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SOLVING OF WAITING LINES MODELS IN THE AIRPORT USING QUEUING THEORY MODEL AND LINEAR PROGRAMMING THE PRACTICE CASE : A.I.M.H.B

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Abstract

Waiting lines and service systems are important parts of the business world .In this article we describe several common queuing situations and present mathematical models for analysing waiting lines following certain assumptions. Those assumptions are that (1) arrivals come from an infinite or very large population, (2) arrivals are Poisson distributed,(3) arrivals are treated on a FIFO basis and do not balk or renege,(4) service times follow the negative exponential distribution or are constant, and (5) the average service rate is faster than the average arrival rate. The model illustrated in this airport for passengers on a level with reservation is the multiple-channel queuing model with Poisson Arrival and Exponential Service Times (M/M/S).After a series of operating characteristics are computed, total expected costs are studied, total costs is the sum of the cost of providing service plus the cost of waiting time. We also study the Tunisian aerial transport, while analysing the situation of the latter, we have privately chose to develop the waiting line’s problem on a level with landing on a runway. Among the different cause of this waiting, we were limited in which that in relation to the weakness on a level with the programming of flights by the civil aviation direction, as far as that goes we have been enumerated the main studies which have been consecrated in this reason. Finally, one way to resolve the waiting problem, a good linear programming is taken into consideration. On the basis of this analysis, we have chosen to apply the developed model in to real case in order to value the contribution which is able to generate the settling in such models in Tunisian airport.

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... However, the capacity of the terminal building can be affected by the efficiency and capability of the queuing system. Inefficient service facilities or an insufficient number of service facilities provided can result in severe bottlenecks, affecting overall terminal capacity ( [17]). ...
... Additionally, under the condition where increasing capacity is spatially viable, upgrading the service facilities is also expensive. Hence, an accurate evaluation of the queuing system to identify potential bottlenecks is vital to help airport management improve the queuing system and ensure maximum utilization of available terminal space ( [17]). ...
... The study on queuing theory aims to minimise customers' wait time in queues and optimise utilisation of limited resources. Using queuing theory, analysis of a business's expected queue length, frequency of the queue system being in certain states as well as the customer expected wait time can be derived [17]. ...
Research
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This applied research paper evaluates the flow of passengers through the airport terminal building facilities, e.g. Check-in counters, security checkpoints, immigration facilities, and boarding gates using queueing theory to identify the bottlenecks, then propose some recommendations for the sake of performance improvements.
... Muitos trabalhos têm sido publicados sobre o tráfego aéreo em aeroportos pelo mundo [5], [9], [10], mas a maioria investiga as filas clássicas devidas ao congestionamento em solo ou no ar, o fornecimento de peças de manutenção, com logística eficiente [7]. Desenvolveram-se gráficos de rotas de circulação aérea visando-se reduzir os tempos de espera. ...
... O estudo das filas de espera, chamada de teoria das filas, está entre as técnicas de análise quantitativas mais usadas [5], [8]. Os processos de fila são analisados segundo modelos designados por letras (notação desenvolvida por D.G. Kendall) que representam os padrões de chegadas do sistema e o número de servidores (ou neste caso, o número de pistas de pouso ou decolagem). ...
... Admitidas as condições citadas, desenvolveu-se, cf. [4] e [5], uma série de equações que definem as características de operação da fila, aplicados ao aeroporto de Manaus. ...
Conference Paper
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In this paper, we applied a stochastic model to the records of the arrival times of aircraft from the International Airport of Manaus Eduardo Gomes, based on the Poisson process. The suitability of this process was validated by comparing the theoretical estimates with the distribution of arrivals. The service capacity of the airport was investigated through the theory of queues. It is shown that the utilization factor is 80% (2010), with a rate of aircraft arrivals of 1.58 / h. However, we found a 65% probability of late arrival of aircraft that exceeds 15 min. Neste artigo, aplicou-se um modelo estocástico aos registros dos tempos de chegadas de aeronaves do Aeroporto Internacional Eduardo Gomes de Manaus, com base no Processo de Poisson. A adequação deste processo foi validada comparando-se as estimativas teóricas com as distribuições das chegadas. Investigou-se, através da teoria das filas, a capacidade de serviço do aeroporto. Mostra-se que o fator de utilização é de 80% (2010), com taxa de chegadas de 1,58 aeronaves/h. Contudo, há 65% de probabilidade do atraso de chegada de aeronave ultrapassar 15 min.
