scholarly journals Applications of Queuing Theory in Quantitative Business Analysis

2020 ◽  
pp. 253-257
Keyword(s):  
Quantitative Analysis ◽  
Waiting Time ◽  
Queuing Theory ◽  
Single Channel ◽  
Analysis Approach ◽  
Single Server ◽  
Expected Number ◽  
Queuing Model ◽  
Infinite Population ◽  
Expected Waiting Time

Queuing Theory provides the system of applications in many sectors in life cycle. Queuing Structure and basic components determination is computed in queuing model simulation process. Distributions in Queuing Model can be extracted in quantitative analysis approach. Differences in Queuing Model Queue discipline, Single and Multiple service station with finite and infinite population is described in Quantitative analysis process. Basic expansions of probability density function, Expected waiting time in queue, Expected length of Queue, Expected size of system, probability of server being busy, and probability of system being empty conditions can be evaluated in this quantitative analysis approach. Probability of waiting ‘t’ minutes or more in queue and Expected number of customer served per busy period, Expected waiting time in System are also computed during the Analysis method. Single channel model with infinite population is used as most common case of queuing problems which involves the single channel or single server waiting line. Single Server model with finite population in test statistics provides the Relationships used in various applications like Expected time a customer spends in the system, Expected waiting time of a customer in the queue, Probability that there are n customers in the system objective case, Expected number of customers in the system

scholarly journals Transient Solution of a Single Server Queuing Model with Correlated Reneging Using Runge-Kutta Method

2020 ◽  
Vol 5 (5) ◽  
pp. 886-896
Author(s):  
Rakesh Kumar ◽  
Bhavneet Singh Soodan
Keyword(s):  
Queuing Theory ◽  
Real Life ◽  
System Size ◽  
Single Server ◽  
Kutta Method ◽  
Transient Solution ◽  
Queuing Model ◽  
Runge Kutta Method ◽  
Runge Kutta ◽  
Expected Waiting Time

In this paper, the concept of correlated reneging is introduced in queuing theory. The reneging considered so far is dependent on system size, but there are many real life situations where customers may renege due to exogenous factors other than the state of the system. Further, the reneging of customer may induce the other customers to renege at two successive time points. Such reneging is called correlated reneging. An M/M/1/K queuing model with correlated reneging is studied. Runge-Kutta method of fourth order is presented to obtain the transient solution of the model. Some performance measures like expected system size and expected waiting time in the system are studied.

Development of a Heuristics Model for Simplifying a Multi-Channel Queuing System

2011 ◽  
Vol 367 ◽  
pp. 647-652
Author(s):  
B. Kareem ◽  
A. A. Aderoba
Keyword(s):  
Waiting Time ◽  
Channel Model ◽  
Single Channel ◽  
Queuing System ◽  
Queuing Model ◽  
Average Waiting Time ◽  
Queuing Models ◽  
Significant Difference ◽  
Number Of Customers ◽  
Proportionality Principle

Queuing model has been discussed widely in literature. The structures of queuing systems are broadly divided into three namely; single, multi-channel, and mixed. Equations for solving these queuing problems vary in complexity. The most complex of them is the multi-channel queuing problem. A heuristically simplified equation based on relative comparison, using proportionality principle, of the measured effectiveness from the single and multi-channel models seems promising in solving this complex problem. In this study, six different queuing models were used from which five of them are single-channel systems while the balance is multi-channel. Equations for solving these models were identified based on their properties. Queuing models’ performance parameters were measured using relative proportionality principle from which complexity of multi-channel system was transformed to a simple linear relation of the form = . This showed that the performance obtained from single channel model has a linear relationship with corresponding to multi-channel, and is a factor which varies with the structure of queuing system. The model was tested with practical data collected on the arrival and departure of customers from a cocoa processing factory. The performances obtained based on average number of customers on line , average number of customers in the system , average waiting time in line and average waiting time in the system, under certain conditions showed no significant difference between using heuristics and analytical models.

scholarly journals Markovian Queueing System with Discouraged Arrivals and Self-Regulatory Servers

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
K. V. Abdul Rasheed ◽  
M. Manoharan
Keyword(s):  
Queueing System ◽  
Queueing Systems ◽  
Single Server ◽  
Expected Number ◽  
Multiple Servers ◽  
Special Cases ◽  
Service Rates ◽  
Expected Waiting Time ◽  
Number Of Customers ◽  
Steady State Probabilities

