Server Queueing System Research Articles

Simulation of Service Queue for Dental Doctor Patients at Kindergarten Hospital. IV 01.07.02 Binjai Using the Exponential Method

One of the systems that can be simulated is a queue. The queuing system consists of a collection of customer servers, a queue that regulates service to customers. The utilization of queuing simulations is to optimize services by designing service resources so that services can be effective and efficient. In the queuing system there are several problems that often occur, for example queuing queues, the number of queues will cause problems such as bored customers, and discomfort will make customers dissatisfied with the service. The Application of the Exponensial Method in the Dentist Patient Service Queuing System There are 28 general populations in this study, namely all consumers at the Kesrem Binjai Hospital, while the target population is the population that is actually used as a data source for patients who queue at the Kesrem Binjai Hospital to get the best service. is the target population in this study.

Time-dependent behaviour of an M/M/3 heterogeneous server queueing system with multiple vacations subject to system disaster

This research paper investigates the dynamic behaviour of a heterogeneous three-server queuing model with multiple vacation. The model also accounts for the possibility that a disaster could occur during busy periods or on vacation, in which case the restoration process would begin immediately. The time-dependent probabilities of system size are presented in the work with explicit equations computed in terms of modified Bessel functions, employing generating functions. To support the theoretical conclusions, numerical examples are given.

Analisis Sistem Antrean untuk Mengoptimalkan Pelayanan pada Coffeeshop Teman Sejalan .Co di Karanganyar

Teman Sejalan.co is a Coffeeshop located in Karanganyar and was established in December 2022. Operations in the Teman Sejalan.co Coffeeshop business certainly include from the initial order to pickup. This is related to the queuing system which must improve its service so that customers do not leave if there is a queue. This research uses the Single Channel Multiphase method which is in accordance with the current conditions of Teman Sejalan.co's servers and services. This data was obtained by going directly to the research object during the "Makgedebrews" event by calculating the customer queue time with the number of customers at that time being 103 customers. The results of the research regarding the server line service queue system with H1 and H2 were not proven to be true because the number of customers who were enthusiastic about the event held by Teman Sejalan.co. The use of 1 server lane is not optimal at events that are quite popular with customers which causes queues to pile up, so it is better to use 2 lanes at future events so that it is effective when it is busy.

Single server queueing model with Poisson arrival and gamma service time distribution

Queueing theory is pivotal in understanding waiting lines and their pervasive role in everyday life. Its profound application spans across diverse sectors, including computer programming networks, healthcare, transportation, and so on. Researchers have applied many statistical distributions in analyzing queueing data. This article focuses on the analysis of a single server queueing system with Poisson input and service times distributed according to a two-parameter gamma distribution. The study elaborates on the construction and estimation of key queueing properties such as steady state equations, average number of customers in the system, average queue length, expected size of the non-empty queue, distribution of waiting time, average waiting time in the system, and average waiting time in the queue of the M/Gamma/1 queueing model using the two-parameter gamma distribution. Keywords: Gamma distribution; Poisson; service; single server; queuing model.

Study of a two types of general heterogeneous service queueing system in a single server with optional repeated service and feedback queue

This paper addresses a model on a single server queue and two service representatives. After a customer is served, he/she has the three options: opting for receive the same service again (re-service), joining as a new customer for another regular service (feedback), or leaving the service system altogether. To ensure the queueing system is Markovian, we introduce an additional variable (supplementary variable) and using this approach, we derive the explicit distribution of queue size at random and departure epochs. Additionally, we determine the distribution of response time, inter-departure time, and busy period. By using the embedded Markov chain technique we have also derived the queue size distribution at departure epoch. We have also presented the cost analysis of the model with some numerical examples. The numerical illustration validates our findings and provides valuable insights into the queuing system.