... A queue essentially describes waiting in lines (Ashley, 2000;Dhar & Rahman, 2013;Mehri, Djemel, & Kammoun, 2008;Sheikh, Singh, & Kashyap, 2013). It could be queues of people or things and is a common feature of most service centres. ...
... It is born out of delays that are occasioned by the gap between people requesting for service and inability of the service provider to satisfy their requests (Kandemir-Caues & Cauas, 2007). In the opinion of Mehri et al. (2008) and Sharma (2011) queues are a daily occurrence and Nnaemeka (2013) opines that having to wait for services is a feature of our daily life. Mehri et al. (2008) however reiterated that the occurrence of queues affects people adversely beyond the ordinary. ...
... In the opinion of Mehri et al. (2008) and Sharma (2011) queues are a daily occurrence and Nnaemeka (2013) opines that having to wait for services is a feature of our daily life. Mehri et al. (2008) however reiterated that the occurrence of queues affects people adversely beyond the ordinary. Aradhye and Kallurkar (2014) in this regard asserts that the experience of having to wait is a universal problem which causes an enormous waste of time for everyone that faces it. ...
... On l'utilise largement pour indiquer le nombre d'arrivées dans un système de files d'attente dans l'intervalle ]0, t]. Soit λ le débit moyen auquel les clients arrivent à un service [8]. ...
... CHAPITRE 1. LES FILES D'ATTENTE 1.6. PROCESSUS DE POISSON Les symboles communs pour A et B comprennent M (exponentiel), D (constant ou déterministe), Ek (Erlang d'ordre k), et G (arbitraire ou général).Les trois derniers paramètres ne sont pas explicités si leur valeurs sont D = F IF O, E = ∞, F = ∞[8]. ...
Thesis
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Modeling, simulation and analytic resolution of closed queuing network models is becoming a challenge for resolution system designers today. The complexity and size of these models makes understanding of these models more difficult. In this project, we propose a technique composed of several transformation rules by applying the principle of "reduction" which consists in successively replacing the initial model with another that is equivalent and reduced. The main objective is to reduce the time of analysis, simulation and facilitate the understanding of the reduced model. The reduction process is repeated until a very small model becomes elementary and is equivalent to the original model. Thus, the simulation and the resolution of the reduced model give practically either the same results as those of the initial model, or approximate results.
... As the system has less ability to promptly service the arrivals and departures rowdiness/randomness occur resulting to some waiting lines. According to Mehri et al (2009), queuing manifests at arrival, service facilities and actual waiting lines. These can be modeled for solutions based on performance evaluation metrics that include flight delays, cancellations and passenger delays (Subramanian 2007). ...
... As this work is a follow up to the work of Ademoh and Anosike (2014), similar distribution assumptions were used to enable close comparison. According to Mehri et al (2009), study assumptions are that; ...
Article
A nation's air industry is vital to her development as it offers inter-linkages for all the economic sectors. International airport of a country's capital city acts as gateway and gives lots of first hand impression of her integrity. Nnamdi Azikiwe International Airport, the gateway to Nigeria's capital city, Abuja, faces problem of passengers queuing for boarding, departure and arrival at different rates due to ineffectiveness in management of travelers using the facility. This never gave travelers, particularly international passengers a good impression of the country. As part solution, this study developed a queuing model using Birth and Death Rate approach to simulate the problem and find enduring solution. Four air transport companies consisting two each of domestic and international operators that frequently use the facility was adopted as study samples. Their 2013 flight data were used to simulate model for validation. Result showed that in order to meet current daily passenger need each domestic airline required at least 5 aircrafts. Each international airline required one additional aircraft to effectively service the monthly average demands of 21,863 passengers. The system required 0.5 service factor and utilization factors of 0.4, 0.6 and 0.9 at 5% significance.
