scholarly journals Application of queuing theory to a fast food outfit: a study of blue meadows restaurant

2017 ◽  
Vol 8 (2) ◽  
pp. 441 ◽  
Author(s):  
Seigha Gumus ◽  
Gordon Monday Bubou ◽  
Mobolaji Humphrey Oladeinde
Keyword(s):  
Waiting Time ◽  
Fast Food ◽  
Queuing Theory ◽  
Goodness Of Fit ◽  
Arrival Rate ◽  
Time Frame ◽  
Utilization Rate ◽  
Service Rate ◽  
Operating Characteristics ◽  
Number Of Customers

The study evaluated the queuing system in Blue Meadows restaurant with a view to determining its operating characteristics and to improve customers’ satisfaction during waiting time using the lens of queuing theory. Data was obtained from a fast food restaurant in the University of Benin. The data collected was tested to show if it follows a Poisson and exponential distribution of arrival and service rate using chi square goodness of fit. A 95% confidence interval level was used to show the range of customers that come into the system at an hour time frame and the range of customers served at an hour time frame. Using the M/M/s model, the arrival rate, service rate, utilization rate, waiting time in the queue and the probability of customers likely balking from the restaurant was derived. The arrival rate (λ) at Blue Meadows restaurant was about 40 customers per hour, while the service rate was about 22 customers per hour per server. The number of servers present in the system was two. The average number of customers in the system in an hour window was 40 customers with a utilization rate of 0.909. The paper concludes with a discussion on the benefits of performing queuing analysis to a restaurant.

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.

Application of Queuing Theory to Address Traffic Problems at a Highway Toll Plaza

2014 ◽  
Vol 592-594 ◽  
pp. 2583-2587 ◽  
Author(s):  
Dheeraj Duhan ◽  
Nishant Arya ◽  
Prateek Dhanda ◽  
Lalit Upadhayay ◽  
K. Mathiyazhagan
Keyword(s):  
Data Analysis ◽  
Waiting Time ◽  
Traffic Congestion ◽  
Queuing Theory ◽  
Arrival Rate ◽  
North India ◽  
Service Rate ◽  
Operational Effectiveness ◽  
Toll Plazas ◽  
Toll Plaza

In India, due to the escalating traffic issues, a large number of highways have been built in the recent past, which are maintained by tax collection at toll plazas, by various operating agencies. Due to smooth and hassle free driving on highways, the arrival rate of vehicles at Toll Plazas increases. The arrival rate goes beyond control if the traffic on the highway increases in an uncontrolled manner, with the passage of time. Thus, one of the irrefutable drawbacks of putting up Toll Plazas, is the traffic congestion. The waiting time, in the service lanes, due to such a congestion becomes high and excruciating for the commuters on the route. The objective of this study is to analyze the current situation, of traffic congestion, at a highway toll plaza using queuing theory and suggest possible solutions to encourage greater efficiency, thus reducing waiting time of the customers and money wasted because of that. This study has been carried out in various phases, i.e. problem identification, data collection, data analysis and results at a selected Toll Plaza in North India. The data analysis in the study helps to find out the current operational effectiveness of the Toll Plaza through parameters like, Arrival Rate, Service Rate and Number of toll booths. Finally, possible solutions have been put forward which can be recommended and implemented on various Toll Plazas in the country.

scholarly journals Performance Modelling of Health-care Service Delivery in Adekunle Ajasin University, Akungba-Akoko, Nigeria Using Queuing Theory

2020 ◽  
pp. 119-127
Author(s):  
Orimoloye Segun Michael
Keyword(s):  
Health Care ◽  
Service Delivery ◽  
Queuing Theory ◽  
Health Care Service ◽  
Health Centre ◽  
Arrival Rate ◽  
Queuing System ◽  
Service Rate ◽  
Suitable Model ◽  
The Mean

The queuing theory is the mathematical approach to the analysis of waiting lines in any setting where arrivals rate of the subject is faster than the system can handle. It is applicable to the health care setting where the systems have excess capacity to accommodate random variation. Therefore, the purpose of this study was to determine the waiting, arrival and service times of patients at AAUA Health- setting and to model a suitable queuing system by using simulation technique to validate the model. This study was conducted at AAUA Health- Centre Akungba Akoko. It employed analytical and simulation methods to develop a suitable model. The collection of waiting time for this study was based on the arrival rate and service rate of patients at the Outpatient Centre. The data was calculated and analyzed using Microsoft Excel. Based on the analyzed data, the queuing system of the patient current situation was modelled and simulated using the PYTHON software. The result obtained from the simulation model showed that the mean arrival rate of patients on Friday week1 was lesser than the mean service rate of patients (i.e. 5.33> 5.625 (λ > µ). What this means is that the waiting line would be formed which would increase indefinitely; the service facility would always be busy. The analysis of the entire system of the AAUA health centre showed that queue length increases when the system is very busy. This work therefore evaluated and predicted the system performance of AAUA Health-Centre in terms of service delivery and propose solutions on needed resources to improve the quality of service offered to the patients visiting this health centre.