We consider discouraged arrival of Markovian queueing systems whose service speed is regulated according to the number of customers in the system. We will reduce the congestion in two ways. First we attempt to reduce the congestion by discouraging the arrivals of customers from joining the queue. Secondly we reduce the congestion by introducing the concept of service switches. First we consider a model in which multiple servers have three service ratesμ1,μ2, andμ(μ1≤μ2<μ), say, slow, medium, and fast rates, respectively. If the number of customers in the system exceeds a particular pointK1orK2, the server switches to the medium or fast rate, respectively. For this adaptive queueing system the steady state probabilities are derived and some performance measures such as expected number in the system/queue and expected waiting time in the system/queue are obtained. Multiple server discouraged arrival model having one service switch and single server discouraged arrival model having one and two service switches are obtained as special cases. A Matlab program of the model is presented and numerical illustrations are given.

scholarly journals Determination of Optimal Number of Servers at Network Queuing Nodes to Reduce Waiting Time in a Tertiary Institution Clinic in Bida, Nigeria

2020 ◽  
Vol 24 (9) ◽  
pp. 1631-1639
Author(s):  
I. Muhammad ◽  
L. Adamu
Keyword(s):  
Waiting Time ◽  
Current System ◽  
Optimal Number ◽  
Queuing System ◽  
Tertiary Institution ◽  
Queuing Model ◽  
Direct Observations ◽  
Expected Waiting Time ◽  
System Nodes

In this paper, a network queuing model that determines optimal numbers of servers at the nodes of the school clinic network queuing system to  reduce waiting time of the patients has been presented. The relevant data was collected for a period four weeks, through direct observations and interviews. The number of arrivals and departures were also obtained. The total expected waiting time of the patient in the current system before modification was 50minutes with total number of 10 servers in all the nodes, while the total new expected waiting time of patient in the system after modification was reduced to 19 minutes with total number of 17 servers in all the nodes. The study has determined optimal number of servers at the nodes of the school clinic network system. Results from this study is an important information to the management of the school clinic for proper planning and better service delivery. Keywords: Network Queuing System, Nodes, Servers, School Clinic.

A note on the convexity of performance measures of M/M/c queueing systems

1983 ◽  
Vol 20 (04) ◽  
pp. 920-923 ◽  
Author(s):  
Hau Leung Lee ◽  
Morris A. Cohen
Keyword(s):  
Performance Measures ◽  
Waiting Time ◽  
Queueing System ◽  
Queueing Systems ◽  
Arrival Rate ◽  
Control Problems ◽  
Traffic Intensity ◽  
Expected Number ◽  
Expected Waiting Time

Convexity of performance measures of queueing systems is important in solving control problems of multi-facility systems. This note proves that performance measures such as the expected waiting time, expected number in queue, and the Erlang delay formula are convex with respect to the arrival rate or the traffic intensity of the M/M/c queueing system.

scholarly journals On Mx/(G1G2)/1/G(BS)/Vs vacation queue with two types of general heterogeneous service

2005 ◽  
Vol 2005 (3) ◽  
pp. 123-135 ◽  
Author(s):  
Kailash C. Madan ◽  
Z. R. Al-Rawi ◽  
Amjad D. Al-Nasser
Keyword(s):  
Steady State ◽  
Performance Measures ◽  
Waiting Time ◽  
Busy Period ◽  
Single Server ◽  
Queue Size ◽  
Single Vacation ◽  
The Mean ◽  
Expected Waiting Time ◽  
Heterogeneous Service

We analyze a batch arrival queue with a single server providing two kinds of general heterogeneous service. Just before his service starts, a customer may choose one of the services and as soon as a service (of any kind) gets completed, the server may take a vacation or may continue staying in the system. The vacation times are assumed to be general and the server vacations are based on Bernoulli schedules under a single vacation policy. We obtain explicit queue size distribution at a random epoch as well as at a departure epoch and also the mean busy period of the server under the steady state. In addition, some important performance measures such as the expected queue size and the expected waiting time of a customer are obtained. Further, some interesting particular cases are also discussed.

scholarly journals Minimal cost service rate in priority queuing models for emergency cases in hospitals

