Queueing System Research Articles

M/M/1/K Loss and Delay Interdependent Queueing Model with Vacation and Controllable Arrival Rates

Objectives: In this study, we assume that the vacation is taken while there are no consumers in the queue. There are several servicemen who will take the synchronous multiple vacations in the system. Methods: Assumed some loss and delay in consumers (Elective and emergency) and solve the steady-state probability equations using recursive approach and acquired some obvious iterative expressions. Findings: Carried out some numerical analysis using MATLAB and investigated the movement of , , and through graph. Further, , , and increase when increases; decrease when M increases. Additionally, when L increases remains constant and increase. Novelty: Expanded the preceding models in this study by including vacations and performing the numerical analysis. Using vacation with controllable arrival rates in an optimal way in order to benefit both the server and the customer will minimise waiting time and provide the most feasible, affordable service to the consumer. Keywords: Markovian Queueing System, Vacation, Loss and Delay, Finite Capacity, Interdependent Arrival and Service Rates, Varying Arrival Rates, Bivariate Poisson Process

Analisis Antrian pada SS Freis Chicken untuk Menentukan Pelayanan yang Optimal

This study was conducted to determine the optimal service with the theory of multi-channel-single phase queues, which is anytime two or more are flowed by a single queue. The research method is a single channel multi-phase method. The variables seen are level of utility, probability, average amount, time. The data used for queuing system analysis is the average number of arrivals per hour and the average number of services per hour. Data collection was based on direct observation at SSFC. The results of this study showed that SS Freis Chicken had to increase its chicken stock. So that the service at SSFC is optimal for customers. Queuing is an unavoidable phenomenon today, manufacturing and service companies are required to be able to reduce queues in providing services to customers. The addition of cashiers is carried out in phase 1, namely the payment stage to 2 people so that it can reduce the average customer waiting in the queue which was originally 10 queues to 0 queues and reduce the average time of customers waiting in the queue which was originally 19.33 minutes / person to 1,002 minutes / person. The addition of cashiers can make the performance of the queuing system more optimal.

Bayesian estimation of finite buffer size in single server Markovian queuing system

Bayesian estimation of finite buffer size in single server Markovian queuing system

Applied of The Simulation of The Queue System in Restaurant Mie Gacoan Branch Gresk Using Arena 14.0

A system design certainly cannot be separated from the term simulation. There is no need to calculate the simulation manually because a system called the Arena application is available. The Arena is a windows-based simulation software used to simulate and analyze a system. This study aims to enable the practitioner to know and run a queuing system simulation into the tools in the Arena 14.0 software, which in turn can apply it in real conditions to the queuing system at Mie Gacoan Restaurant Gresik Branch. The method used in this case is the simulation queuing method. The queuing model consists of 2 single servers consisting of a general queue and an online ojek queue. The simulation queuing presentation uses the FIFO (first in, first out) rule. That is, consumers who come first to make payments are the first to be served by the system. The analysis results show that the queue rate on server 2 (online ojek queue) has a slightly longer time difference than on server 1 (general queue).

Implementation Of a Web-Based Queuing System in Hospital Polyclinic Services Using the FIFO Method

This study uses a web-based queueing system to enhance efficiency in hospital outpatient clinics by employing the First-In, First-Out (FIFO) approach. The implemented technology is seamlessly incorporated into the preexisting hospital information system to streamline the operations of registration and queue monitoring. The First-In, First-Out (FIFO) method will be utilized to forecast the number of incoming patients and approximate service durations using previous data from outpatient services. By employing this approach, the hospital is anticipated to optimize resource allocation, minimize patient waiting periods, and improve patient contentment. This study will employ software development methodologies such as requirement analysis, system design, implementation, and assessment. Data collection will be carried out using observation, interviews, and current system documentation. The findings of this study are expected to enhance the standard of treatment in hospital outpatient clinics and guide other healthcare organizations in deploying web-based queueing systems utilizing the FIFO method. This research aims to enhance comprehension of the advantages and obstacles of implementing a web-based queueing system in healthcare services.