Modern Hypermarket Receiving Yard Utilization: The Implementation of a Simulation Model

2017 ◽  
Vol 2 (4) ◽  
pp. 33-39
Author(s):  
Mohammad Annas
Keyword(s):  
Simulation Model ◽  
Exponential Distribution ◽  
Poisson Distribution ◽  
Waiting Time ◽  
Arrival Rate ◽  
Jel Classification ◽  
Utilization Rate ◽  
Processing Times ◽  
Kolmogorov Smirnov ◽  
Using Data

Objective - This research is a direct observation of initial queuing, using data that is categorised into two clusters: the number of people queuing at busy hours, and processing times in the same circumstances. Methodology/Technique - The raw data was converted for use in the Poisson distribution test, as well as the Kolmogorov-Smirnov exponential distribution options. An arena simulation model was also applied to identify the vendor's waiting time and to analyse receiving yard utilization. The average waiting time according to the Poisson distribution, the average serving time per vendor by an exponential distribution, and the number of receiving yards, are all essential factors effecting the utilization of receiving yards. Findings - The study compares the length of queues, serving times, arrival rate, and time in the system using dual and single receiving yard systems. However, the utilization rate on a two receiving yards system is less than the rate on single receiving yard system. As the aim of this study is to identify the utilization rate of the receiving yard, a single receiving yard operation is more representative of modern hypermarkets, and more efficient in terms of resource efficiency. Novelty - This study depends fully on the homogeneous operating hours of the retailers' receiving yards, the type of vehicle used by vendors to unload merchandises, procedures on moving the products to the inspections phase, a generalization of the products delivered by the vendors and the size of the modern hypermarkets business itself. Type of Paper: Empirical. Keywords: Receiving Yard Utilization; Hypermarket Receiving Yard; Queuing Simulation. JEL Classification: M1, M10, M19.

Convexity results for single-server queues and for multiserver queues with constant service times

1990 ◽  
Vol 27 (02) ◽  
pp. 465-468 ◽  
Author(s):  
Arie Harel
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Sojourn Time ◽  
Interarrival Time ◽  
Service Rate ◽  
Single Server ◽  
Multiserver Queues ◽  
Service Rates ◽  
Constant Service Times ◽  
Number Of Customers

We show that the waiting time in queue and the sojourn time of every customer in the G/G/1 and G/D/c queue are jointly convex in mean interarrival time and mean service time, and also jointly convex in mean interarrival time and service rate. Counterexamples show that this need not be the case, for the GI/GI/c queue or for the D/GI/c queue, for c ≧ 2. Also, we show that the average number of customers in the M/D/c queue is jointly convex in arrival and service rates. These results are surprising in light of the negative result for the GI/GI/2 queue (Weber (1983)).

Minimum carbon dioxide emission based selection of traffic route with unsignalised junctions in tandem network

2019 ◽  
Vol 30 (3) ◽  
pp. 657-675 ◽  
Author(s):  
Anand Jaiswal ◽  
Cherian Samuel ◽  
Chirag Chandan Mishra
Keyword(s):  
Carbon Dioxide ◽  
Queuing Theory ◽  
Mathematical Formulation ◽  
Carbon Dioxide Emission ◽  
Arrival Rate ◽  
Selection Strategy ◽  
Service Rate ◽  
Content Type ◽  
Fuel Consumption Rate ◽  
Route Choices

Purpose The purpose of this paper is to provide a traffic route selection strategy based on minimum carbon dioxide (CO2) emission by vehicles over different route choices. Design/methodology/approach The study used queuing theory for Markovian M/M/1 model over the road junctions to assess total time spent over each of the junctions for a route with junctions in tandem. With parameters of distance, mean service rate at the junction, the number of junctions and fuel consumption rate, which is a function of variable average speed, the CO2 emission is estimated over each of the junction in tandem and collectively over each of the routes. Findings The outcome of the study is a mathematical formulation, using queuing theory to estimate CO2 emissions over different route choices. Research finding estimated total time spent and subsequent CO2 emission for mean arrival rates of vehicles at junctions in tandem. The model is validated with a pilot study, and the result shows the best vehicular route choice with minimum CO2 emissions. Research limitations/implications Proposed study is limited to M/M/1 model at each of the junction, with no defection of vehicles. The study is also limited to a constant mean arrival rate at each of the junction. Practical implications The work can be used to define strategies to route vehicles on different route choices to reduce minimum vehicular CO2 emissions. Originality/value Proposed work gives a solution for minimising carbon emission over routes with unsignalised junctions in the tandem network.

