Queueing theory

This paper examines the relationship between lot release variability and queuing time in a simple six operation manufacturing process line operating under a push-type lot release policy. Five different lot release strategies are modelled, based on two different operation capacity scenarios. The performance resulting from the departure variability caused by each of the release strategies is analyzed, as well as the queuing impact due to capacity.

Efficient implementations of Dijkstra's shortest path algorithm are investigated. A new data structure, called the radix heap , is proposed for use in this algorithm. On a network with n vertices, m edges, and nonnegative integer arc costs bounded by C , a one-level form of radix heap gives a time bound for Dijkstra's algorithm of O ( m + n log C ). A two-level form of radix heap gives a bound of O ( m + n log C /log log C ). A combination of a radix heap and a previously known data structure called a Fibonacci heap gives a bound of O ( m + n a @@@@log C ). The best previously known bounds are O ( m + n log n ) using Fibonacci heaps alone and O ( m log log C ) using the priority queue structure of Van Emde Boas et al. [ 17].

The present survey is based on the principle of retrials in queueing theory i.e. the customers who repeatedly try to avail the services from the server, on finding dejection, because of the inactivity of the server to provide service at an instant of selection from the queue. A bunch of work has previously been done on this front from past since it is realistic phenomena of many service system. The current investigation aims to present a brief review of the major works done on retrial queueing systems in recent years. The bibliography consists of research articles which were published in journals of repute during the period 2010-2015. In addition to the above references, an exhaustive list of books and survey papers on retrial queueing systems is also prepared so as to provide a detailed enough catalog for further understanding and research in retrial queueing domain. We have classified the journal papers according to the year of publishing. The aim of the present study is to turn up at a broad enough for a collection of important results in the theory of retrial queueing systems and their applications in solving several realistic problems. The main contribution is the bibliography of recent papers and books collected from different databases and private sources. At last, we have arranged some of the references according to the classification based on analysis and solution technique. The author(s) hope that this survey paper could be of help to learners contemplating research on retrial queues.

We present a model to describe the inbound air traffic over a congested hub and we show that this model gives a very accurate description of the traffic by comparing our theoretical distribution of the queue with the actual distribution observed at Heathrow airport. We also discuss the robustness of our model.

This book, written in Portuguese, deals with Operational Research topics, such as linear programming models and direct techniques for solving Ax = b systems, revised simplex method, Markov processes and queuing systems, in addition to Monte Carlo simulation.

Traffic models play an important role in both today's traffic research and in many traffic applications such as traffic flow prediction, incident detection and traffic control. Modelling traffic dynamics and optimising the control signal are two interrelated problems. Modelling provides fundamental understanding of traffic dynamics and behaviour. In this paper, traffic signal is modelled as a M/M/l queueing theory. The validation of a simulation model (M/M/l queue) with different arrival rates is presented. From the result, a traffic light model was developed by applying M/M/l queue theory for single intersection. In the optimisation strategy, the Markov decision control is applied to minimize queue length and waiting time. Simulation results show the excellent potential of this approach

With the current shift toward a service prominent economy, there exists a necessity in continuous improvements of service provision. Hospitality services have emerged as a foremost service under these circumstances. A university cafeteria is among the most time intensive services within a university premise. The tight schedules of the students and the staff influence the rushed atmosphere at the cafeterias that leads to customer dissatisfaction and brand switching. The study identified the congession at a hostel cafeteria of a state university. The objective of the study was to improve performance by reducing in the waiting times. The cafeteria was studied and primary data were collected during the rushed hours of weekdays for two weeks. The obtained data were simulated with Rockwell ARENA 14.5 version. Existing system allowed a waiting time of 3.30 minutes in the queue. The total time in the system was 4.81 minutes. Two model developments of increasing the service provision and the addition of another counter were simulated on the software. The waiting times resulted in the simulations depicted the efficiency in the increment of the service provision by twofold at the counter. The simulations for the data available depicted the addition of resources to the counter as the most efficient alternative. It obtained a reduction in waiting time by 74.84 percent and the service provision was increased by 67.54 percent in the system. The developments can be acheived by the standardization of the food serving and the payment handling at the counters.