Analisis Sistem Antrian Cafe Ipong Kane Menggunakan Metode Single Channel

The purpose of this research is to find out how long it takes customers when experiencing a queue for service at Cafe Ipong Kane using the single channel method. The research methodology used is descriptive observational research by directly observing the queuing system that occurs at the Ipong Kane Café. The results and discussion of this research are the arrival of data and services, and queue calculations. The conclusion of the research that has been carried out is: Single channel model queuing process, from the calculation that the average number of customers waiting in line is around 10 customers within 25 minutes in busy conditions. The average time spent by customers waiting in line is around 9.6 minutes at the longest and 3 minutes at the fastest

Assessment of the quality of the ophthalmological Service at the Hospital of the State Public Servant of São Paulo based on the number of ombudsman cases

This study aims to highlight improvements in the quality indicators of ophthalmology services provided by the Hospital do Servidor Público Estadual de São Paulo, resulting from a significant change in the organization of the cataract surgery queue. The transition from an obsolete and inflexible system, represented by an outdated spreadsheet, to a dynamic virtual queue system had a positive impact on the operationalization of services. This research analyzes the reduction in both absolute and proportional complaints received through ombudsman channels, specifically related to cataracts, and the reduction in waiting time for surgery, emphasizing that most surgeries are now performed within the timeframe established by medical literature. Furthermore, it investigates the impact of ombudsman services on the evaluation of service quality, relying on relevant scientific evidence.

Analysis of a Single Server Retrial Queueing System with Finite Capacity, F-Policy, Balking, Reneging and Server Maintenance

In this paper, we determine a single server retrial queuing system with finite capacity, F-policy, balking, reneging and server maintenance. The arriving customer when notices the server becomes free, then they get service immediately. In case server becomes busy, the customers are move to either orbit or may balk the system. In the orbit, after some random time the customer repeats their attempts for service. The customers are waiting in the orbit for longer time become impatient and leaves the orbit without getting service. Once the number of customers in the orbit reaches its full capacity then the arrival of customer is not allowed to enter into the orbit. The new customer is allowed into the orbit when the F-policy level is reached. If no more customer in the orbit, server will move to the vacation. By using recursive technique, the steady state distributions are obtained and we have developed various performance measures.

Sustainable and integrated rail operations planning for grain exports

ABSTRACT The grain export in Brazil is operated by several players and regulated by a few governmental agencies. Although players have particular interests, sustainability is an increasing concern that poses a common challenge to rail operations: reducing CO2 emissions. This work proposes a simulation-optimisation approach for assigning trains to routes in a complex queuing system, minimising CO2 emissions of the country-wide rail operations without compromising the delivery of planned volume exports. The model considers a multi-modal logistic system, i.e., terminals, railways, and ports integrated into a closed circuit. The computational experiments using real-world data of 2021 reveal that the CO2 emissions could be reduced by 5.32 kilo tons and still increase the grain export by 2.20% per year.

Presenting a mathematical model of blood supply chain considering the efficiency of collection centers and development of metaheuristic algorithm in M/M/C/K queuing system.

In this study, a multiobjective model was devoted to the objectives of minimizing blood supply chain costs and minimizing the waiting time of blood donors for blood transfusion and minimizing blood transfusion schedule and increasing the efficiency of fixed and mobile centers in collecting blood. One of the most important constraints considered in the mathematical model is the capacity constraints of considering fixed and mobile blood facilities and management of the transfer of blood products to centers for collecting and distinguishing healthy and unhealthy blood. A multiobjective model was considered with the objectives of minimizing blood supply chain costs, the waiting time of blood donors for blood transfusion, and blood transfusion timing and increasing the efficiency of fixed and mobile centers in blood collection. The model findings were analyzed in order to validate the model on a larger scale, using the meta-innovative algorithm NSGAII and MOSPO. According to the research findings, we suggest that fuzzy uncertainty and fair distribution problem shouldn't be added to the dimensions of the main problem, and further analysis should be done in this area. It was shown that the NSGAII algorithm's performance was better than the MOPSO meta-heuristic algorithm.