On a Single Server Vacation Queue with Two Types of Service and Two Types of Vacation

We study a single server queueing system that receives singly arriving customers according to a Poisson process. The server offers one of the two types of heterogeneous services. Before the beginning of a service, , the customer can choose an exponential service with probability p1 or a deterministic service with probability p2, where p1+p2=1 Immediately after a service is completed, the server has a choice of taking a vacation with probability δ, or, with probability 1-δ, the server may continue staying in the system. We further assume that if the server opts to take a vacation, then with probability α1, he may take a vacation of an exponential duration with mean vacation time 1/u (u>0) or with probability he may want to take a deterministic vacation with constant duration d>0, where α1+α2=1. After a vacation is complete, the server instantly starts providing service if there is at least one customer in the system or the server remains idle in the system till a new customer arrives for service. We find a steady state solution in terms of the generating function of the queue length as well as the steady state probabilities for all different states of the system.

Evaluasi Sistem Informasi Layanan Antrian Paspor Online Menggunakan Framework Information Technology Infrastructure Library V3

Palembang Class 1 Immigration Office is a service provider agency in the immigration sector that has the authority to arrange passports or Travel Letters of the Republic of Indonesia (SPRI). In meeting the needs of the community in passport processing, Palembang Class 1 Immigration Office has implemented an Online Passport Queuing Service System. Until now, the system still experiences problems such as errors in the system, exhausted quotas, inappropriate applicant NIK, slow access to the system, and system handling that always involves the Immigration Head Office. Therefore, an evaluation of the online passport queue service information system is needed which can be used as a benchmark for the sustainability of the system. The framework used is the Information Technology Infrastructure Library (ITIL) V3 framework with the domain of Service Operation and Continual Service Improvement. This research was conducted by distributing questionnaires, interviews and observations to obtain maturity level scores. The results of the maturity level calculation in the Service Operation (SO) domain show that the average value of maturity level in the SO domain is 3.49 or is at level 3 (Define Process) and for the Continual Service Improvement (CSI) domain is 3.47 or is at level 3 (Define Process). From the evaluation results of the Online Passport Queuing Service System based on the maturity level calculation, several recommendations for the Service Operation (SO) and Continual Service Improvement (CSI) domains can be taken into consideration in improving service operations and improving the Online Passport Queuing Service System on an ongoing basis.

Analysis of heterogeneous two server queueing system with multiple working vacations and server breakdowns

The steady state analysis and the time-dependent behaviour of a heterogeneous two-server multiple vacation queueing model is examined in this research work. The model also takes into account the possibility of a breakdown happening when server 1 is busy while server 2 is on working vacation and both servers are busy, with the restoration procedure starting right away. The stability condition is established through the use of matrix geometric technique, and the steady-state probability vector of the system?s number of customers has been evaluated as a quasi-birth and death (QBD) process. Some system performance measures are obtained. Numerical analysis for both steady-state and transient analysis are given to our proposed model.

Dynamic service management and priority handling in dual server queuing systems with breakdowns

Dynamic service management and priority handling in dual server queuing systems with breakdowns

Tax counseling and assistance in implementing an E-KTP-based service queue system in Randubango Village, Mojokerto

Taxation stands as a potential income factor, significantly contributing to regional revenue. The objective of community service in Randubango Village, Mojokerto, is to elevate public awareness of tax payments and foster innovation in the queuing system for administrative services. The implementation of this community service unfolds in three stages: licensing, awareness-raising counseling, and assistance in deploying the queuing system for administrative services, integrating KTP scanning and monitoring. The outcome of this program manifests in an increased awareness of the importance of tax payments and the improved operation of the administrative services queue system.

