implementation of the improvement is 2 Keywords: Queue; Finite Population; Garbage truck

Minimum carbon dioxide emission based selection of traffic route with unsignalised junctions in tandem network

2019 ◽  
Vol 30 (3) ◽  
pp. 657-675 ◽  
Author(s):  
Anand Jaiswal ◽  
Cherian Samuel ◽  
Chirag Chandan Mishra
Keyword(s):  
Carbon Dioxide ◽  
Queuing Theory ◽  
Mathematical Formulation ◽  
Carbon Dioxide Emission ◽  
Arrival Rate ◽  
Selection Strategy ◽  
Service Rate ◽  
Content Type ◽  
Fuel Consumption Rate ◽  
Route Choices

Purpose The purpose of this paper is to provide a traffic route selection strategy based on minimum carbon dioxide (CO2) emission by vehicles over different route choices. Design/methodology/approach The study used queuing theory for Markovian M/M/1 model over the road junctions to assess total time spent over each of the junctions for a route with junctions in tandem. With parameters of distance, mean service rate at the junction, the number of junctions and fuel consumption rate, which is a function of variable average speed, the CO2 emission is estimated over each of the junction in tandem and collectively over each of the routes. Findings The outcome of the study is a mathematical formulation, using queuing theory to estimate CO2 emissions over different route choices. Research finding estimated total time spent and subsequent CO2 emission for mean arrival rates of vehicles at junctions in tandem. The model is validated with a pilot study, and the result shows the best vehicular route choice with minimum CO2 emissions. Research limitations/implications Proposed study is limited to M/M/1 model at each of the junction, with no defection of vehicles. The study is also limited to a constant mean arrival rate at each of the junction. Practical implications The work can be used to define strategies to route vehicles on different route choices to reduce minimum vehicular CO2 emissions. Originality/value Proposed work gives a solution for minimising carbon emission over routes with unsignalised junctions in the tandem network.

Multiple channel queues in heavy traffic. I

1970 ◽  
Vol 2 (01) ◽  
pp. 150-177 ◽  
Author(s):  
Donald L. Iglehart ◽  
Ward Whitt
Keyword(s):  
Heavy Traffic ◽  
Arrival Rate ◽  
Standard System ◽  
Interarrival Time ◽  
Service Rate ◽  
Service Channel ◽  
Multiple Channel ◽  
System A ◽  
The Mean ◽  
Service Channels

The queueing systems considered in this paper consist of r independent arrival channels and s independent service channels, where as usual the arrival and service channels are independent. Arriving customers form a single queue and are served in the order of their arrival without defections. We shall treat two distinct modes of operation for the service channels. In the standard system a waiting customer is assigned to the first available service channel and the servers (servers ≡ service channels) are shut off when they are idle. Thus the classical GI/G/s system is a special case of our standard system. In the modified system a waiting customer is assigned to the service channel that can complete his service first and the servers are not shut off when they are idle. While the modified system is of some interest in its own right, we introduce it primarily as an analytical tool. Let λ i denote the arrival rate (reciprocal of the mean interarrival time) in the ith arrival channel and μ j the service rate (reciprocal of the mean service time) in the jth service channel. Then is the total arrival rate to the system and is the maximum service rate of the system. As a measure of congestion we define the traffic intensity ρ = λ/μ.

Application of Queuing Theory to Address Traffic Problems at a Highway Toll Plaza

2014 ◽  
Vol 592-594 ◽  
pp. 2583-2587 ◽  
Author(s):  
Dheeraj Duhan ◽  
Nishant Arya ◽  
Prateek Dhanda ◽  
Lalit Upadhayay ◽  
K. Mathiyazhagan
Keyword(s):  
Data Analysis ◽  
Waiting Time ◽  
Traffic Congestion ◽  
Queuing Theory ◽  
Arrival Rate ◽  
North India ◽  
Service Rate ◽  
Operational Effectiveness ◽  
Toll Plazas ◽  
Toll Plaza

In India, due to the escalating traffic issues, a large number of highways have been built in the recent past, which are maintained by tax collection at toll plazas, by various operating agencies. Due to smooth and hassle free driving on highways, the arrival rate of vehicles at Toll Plazas increases. The arrival rate goes beyond control if the traffic on the highway increases in an uncontrolled manner, with the passage of time. Thus, one of the irrefutable drawbacks of putting up Toll Plazas, is the traffic congestion. The waiting time, in the service lanes, due to such a congestion becomes high and excruciating for the commuters on the route. The objective of this study is to analyze the current situation, of traffic congestion, at a highway toll plaza using queuing theory and suggest possible solutions to encourage greater efficiency, thus reducing waiting time of the customers and money wasted because of that. This study has been carried out in various phases, i.e. problem identification, data collection, data analysis and results at a selected Toll Plaza in North India. The data analysis in the study helps to find out the current operational effectiveness of the Toll Plaza through parameters like, Arrival Rate, Service Rate and Number of toll booths. Finally, possible solutions have been put forward which can be recommended and implemented on various Toll Plazas in the country.