Analisis Model Antrian Multi Channel-Single Phase Pada Doorsmeer Mobil dengan Menggunakan Software POM-QM for Windows

Queuing is the activity of a group of people or goods in a waiting line to wait for a service. The queueing system can be interpreted as the arrival of customers for a service, waiting to get service, and leaving the system after getting service. This research is applied research using the observation method. This research aims to provide solutions to queuing problems at Agung Auto Service car doorsmer Jl. S.M. Raja No. 3, Rantauprapat, North Sumatra. Data is taken by paying attention to the time of arrival of customers and how many customers can be served. This car doorman applies the First Come, First Served (FCFS) discipline, where the first customer to arrive will get the first service through the queuing process. Therefore, the model that can be used is the multi-channel single-phase model, where there are two or more service facilities flowed by a single queue. From the results of the calculation of the model simulation in POM-QM for Windows, it can be seen that the performance of the service system at the Agung Auto Service car doorsmeer is not optimal because initially there were only 3 service servers, causing queues. Therefore, it is necessary to add up to six service servers to produce optimal service

Simulation Modeling of QS with Hyper-Erlang and Erlang Distributions

The article is devoted to the construction of simulation models of customer delay in the queue in the form of a queuing system (QS) described by both ordinary and right-shifted hyper-Erlang and second-order Erlang distributions. This article is a logical continuation of previous works devoted to the construction of numerical-analytical QS models with shifted distribution laws. In the article, the Erlang distribution is considered as a special case of the more general Gamma distribution law, in contrast to the normalized Erlang distribution. These two forms of the Erlang distribution differ in numerical characteristics, except for the coefficient of variation. To solve the problem, the system of discrete-event modeling GPSS WORLD was used.

Stalling in Queuing Systems with Heterogeneous Channels

The present paper considers a model of stalling in a queueing system (QS) with any number of different capacities of heterogeneous servers. The state graph and the corresponding linear system for steady-state probabilities are derived using the standard Markov chain technique. The obtained solution of the steady-state probabilities model is numerically stable; the complexity of the corresponding expressions does not depend on the number of QS states; thus, they enable us to analytically study the QS characteristics. Optimization of a stalling buffer is considered as well, and it is shown that stalling helps us to solve the slow server problem under an appropriate choice of stalling buffer size, making the slow servers usable under various values of system load. The asymptotic conditions of optimal query distribution in channels, when the ratio of the capacities of the fast and slow servers is increasing, are also established. Moreover, some applications of the developed model in heterogeneous server clusters and in work productivity modelling for forest harvesting applications are discussed.

A queueing system with an SIR-type infection

Abstract We consider the propagation of a stochastic SIR-type epidemic in two connected populations: a relatively small local population of interest which is surrounded by a much larger external population. External infectives can temporarily enter the small population and contribute to the spread of the infection inside this population. The rules for entry of infectives into the small population as well as their length of stay are modeled by a general Markov queueing system. Our main objective is to determine the distribution of the total number of infections within both populations. To do this, the approach we propose consists of deriving a family of martingales for the joint epidemic processes and applying classical stopping time or convergence theorems. The study then focuses on several particular cases where the external infection is described by a linear branching process and the entry of external infectives obeys certain specific rules. Some of the results obtained are illustrated by numerical examples.

Transient Solution of a Two Homogeneous Servers Markovian Queueing System with Environmental, Catastrophic and Restoration Effects

In this paper we consider a finite capacity Markovian queueing system with two identical servers under two environmental conditions. Change in environmental conditions also affects the state of the queueing system. Further the system is also suffered by randomly occurring disasters, which destroys all the present customers of the system in both the environmental conditions. Then a repair process is started and after the successful repair the system is ready for working. Here, repair time is known as the restoration time. We modeled this queueing system and obtained the transient state solution by using probability generating function technique.

Analisis Sistem Antrian pada Proses Pelayanan Konsumen di Warung Ayam Geprek Najwa Menggunakan E-WOM

This study aims to determine the effect of e-Wom, food quality and service quality on Purchase Satisfaction at Najwa geprek chicken stall. This research method was quantitative through an online questionnaire with a total of 145 respondents. The data used for the analysis of this queuing system is primary data, which is in the form of customer arrival time data and service time data (server), for time measurement carried out using the help of a stopwatch. The results of data analysis showed that the enthusiasm of Rantauprapat residents towards Najwa geprek chicken stall was very high, this made Najwa geprek chicken stall does not empty of visitors, resulting in queues

Chat service in a multichannel system under competition where customers are boundedly rational