The IEEE 802.11ai is an upcoming fast initial link setup (FILS) amendment that could enable a STA to achieve secure link setup in less than 100 ms. A successful link setup process will then allow the STA to send IP traffic with a valid IP address through the AP. In this paper, we first present a performance analysis on how well the legacy 802.11 can support FILS. We then demonstrate that the rate at which the medium saturates is mainly dependent on the offered load which has strong dependencies on the active scan rates (i.e., amount of transmitted probe request frames) and number of responding APs (i.e., amount of transmitted probe response frames) among others. Moreover, the average active scanning duration per channel could be maintained below 5 ms provided the medium is not saturated. Our results also indicate that a combination of the enhanced distributed channel access (EDCA) procedure and the proposed active scanning enhancements provides at least 20% and up to 250% improvements in supporting the functional requirements of FILS as compared to the 802.11 EDCA and legacy distributed coordination function (DCF), respectively.

- ATM enables the customers perform financial transactions without the need for a human cashier, clerk or bank teller. Queuing is the activity where customers avail the desired service, which could be processed or distributed one at a time. Thus, to maintain the customers, the service time needs to be improved. In this paper we analyze how queuing theory can be used to accurately predict the arrival rate of the customers and service rate of service facility. We collected data from an ATM in the city. The M/M/1 queuing model has been used to obtain the average arrival rate and the average service rate . The results of the analytic model are compared with the simulation model developed using MATLAB. The benefits of a queuing model are also discussed.

3. CODINGAN :
#include <stdio.h>
#include <conio.h>

typedef struct
{
            int data[100];
            char data1[100][20];
            char data2[100][30];
            char data3[100][15];
            int depan;
            int belakang;
}Queue;
Queue antrian;
Queue no;
Queue nama;
Queue poli;

int pilihan, data, i, j;
char data1[20], data2[30], data3[15];

int isEmpty()
{
            if (antrian.belakang==-1)
                        return 1;
            else
                        return 0;
}

int isFull()
{
            if(antrian.belakang==100)
                     

return 1;
            else
                        return 0;
}

void Enqueue(int data, char data1[20], char data2[30], char data3[15])
{
            if(isEmpty()==1)
            {
                        antrian.depan=antrian.belakang=0;
                        nama.depan=nama.belakang=0;
                        poli.depan=poli.belakang=0;
                        no.depan=no.belakang=0;
                        antrian.data[antrian.belakang]=data;
                        for(i=0;i<20;i++)
                        {nama.data1[nama.belakang][i]=data1[i];}
                        for(i=0;i<30;i++)
                        {poli.data2[poli.belakang][i]=data2[i];}
                        for(i=0;i<15;i++)
                        {no.data3[no.belakang][i]=data3[i];}
                        printf("data anda telah masuk. silahkan menunggu panggilan");
            }
            else if(isFull()==0)
            {
                        antrian.belakang++;
                        nama.belakang++;
                        poli.belakang++;
                        no.belakang++;
                        antrian.data[antrian.belakang]=data;
                        for(i=0;i<20;i++)
                        {nama.data1[nama.belakang][i]=data1[i];}
                        for(i=0;i<30;i++)
                        {poli.data2[poli.belakang][i]=data2[i];}
                        for(i=0;i<15;i++)
                        {no.data3[no.belakang][i]=data3[i];}
                        printf("data anda telah masuk. silahkan menunggu panggilan");
            }
}

int Dequeue()
{
            if(isEmpty()==0)
            {
            int i,e ;
            char a[20], b[30];
         