Multiple channel queues in heavy traffic. I

1970 ◽  
Vol 2 (1) ◽  
pp. 150-177 ◽  
Author(s):  
Donald L. Iglehart ◽  
Ward Whitt
Keyword(s):  
Heavy Traffic ◽  
Arrival Rate ◽  
Standard System ◽  
Interarrival Time ◽  
Service Rate ◽  
Service Channel ◽  
Multiple Channel ◽  
System A ◽  
The Mean ◽  
Service Channels

The queueing systems considered in this paper consist of r independent arrival channels and s independent service channels, where as usual the arrival and service channels are independent. Arriving customers form a single queue and are served in the order of their arrival without defections. We shall treat two distinct modes of operation for the service channels. In the standard system a waiting customer is assigned to the first available service channel and the servers (servers ≡ service channels) are shut off when they are idle. Thus the classical GI/G/s system is a special case of our standard system. In the modified system a waiting customer is assigned to the service channel that can complete his service first and the servers are not shut off when they are idle. While the modified system is of some interest in its own right, we introduce it primarily as an analytical tool. Let λi denote the arrival rate (reciprocal of the mean interarrival time) in the ith arrival channel and μj the service rate (reciprocal of the mean service time) in the jth service channel. Then is the total arrival rate to the system and is the maximum service rate of the system. As a measure of congestion we define the traffic intensity ρ = λ/μ.

Queues with time-dependent arrival rates. III — A mild rush hour

1968 ◽  
Vol 5 (3) ◽  
pp. 591-606 ◽  
Author(s):  
G. F. Newell
Keyword(s):  
Queueing Theory ◽  
Queue Length ◽  
Arrival Rate ◽  
Time Dependent ◽  
Service Rate ◽  
Diffusion Approximations ◽  
Dimensionless Form ◽  
Queue Lengths ◽  
The Mean ◽  
Mean Queue Length

The arrival rate of customers to a service facility is assumed to have the form λ(t) = λ(0) — βt2 for some constant β. Diffusion approximations show that for λ(0) sufficiently close to the service rate μ, the mean queue length at time 0 is proportional to β–1/5. A dimensionless form of the diffusion equation is evaluated numerically from which queue lengths can be evaluated as a function of time for all λ(0) and β. Particular attention is given to those situations in which neither deterministic queueing theory nor equilibrium stochastic queueing theory apply.

Optimization of Queuing Theory Based on Vague Environment

2016 ◽  
Vol 5 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Verónica Andrea González-López ◽  
Ramin Gholizadeh ◽  
Aliakbar M. Shirazi
Keyword(s):  
Everyday Life ◽  
Real World ◽  
Queuing Theory ◽  
Arrival Rate ◽  
Service Rate ◽  
New Approach ◽  
The Real ◽  
Processing Times ◽  
Queuing Models ◽  
Service Rates

Waiting lines or queues are commonly occurred both in everyday life and in a variety of business and industrial situations. The various arrival rates, service rates and processing times of jobs/tasks usually assumed are exact. However, the real world is complex and the complexity is due to the uncertainty. The queuing theory by using vague environment is described in this paper. To illustrate, the approach analytical results for M/M/1/8 and M/M/s/8 systems are presented. It optimizes queuing models such that the arrival rate and service rate are vague numbers. This paper results a new approach for queuing models in the vague environment that it can be more effective than deterministic queuing models. A numerical example is illustrated to check the validity of the proposed method.

scholarly journals A Study of Service in Restaurant by Using Queuing Model

2013 ◽  
Vol 5 ◽  
pp. 14-18
Author(s):  
G.D. Mishra ◽  
Vijiya Singh Chauhan ◽  
Nikita Chandra
Keyword(s):  
Numerical Model ◽  
Waiting Time ◽  
Queuing Theory ◽  
Arrival Rate ◽  
Utilization Rate ◽  
Service Rate ◽  
Case Scenario ◽  
Queuing Model ◽  
Restaurant Management ◽  
Potential Customers

The restaurants want to avoid losing their customers due to a long wait on the line. This shows a need of a numerical model for the restaurant management to understand the situation better. This paper aims to show that queuing theory satisfies the model when tested with a real-case scenario. We obtained the data from a restaurant. We then derive the arrival rate, service rate, utilization rate, waiting time in queue and the probability of potential customers to balk based on the data using Little’s Theorem and M/M/1 queuing model. We conclude the paper by discussing the benefits of performing queuing analysis to a busy restaurant.

Queues with time-dependent arrival rates. III — A mild rush hour

1968 ◽  
Vol 5 (03) ◽  
pp. 591-606 ◽  
Author(s):  
G. F. Newell
Keyword(s):  
Queueing Theory ◽  
Queue Length ◽  
Arrival Rate ◽  
Time Dependent ◽  
Service Rate ◽  
Diffusion Approximations ◽  
Dimensionless Form ◽  
Queue Lengths ◽  
The Mean ◽  
Mean Queue Length

The arrival rate of customers to a service facility is assumed to have the formλ(t) =λ(0) —βt2for some constantβ.Diffusion approximations show that forλ(0) sufficiently close to the service rateμ, the mean queue length at time 0 is proportional toβ–1/5. A dimensionless form of the diffusion equation is evaluated numerically from which queue lengths can be evaluated as a function of time for allλ(0) andβ.Particular attention is given to those situations in which neither deterministic queueing theory nor equilibrium stochastic queueing theory apply.

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