... This theory is a branch of operation research (because of the need to make business decisions about the resources of the service) that analyzes the relationship between a request in the service system and the waiting time of the user in this system. The queueing theory is based on modelling, analyzing, and designing several processes that control human activities, such as telecommunications [5], reservation counters [6], and supermarkets [7]. This theory is also used to determine the sequence of computer operations (BLUM), computer performance [8], health services [9], and airport traffic [6]. ...
... The queueing theory is based on modelling, analyzing, and designing several processes that control human activities, such as telecommunications [5], reservation counters [6], and supermarkets [7]. This theory is also used to determine the sequence of computer operations (BLUM), computer performance [8], health services [9], and airport traffic [6]. In Computerized parallel and distributed systems are also based on queue models [10]. ...
Conference Paper
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The queue size distribution and average waiting time for a time-shared system using round-robin (RR) scheduling, with and without overhead, are determined. In this study, the incoming processes are prioritized, and dynamic quantum times are assigned depending on the level of priority. With these parameters, RR versus priority dynamic quantum time round robin scheduling algorithm is analyzed to explore the effect of changing the quantum time of processes and determine the optimum context switches, turnaround time, and waiting time.
... As the system has less ability to promptly service the arrivals and departures rowdiness/randomness occur resulting to some waiting lines. According to Mehri et al (2009), queuing manifests at arrival, service facilities and actual waiting lines. These can be modeled for solutions based on performance evaluation metrics that include flight delays, cancellations and passenger delays (Subramanian 2007). ...
... As this work is a follow up to the work of Ademoh and Anosike (2014), similar distribution assumptions were used to enable close comparison. According to Mehri et al (2009), study assumptions are that; ...
... Eight years later he published a report addressing the delays in automatic dialling equipment, and that research work can be considered the beginning of the Queuing theory. According to Houda, Taoufik and Hichem (2008), after the World War II, Erlang's early work was extended to more general problems and to business applications of waiting lines. ...
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The waiting lines are a part o our existence, more or less. Nobody wants to spend time in a waiting line, but, in order to have access to certain goods or services, we agree to do it. That's why the aim of this paper is, on one hand, to identify ways to reduce the cases in which waiting lines occur, but on the other hand, to find some helpful ideas to improve the quality of the time spent by customers in the waiting lines.
... Barnhart (2003) in his paper studied several important areas of operations research applications in the air transport industry. Mehri et al. (2008) in their paper studied solving of waiting lines models in the airport using queuing theory model and linear programming. The model about airport for passengers on a level with reservation is the multiple-channel queuing model with Poisson arrival and exponential service times (M/M/S). ...
Article
Waiting period is a global problem that almost everyone has to face, which causes a great waste of time for everyone. It is well known that all these waiting line problems critically restrict further development. The focus of this study is to deal with passengers' queue issues of the international airport terminals of Kerala. Queuing theory is a mathematical approach to the study of waiting period in queues. This study evaluates the effectiveness of multi-server queuing model. The multi server approach of modelling was adopted in this cram to develop a mathematical model to solve problem of queuing of air transport passengers at the international airports in Kerala. The airport in the aviation industry of the country faces problems of many passengers queuing for boarding, departure with different arrival rate due to non availability of state of the art logistics management mechanisms for predicting the nature and service demands of travellers. The passengers' average wait time for reaching the gate area measures system performance. A mathematical queuing model was developed in this study and comparisons are made using analysis of variance (ANOVA).
... Waled Cirebon", (Febi Firman Saputra, 2019). "Solving Of Waiting Lines Models in The Airport Using Queuing Theory Model and Linear Programming the Practice Case: A.I.M.H.B", (Mehri et al., 2008). "Improving queuing service at McDonald's", (Koh et al., 2014). ...