Analisis Strategi Pemasaran Untuk Meningkatkan Penjualan Produk Box Panel

Queues are part of everyday life. Queues occur when the number of customers to be served exceeds the available service capacity. This queuing situation can be found on several occasions, one of which is at the delivery counter at PT Batik Ekspedisi Indonesia. The aim of this research is to analyze the customer service queuing system that occurs at PT BEI at the delivery counter. Which describes how the queue conditions are and to find out whether the service provided to customers has been carried out optimally, even though the company already has several goods delivery counters. For this reason, modeling and simulation using the Monte Carlo method with a Multi Channel Single Phase queuing system are used. And using Arena software to create a simulation model of the queue model at PT BEI. This research uses the observation method or goes directly into the field and carries out library research and laboratory research. The results displayed are in the form of a simulation using Arena software on the desktop layer.

Two Server Queueing System One with Working Vacation and Failure

In this paper we modeled the system as a Markovian two heterogeneous servers in a queueing system, with Server-1 being completely dependable. Whenever the system, server-1, lacks any users, remains idle and gets ready to serve the arriving new customers. But Server-2 switches over to the working Vacation (WV) mode. Failures occur only when Server-2 is operational. We obtained some performance measures.

Perbandingan Waktu Tunggu Dan Waktu Pelayanan Sistem Pembayaran Cash Dan Cashless Di Parkiran Menggunakan Discrete Event Simulation

Congestion can take a lot of time for people. Congestion does not only occur on roads but also occurs in public facilities such as parking facilities. where one of the causes is the queue in and out of parking in the business area, which has an impact on discomfort. The purpose of this study was to assess the effectiveness of the cash and non-cash payment service queuing system in terms of waiting time and service time. The stages of the research are observation, data collection on service time, data sampling, data processing and analysis using the discrete event simulation (DES) approach, validation, and suggestions for improvement. The results of the analysis show that the payment system with the cashless method is more effective than the cash payment method. Therefore, the cashless method can be used as a reference for parking service providers in the modern market to be implemented in a parking payment system, with an average service time of the Cashless method of 15.2365 seconds compared to an average service time of the cash method of 42.6812 seconds. seconds or an increase in server time from cash to cashless by 2.81% and a decrease in waiting time using cashless compared to cash by 9.31%. Keywords: Discrete Event Simulation, payment method cashless, Queue System

MATHEMATICAL MODELLING IN WAITING QUEUE IN SHOPPING MALL

This project is an attempt to analyze the use of queuing theory in a local shopping mall. Also considers the mall as a multi server queuing system following Poisson arrival and Exponential service based system. A comparison of the results using MATLAB pertaining to double server and multiple server queuing system is also provided.

Equilibrium Analysis for Batch Service Queueing Systems with Strategic Choice of Batch Size

Various transportation services exist, such as ride-sharing or shared taxis, in which customers receive services in a batch of flexible sizes and share fees. In this study, we conducted an equilibrium analysis of a variable batch service model in which customers who observe no waiting customers in an incomplete batch can strategically select a batch size to maximize the individual utilities. We formulated this model as a three-dimensional Markov chain and created a book-type transition diagram. To consider the joining/balking dilemma of customers for this model, we proposed an effective algorithm to construct a necessary and sufficient size of state space for the Markov chain provided that all customers adopt the threshold-type equilibrium strategy. Moreover, we proved that the best batch size is a non-decreasing function for i if the reward for the completion of batch service with size l is an increasing function of l assuming that a tagged customer observes i complete batches in the system upon arrival; in other words, the fee decreases as the batch becomes larger. We then derive several performance measures, such as throughput, social welfare, and monopolist’s revenue. Throughout the numerical experiment, a comparison between the present variable batch service model and regular batch service model in which customers were served in a constant batch, was discussed. It was demonstrated that the three performance measures can be optimized simultaneously in the variable batch service model, as long as the fee was set relatively high.