  e=antrian.data[antrian.depan];
            for(i=0;i<20;i++)
            {
                        a[i]=nama.data1[nama.depan][i];
            }
            for(i=0;i<30;i++)
            {
                        b[i]=poli.data2[poli.depan][i];
            }
            for(i=antrian.depan;i<antrian.belakang;i++)
            {
                        antrian.data[i]=antrian.data[i+1];
                        for(j=0;j<20;j++)
                        {nama.data1[i][j]=nama.data1[i+1][j];}
                        for(j=0;j<30;j++)
                        {poli.data2[i][j]=poli.data2[i+1][j];}
                        for(j=0;j<15;j++)
                        {no.data3[i][j]=no.data3[i+1][j];}
            }
            antrian.belakang--;
            nama.belakang--;
            poli.belakang--;
            no.belakang--;
            printf("antrian no %i dengan nama %s silahkan memasuki poli %s !", e, a, b);
            return e;
            return a[20];
            return b[30];
            }
            else
            {
                        printf("antrian kosong");
            }
}

void buat()
{
            antrian.depan=antrian.belakang=-1;
            nama.depan=nama.belakang=-1;
            poli.depan=poli.belakang=-1;
            no.depan=no.belakang=-1;
}

int main()
{
            int n;
            buat();
         
  n=1;
            do
            {
                        ("cls");
                        puts("aplikasi antrian rumah sakit");
                        puts("============================\n");
                        puts(" menu :");
                        puts("1. masukkan antrian");
                        puts("2. panggil antrian");
                        puts("3. lihat antrian");
                        puts("4. exit");
                        printf("silahkan masukkan pilihan (1-4) : "); scanf("%i", &pilihan);
                        switch(pilihan)
                        {
                                    case 1 :
                                                printf("no antrian anda adalah %i\n", n);
                                                data=n;
                                                printf("masukkan no. rekam medis anda :"); scanf("%s",&data3);
                                                printf("masukkan nama lengkap anda(gunakan tanda (_) untuk spasi) :"); scanf("%s",&data1);
                                                printf("masukkan poli berobat anda (gunakan tanda (_) untuk spasi):"); scanf("%s",&data2);
                                                Enqueue(data, data1, data2, data3);
                                                n++;
                                    break;

                                    case 2 :
                                                Dequeue();
                                    break;

                                    case 3 :
                                                if(isEmpty()==1)
                                                {
                                                            printf("antrian kosong !");
                                                            break;
                                                }
                                                puts("no antrian          no.reka medis              nama lengkap              poli berobat");
                                                for(i=antrian.depan;i<=antrian.belakang;i++)
                                                {
                                                            printf("%i                    %s                  %s                  %s\n", antrian.data[i], no.data3[i], nama.data1[i], poli.data2[i]);
                                                }

                                    break;
                                 
  case 4 :
                                                printf("terimakasih atas partisipasinya !!!");
                                    break;
                                    default :
                                                puts("salah tuh pilihannya !!!");
                                    break;
                        }
                        getch();
            }while(pilihan!=4);

}

This research intends to discuss effectiveness of queue management systems with regards to processing speed and convenience of applicants, its maximum potential and limits on how to improve the system itself and decrease delay time, and the impact of its application in operations and customer flow in offices.

Queuing is an inevitable situation experienced in everyday life. In any service system, a queue forms whenever current demand exceeds the current capacity to serve. In this paper, an analysis of the queuing situation at the ticket windows in the Nigerian Railway Corporation Lagos Terminus was carried out. To achieve this, primary data was obtained by observation and an appropriate queuing model was used to analyze the system and calculated its performance measures. Results showed that increasing the number of servers lead to a decrease in the average waiting time of passengers in queue and a decrease in the average waiting time of passenger in the system. Therefore by applying Queuing theory, the waiting time of passengers can be determined and improved upon. The study therefore recommends that management in railway stations can use results from queuing analysis in making decisions that increase the efficiency of operations at their ticket windows.

We study the 'Creation of Pooling in Inventory and Queueing Models'. This research consists of the study of sharing a scarce resource (such as inventory, server capacity, or production capacity) between multiple customer classes. This is called pooling, where the goal is to achieve cost or waiting time reductions. For the inventory and queueing models studied, both theoretical, scientific insights are generated, as well as strategies which are applicable in practice.