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Jumlah sepeda motor yang terdapat di Indonesia pada tahun 2020 mencapai 112.771.136 unit. Pengguna sepeda motor di Indonesia bahkan mencapai 81,78% dibandingkan dengan jenis kendaraan lainnya. Jumlah pengguna sepeda motor juga bisa dilihat dari banyaknya moda transportasi motor terutama ojek berbasis aplikasi atau ojek online. Banyaknya pengguna sepeda motor dan meningkatnya popuaritas ojek online ini juga mengakibatkan peningkatan dari penggunaan bahan bakar minyak (BBM). Oleh karena itu diperlukan suatu sistem pelayanan yang baik pada Stasiun Pengisian Bahan Bakar Umum (SPBU) untuk melayani peningkatan pembelian bahan bakar sehingga tidak terjadi antrean yang panjang. Menggunakan model antrean atau queuing system untuk mengatasi dan mencari solusi dari permasalahan pada SPBU tersebut, di mana pada kasus ini dicari jalur fasilitas optimal untuk menghindari penumpukan customer. Metode analisis dengan menggunakan analisis teori antrean yang sesuai dengan model antrean yang diterapkan pada SPBU yakni model antrean jalur berganda yang artinya terdapat lebih dari satu jalur pelayanan dan hanya terdapat satu tahapan pelayanan yang harus dilalui oleh pelanggan untuk menyelesaikan pelayanan. Kedatangan pelanggan dan waktu pelayanan mengikuti distribusi Poisson dan distribusi eksponensial. Hasil dari penelitian diperoleh dua jalur optimal, berdasarkan hasil perhitungan biaya per fasilitas pelayanan dan lama waktu menunggu customer yang datang ke SPBU. Penambahan jalur tidak diperlukan. Kata Kunci: Antrean, Distribusi Poisson, SPBU The number of motorcycles in Indonesia in 2020 reached 112,771,136 units. Motorcycle users in Indonesia even reached 81.78% compared to other types of vehicles. The number of motorcycle users can also be seen from the many modes of motorcycle transportation, especially app-based motorcycle taxis or online motorcycle taxis. The number of motorcycle users and the increasing popularity of online motorcycle taxis also increased the use of fuel oil. Therefore, a good service system is needed at public fueling stations (gas stations) to serve the increase in fuel purchases so that there are no long lines. Using the queue model or queuing system to overcome and find solutions to the problem of gas stations, wherein in this case the optimal facility path is sought to avoid customer buildup. The method of analysis with the analysis of queue theory following the queue model applied to the gas station is the double line queue model means that there is more than one line of facilities and there is only one stage of service that must be passed by the customer to complete the service. Arrival rate and service rate follow the Poisson distribution and exponential distribution. The results of the study obtained two optimal paths, based on the results of calculating the cost per service facility and the length of waiting time for customers who come to the gas station. Line addition is unnecessary. Keyword: Queue, Poisson Distribution, Gas Station
... by minimize the sum of service costs and waiting costs. [7]. ...
... by minimize the sum of service costs and waiting costs. [7]. ...
... In this study, the queuing model used is SCMS. Namely a service line structure that shows the existence of two or more services carried out sequentially [1], [19], [20]. After receiving services, the individual can leave the service area because there are still other individuals who must be served. ...