On the Optimal Input Rate in Queues with Batch Service

In recent years, queuing systems with batch service are emerging as powerful and flexible mathematical models in different frameworks. In this paper, we consider a single server queuing system with Poissonian arrivals, infinite buffers, and a constant batch size b. This paper addresses a little-studied optimization problem, namely the existence of an optimal arrival rate that minimizes the average sojourn time. Unlike the classical M/M/1 queue, for any batch size b, the problem admits a non-trivial solution that can be found by solving a polynomial equation of degree b+1. Since, in general, only numerical solutions are available, a simple first-order approximation is also derived and the corresponding deviations (in terms of input rate and sojourn time) are calculated. In more detail, it is shown that the approximation improves as the batch size increases and, in any case, the relative error for the average sojourn time is less than 0.34%. Finally, the paper provides new theoretical results about the asymptotic service rate in the equivalent birth–death process, highlighting how it depends on all queue parameters.

Perishable inventories with random input: a unifying survey with extensions

AbstractThis paper is devoted to the theory of perishable inventory systems. In such systems items arrive and stay ‘on the shelf’ until they are either taken by a demand or become outdated. Our aim is to survey, extend and enrich the probabilistic analysis of a large class of such systems. A unifying principle is to consider the so-called virtual outdating process $$\textbf{V}$$ V , where V(t) is the time that would pass from t until the next outdating if no new demands arrived after t. The steady-state density of $$\textbf{V}$$ V is determined for a wide range of perishable inventory systems. Key performance measures like the rate of outdatings, the rate of unsatisfied demands and the distribution of the number of items on the shelf are subsequently expressed in that density. Some of the main ingredients of our analysis are level crossing theory and the observation that the $$\textbf{V}$$ V process can be interpreted as the workload process of a specific single server queueing system.

Queueing system with server breakdowns and individual customer abandonment

ABSTRACT We consider a single server queueing system with a finite capacity buffer in which the server is subject to breakdowns and repairs. At the time of a breakdown, the customers, if any, present in the system will either decide to stay or abandon according to a probabilistic mechanism. This decision is made by every customer present in the system independent of the others. We assume that the arrivals of customers occur according to a Markovian arrival process (MAP). The shocks that create breakdowns of the servers are also assumed to follow a MAP independent of the other MAP. The service and the repair times of the server are assumed to follow (possibly) different phase type (PH) distributions. An arriving customer finding the buffer full will be lost. Further, an arriving customer finding the server under repair may decide to balk or join the queue at that instant. This queueing system, which generalizes some of the well-known queueing models in the literature, is studied as a GI/ M/ 1- type with a finite state space. The model is analyzed in steady-state and illustrative numerical examples including an optimization problem of interest are presented.

MAX PLUS ALGEBRA OF TIMED PETRI NET FOR MODELLING SINGLE SERVER QUEUING SYSTEMS

This research modified a single server queuing system using timed Petri net. We add two places, a transition and its appropriate arcs. This research also considered all the holding times in the timed Petri net. We found that the Petri net is not stable but stabilizable according to Lyapunov stability criteria. The standard autonomous equation of the system is also determined. Furthermore, this system also has the eigen value which related to its periodical behavior, it is . This means that the periodical behavior of the system only depends on the value of holding times of place W, R, B, and I.

Dynamic Scheduling in a Partially Fluid, Partially Lossy Queueing System

We consider a single server queueing system with two classes of jobs: eager jobs with small sizes that require service to begin almost immediately upon arrival, and tolerant jobs with larger sizes that can wait for service. While blocking probability is the relevant performance metric for the eager class, the tolerant class seeks to minimize its mean sojourn time. In this article, we analyse the performance of each class under dynamic scheduling policies, where the scheduling of both classes depends on the instantaneous state of the system. This analysis is carried out under a certain fluid limit, where the arrival rate and service rate of the eager class are scaled to infinity, holding the offered load constant. Our performance characterizations reveal a (dynamic) pseudo-conservation law that ties the performance of both classes to the standalone blocking probabilities associated with the scheduling policies for the eager class. Furthermore, the performance is robust to other specifics of the scheduling policies. We also characterize the Pareto frontier of the achievable region of performance vectors under the same fluid limit, and identify a (two-parameter) class of Pareto-complete scheduling policies.