Many service systems in various type of industry provide services via chat technologies. This type of service system is characterized by an interesting combination of properties. First, the customer is actively involved in service execution, since the service is comprised of responses of the server and the customer to each other, until the customer's request is satisfied. In addition, in such a system, the service can be provided by a single server in a parallel manner to a number of customers. Motivated by these and others interesting properties of the chat service, we formulate and analyze the stochastic queueing system as a two-dimensional quasi-birth-and-death process and derive its steady-state probabilities using matrix geometric methods. By means of economic analysis, we provide a scheme for deriving the optimal capacity of parallel chats and the optimal response effort that should be made by the server, considering that higher effort lengthens the response time but increases the probability of successful service completion. We next investigate a queueing game that considers a multi-channel service system consisting of a chat service and a traditional multi-server call center, and we consider strategic customers under both a centralized and a decentralized scenario. We show that competition between service channels may lead to lower service utilization even though customers enjoy higher expected utility. Finally, customer bounded rationality is considered and it is shown that customers who are less rational may enjoy higher utility. Sensitivity analyses are conducted for all scenarios.

Learning-Based Optimal Admission Control in a Single-Server Queuing System

We consider a long-term average profit–maximizing admission control problem in an M/M/1 queuing system with unknown service and arrival rates. With a fixed reward collected upon service completion and a cost per unit of time enforced on customers waiting in the queue, a dispatcher decides upon arrivals whether to admit the arriving customer or not based on the full history of observations of the queue length of the system. Naor [Naor P (1969) The regulation of queue size by levying tolls. Econometrica 37(1):15–24] shows that, if all the parameters of the model are known, then it is optimal to use a static threshold policy: admit if the queue length is less than a predetermined threshold and otherwise not. We propose a learning-based dispatching algorithm and characterize its regret with respect to optimal dispatch policies for the full-information model of Naor [Naor P (1969) The regulation of queue size by levying tolls. Econometrica 37(1):15–24]. We show that the algorithm achieves an O(1) regret when all optimal thresholds with full information are nonzero and achieves an [Formula: see text] regret for any specified [Formula: see text] in the case that an optimal threshold with full information is 0 (i.e., an optimal policy is to reject all arrivals), where N is the number of arrivals. Funding: A. Cohen is partially supported by the National Science Foundation [Grant DMS-2006305]. V. Subramanian is supported in part by the NSF [Grants CCF-2008130, ECCS-2038416, CNS-1955777, and CMMI-2240981].

Queueing system with batch arrival of heterogeneous orders, flexible limited processor sharing and dynamical change of priorities

<abstract><p>A queueing system with the discipline of flexible limited sharing of the server is considered. This discipline assumes the admission, for a simultaneous service, of only a finite number of orders, as well as the use of a reduced service rate when the bandwidth required by the admitted orders is less than the total bandwidth of the server. The orders arrive following a batch-marked Markov arrival process, which is a generalization of the well-known $ MAP $ (Markov arrival process) to the cases of heterogeneous orders and batch arrivals. The orders of different types have different preemptive priorities. The possibility of an increase or a decrease in order priority during the service is suggested to be an effective mechanism to prevent long processing orders from being pushed out of service by just-arrived higher-priority orders. Under a fixed priority scheme and a mechanism of dynamic change of the priorities, the stationary analysis of this queueing system is implemented by considering a suitable multidimensional continuous-time Markov chain with a generator that has an upper Hessenberg structure. The possibility of the optimal restriction on the number of simultaneously serviced orders is numerically demonstrated.</p></abstract>

Calculations of emergency response capabilities as parameters of the queueing system

The article defines as a scientific problem that requires research the development of a sufficiently simple (for use “in field conditions”) methodology for calculating the capabilities of forces and means of response to man-made, natural and military emergency situations. It is noted that many researchers used the mathematical apparatus of the queueing theory, as well as process modelling with the help of appropriate software, for the theoretical analysis of similar tasks. It is shown that to solve the problem, it is possible to use a mathematical model of the M/M/1 type queueing system (QS), which takes into account the probabilistic nature of the processes of occurrence of emergency situations and response to them, while it was supplemented with an analytical method of calculating the parameters of the QS, which ensure the necessary capability of the forces and means of emergency response. The results of the study are suitable for practical use by emergency services to quickly determine the required number of rescue or repair crews, sanitary teams, vehicles, etc., their equipment and capabilities in responding to emergency situations and overcoming their consequences.