2018 ◽  
Vol 6 (2) ◽  
pp. 50
Author(s):  
Nse S. Udoh ◽  
Idorenyin A. Etukudo
Keyword(s):  
Waiting Time ◽  
Service Rate ◽  
Time Cost ◽  
Service Cost ◽  
Queuing Model ◽  
Total Cost ◽  
Lower Priority ◽  
Queuing Models ◽  
Optimum Cost ◽  
Expected Waiting Time

Performance measures and waiting time cost for higher priority patients with severe cases over lower priority patients with stable cases using preemptive priority queuing model were obtained. Also, a total expected waiting time cost per unit time for service and the expected service cost per unit time for priority queuing models: M/M/2: ∞/NPP and M/M/2: ∞/PP were respectively formulated and optimized to obtain optimum cost service rate that minimizes the total cost. The results were applied to obtain optimum service rate that minimizes the total cost of providing and waiting for service at the emergency consulting unit of hospital.    

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.

scholarly journals ANALYSIS OF COMMUTER LINE TICKET PURCHASE QUEUING SYSTEM IN BOGOR STATION

2017 ◽  
Vol 2 (02) ◽  
pp. 35
Author(s):  
Resista Vikaliana
Keyword(s):  
Queuing Theory ◽  
Service Use ◽  
Single Channel ◽  
Performance Measure ◽  
Queuing System ◽  
Queuing Model ◽  
The One ◽  
Multi Phase ◽  
Ticket Purchase ◽  
First In First Out

Queue is a situation that happen to people, goods, and components that need to wait to get a service. The good quality of service will satisfy the customers and decrease the queue line. Queue often happens in a station especially in weekdays. A long queue line happens in the station is one of the problems that need to be solved. Instead of manual ticket purchasing that served by the operator, today PT KAI Commuter Line also serve ticket purchasing using THB machine. The purpose of this study is to compare the performance of queuing model that happen in Bogor station locket and to determine if the queuing model is efficient by comparing the service standard, between the manual and the one that used THB machine. The method used in this research was descriptive method by using queuing theory calculation. The model of locket queuing using THB machine in Bogor Station is Multi Channel-Multi Phase, in ticket purchasing using THB machine. Besides, in the operator locket service, the queuing model is Single Channel-Single Phase. Both s ticket purchasing service use First In First Out (FIFO) disciple. The maximum amount of the queue line and the source of customers’ arrival are infinite. Based on the value of system performance can be concluded that queuing system and the service given already great and effective (based on the performance measure and probability or passengers’’ chances), passengers who are waiting to buy tickets, either manual or using machine less than 1, or assumed 1 person. From the observation, the use of THB machine decrease the queue line, but need to be socialized because passengers does not know how to use THB machine to buy ticket independently.Keywords: queue, queuing model, commuter line ticket purchasing, Bogor station

scholarly journals Multi-Channel Preemptive Priority Model for Spectrum Mobility in Cognitive Radio Networks

2018 ◽  
Vol 8 (6) ◽  
pp. 5169
Author(s):  
S. E. Saad ◽  
I. F. Tarrad ◽  
A. A. Ammar
Keyword(s):  
Cognitive Radio ◽  
Cognitive Radio Networks ◽  
Waiting Time ◽  
Radio Networks ◽  
Preemptive Priority ◽  
Expected Number ◽  
Secondary Users ◽  
Basic Model ◽  
Proposed Model ◽  
Expected Waiting Time

Cognitive Radio techniques have been proposed for improving utilization of the spectrum by exploiting the unoccupied bands of the licensed spectrum. This paper proposes a preemptive multi-channel access model for prioritized cognitive radio networks using an iterative method of queuing theory to solve the spectrum scarcity problem. The proposed model formulates accurate closed form of an expected waiting time in the queue, an expected number of users in the queue, an expected waiting time in the system, and an expected number of users in the system. The results compared to the basic model (without preemptive priority) show that, the waiting time in queue and the waiting time in the system compared to the basic model will be improved by 92.99% and 33.15% respectively for class one secondary user. The results also show that, the waiting time in queue and the waiting time in the system will be improved by 43.25% and 15.42% respectively for class two secondary users. The proposed model investigates the desirable schedules of primary and secondary users.

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