Article
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span>Satellite communication is a telecommunications technique that uses satellites as a connecting component, for example VSAT. In antenna installation, there is an important process which is called the cross-polarization. Cross-polarization is one process that cannot be released inside installation of VSAT antennas for satellite communication. Sometimes, in this process, a user queue will occur. Queuing theory explain the process is done and also calculate the other factors that are in the process. By knowing queuing theory to the cross-polarization, it will be easy to know the efficiency of queuing theory in the cross-polarization. Based on the characteristics of the cross-polarization, user can be known the queuing model that used and performance of the queuing system. The queuing model for the cross-polarization, using Kendall notation, M/M/1. Based on the analysis that has been done; by using 1 server the value of service level (ρ) is 0.67, using 2 servers = 0.33 and 3 servers = 0.22. The waiting time in the queue is longer if using 1 server which is 0.67 hours or 40 minutes. If a satellite operator uses 2 servers, waiting time in the queue is 25 minutes and 3 servers is 2.8 minutes which means that there is almost no waiting time in the queue.</span
Article
Queues or waiting lines are a natural occurrence in the everyday lives of consumers and the process of every business. Being customers' first point of contact with the business, a customer’s experience in the queue becomes a determining factor of their first impression of the business. Queuing provides the cornerstone of efficiency to businesses as they assist employees and managers in tracking, prioritising, and ensuring the delivery of services and transactions. Inefficiencies in queues are undesired as they can result in substantial losses to a business, such as bad reputation and loss of customers due to balking or reneging behaviour. Previous research has shown that the application of queuing theory enables businesses to analyse their queuing system and the trends of demand for their services. This allows the business to effectively identify measures to improve their queuing system and serve demand at the desired level of service. In this paper, where it examined Cairo International Airport (CAI)’s existing departure queue system and benchmarked it against the optimum wait time suggested in the International Air Transport Association’s (IATA) Level of Service (LoS) concept. The application of Kendall-Lee’s Notation is applied to describe the existing queuing system of the airport. It also suggested areas of improvement after the analysis and recommended that the CAI focus on improving service time for its Check-in, Security, and Boarding process. Although the Immigration process has met IATA’s recommended optimal wait time, training could be provided to employees to enable them to progressively work towards a better service time and prepare for the future higher traffic volume. The team has also suggested for CAI to introduce autonomous technology for the departure process and software which analyses passenger flow and projects a forecast value based on the airport growth trends.
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Book
Banks, J., J. S. Carson II, B. L. Nelson, and D. M. Nicol: Discrete-Event System Simu-lation (5th Edition). Prentice Hall (2010)
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Models are presented for the optimal location of hubs in airline networks, which take into consideration the congestion effects. Hubs, which are typically the most congested airports, are modeled as M/D/c queuing systems. A formula is derived for the probability of a number of customers in the system, which is later used to propose a capacity constraint. This constraint limits the probability of more than b airplanes in queue, to be smaller than or equal to a given value. Due to the computational complexity of the formulation, the model is solved using a heuristic based on tabu search. Computational experience is presented together with an example using a data set available in the literature.Scope and purposeIn order to take advantage of economies of scale, most major airlines have selected some airports as transshipment points (hubs). As hubs become congested, the usual hub siting techniques fail in finding their best locations. We propose new methods for locating congested hubs and allocating runways to hub airports.
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In modern communication networks such as the broadband integrated services digital network, it is possible to re-negotiate the bandwidth of a virtual channel (in queueing terminology the service rate of a server or the number of servers) during the course of a communication session. Many communication protocols have been proposed to take advantage of this flexibility. The basic principle of these protocols is to request more bandwidth when needed and release extra bandwidth when not used. Motivated by one such protocol, we study the steady-state behavior of an M/M/s queueing system in which the number of servers varies between a lower limit and an upper limit. New servers are hired when there are waiting customers in the queue and idle servers are released when the queue has been empty for some time. Using the matrix-analytical technique, we derive formulas in matrix-geometric form for the steady-state probabilities, and formulas for standard performance measures. One interesting feature of our solution is that the rate matrix R can be obtained explicitly without the need for iteration as in many other cases. We also study the optimization problem in which the server utilization is to be maximized subject to the performance constraint that the mean queueing delay does not exceed a pre-determined target. Finally, we compare the optimal utilization with that of the classical M/M/s system in which the number of servers is fixed.
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JERRY BANKS, JOHN S.CARSON, II.« Discrete-event system simulation ».Prentice-Hall International Series, 1989, pp172-223. [5] LEE A.M. « Applied queuing theory ». St Marints press, New York, 1966.