This monograph consists of two parts: pooling and polling . In the first part, pooling is applied to multi-location inventory models. It is studied how cost reduction can be achieved by the use of stock transfers between local warehouses, so-called lateral transshipments. In this way, stock is pooled between the warehouses. The setting is motivated by a spare parts inventory network, where critical components of technically advanced machines are kept on stock, to reduce down time durations. We create insights into the question when lateral transshipments lead to cost reductions, by studying several models.

Firstly, a system with two stock points is studied, for which we completely characterize the structure of the optimal policy, using dynamic programming. For this, we formulate the model as a Markov decision process. We also derived conditions under which simple, easy to implement, policies are always optimal, such as a hold back policy and a complete pooling policy. Furthermore, we identified the parameter settings under which cost savings can be achieved. Secondly, we characterize the optimal policy structure for a multi-location model where only one stock point issues lateral transshipments, a so-called quick response warehouse. Thirdly, we apply the insights generated to the general multi-location model with lateral transshipments. We propose the use of a hold back policy, and construct a new approximation algorithm for deriving the performance characteristics. It is based on the use of interrupted Poisson processes. The algorithm is shown to be very accurate, and can be used for the optimization of the hold back levels, the parameters of this class of policies. Also, we study related inventory models, where a single stock point servers multiple customers classes.

Furthermore, in the first part, the pooling of server capacity is studied. For a two queue model where the head-of-line processor sharing discipline is applied, we derive the optimal control policy for dividing the servers attention, as well as for accepting customers. Also, a server farm with an infinite number of servers is studied, where servers can be turned off after a service completion in order to save costs. We characterize the optimal policy for this model.

In the second part of the thesis, polling models are studied, which are queueing systems where multiple queues are served by a single server. An application is the production of multiple types of products on a single machine. In this way, the production capacity is pooled between the product types. For the classical polling model, we derive a closed-form approximation for the mean waiting time at each of the queues. The approximation is based on the interpolation of light and heavy traffic results. Also, we study a system with so-called smart customers, where the arrival rate at a queue depends on the position of the server. Finally, we invent two new service disciplines (the gated/exhaustive and the k-gated discipline) for polling models, designed to yield 'fairness and efficiency' in the mean waiting times. That is, they result in almost equal mean waiting times at each of the queues, without increasing the weighted sum of the mean waiting times too much.


Slides of presentation during PhD defense: http://tue.academia.edu/SandraVanWijk/Talks/82570/Pooling_and_Polling_Creation_of_Pooling_in_Inventory_and_Queueing_Models

Prediction using different machine learning approaches have been applied in the last few decades in different areas and research fields. Waiting time is an undeniable fact for every queue and it is very important to develop a system that predicts its duration in real life with minimum error. In this paper we applied several machine learning algorithms and among them we chose Support Vector Regression (SVR) in a real-life Banking queue dataset that contains real-life queues of multiple Banks where we predicted waiting time for everyone in the queue. Moreover, we have compared the result of prediction using SVR with different classifications and clustering methods such as K-nearest-neighbor and K means Clustering. We have shown the feasibility of applying SVR in prediction of waiting time in banking queues of developing countries for everyone, which is applicable, and it performs well in queue analysis.

In this paper we consider an unreliable single server retrial queue accepting two types of customers, with negative arrivals, preemptive resume priorities and vacations. A distinguishing feature of the model is that the rates of the Poisson arrival process depends on the server state. For this model we investigate the stability conditions and the joint queue length distribution in steady state. We also prove that our model satisfies the stochastic decomposition property. Transient, as well as steady state solutions for reliability measures are obtained. Finally, numerical results demonstrate the typical features of the model under consideration.

A queueing system with a single server providing two stages of service in succession is considered. Every customer receives service in the first stage and in the sequel he decides whether to proceed to the second phase of service or to depart and join a retrial box from where he repeats the demand for a special second stage service after a random amount of time and independently of the other customers in the retrial box. When the server becomes idle, he departs for a single vacation of an arbitrarily distributed length. The arrival process is assumed to be Poisson and all service times are arbitrarily distributed. For such a system the stability conditions and the system state probabilities are investigated both in a transient and in a steady state. A stochastic decomposition result is also presented. Numerical results are finally obtained and used to investigate system performance.