Optimal control of service rates in networks of queues

1987 ◽  
Vol 19 (1) ◽  
pp. 202-218 ◽  
Author(s):  
Richard R. Weber ◽  
Shaler Stidham
Keyword(s):  
Rate Control ◽  
Queueing Networks ◽  
Arrival Rate ◽  
Service Rate ◽  
Discounted Cost ◽  
Holding Costs ◽  
Optimal Service ◽  
Monotonicity Result ◽  
Service Rates ◽  
Number Of Customers

We prove a monotonicity result for the problem of optimal service rate control in certain queueing networks. Consider, as an illustrative example, a number of ·/M/1 queues which are arranged in a cycle with some number of customers moving around the cycle. A holding cost hi(xi) is charged for each unit of time that queue i contains xi customers, with hi being convex. As a function of the queue lengths the service rate at each queue i is to be chosen in the interval , where cost ci(μ) is charged for each unit of time that the service rate μis in effect at queue i. It is shown that the policy which minimizes the expected total discounted cost has a monotone structure: namely, that by moving one customer from queue i to the following queue, the optimal service rate in queue i is not increased and the optimal service rates elsewhere are not decreased. We prove a similar result for problems of optimal arrival rate and service rate control in general queueing networks. The results are extended to an average-cost measure, and an example is included to show that in general the assumption of convex holding costs may not be relaxed. A further example shows that the optimal policy may not be monotone unless the choice of possible service rates at each queue includes 0.

Convexity results for single-server queues and for multiserver queues with constant service times

1990 ◽  
Vol 27 (2) ◽  
pp. 465-468 ◽  
Author(s):  
Arie Harel
Keyword(s):  
Waiting Time ◽  
Service Time ◽  
Sojourn Time ◽  
Interarrival Time ◽  
Service Rate ◽  
Single Server ◽  
Multiserver Queues ◽  
Service Rates ◽  
Constant Service Times ◽  
Number Of Customers

We show that the waiting time in queue and the sojourn time of every customer in the G/G/1 and G/D/c queue are jointly convex in mean interarrival time and mean service time, and also jointly convex in mean interarrival time and service rate. Counterexamples show that this need not be the case, for the GI/GI/c queue or for the D/GI/c queue, for c ≧ 2. Also, we show that the average number of customers in the M/D/c queue is jointly convex in arrival and service rates.These results are surprising in light of the negative result for the GI/GI/2 queue (Weber (1983)).

scholarly journals Statistical Analysis on the Waiting Line System in Automated Teller Machines (ATM): A Study of Fidelity Bank Plc, Service Point, Plateau State, Nigeria

2020 ◽  
pp. 34-53
Author(s):  
Kuje Samson ◽  
Abubakar, Muhammad Auwal ◽  
Kuje, Habila Akolo ◽  
Moses, Longji Dashal
Keyword(s):  
Statistical Analysis ◽  
Waiting Time ◽  
Average Length ◽  
Service Rate ◽  
Traffic Intensity ◽  
Operating Characteristics ◽  
Line System ◽  
Automated Teller Machines ◽  
Plateau State ◽  
Waiting Line

The purpose of this paper is to find out the operating characteristics of the ATM service point of the Fidelity bank Plc, plateau state. Specifically, a computer package (MS60) was used for analyzing the data. Results obtained from the analysis showed the traffic intensity (ρ) to be 0.96, which indicated that the service facility is highly utilized. The average length of the queue was found to be 21 while the average waiting time in the queue was 1.10 hours. On the basis of this investigation, the conclusion was made that the service utility is highly utilized, implying that there are more customers than the service point can accommodate thus giving rise to the lengthy customer waiting time. It is recommended that one additional ATM be deployed to the bank's premises so as to minimize customer waiting time and to also increase the service rate.

Optimization of Queuing Theory Based on Vague Environment

2016 ◽  
Vol 5 (1) ◽  
pp. 1-26 ◽  
Author(s):  
Verónica Andrea González-López ◽  
Ramin Gholizadeh ◽  
Aliakbar M. Shirazi
Keyword(s):  
Everyday Life ◽  
Real World ◽  
Queuing Theory ◽  
Arrival Rate ◽  
Service Rate ◽  
New Approach ◽  
The Real ◽  
Processing Times ◽  
Queuing Models ◽  
Service Rates

Waiting lines or queues are commonly occurred both in everyday life and in a variety of business and industrial situations. The various arrival rates, service rates and processing times of jobs/tasks usually assumed are exact. However, the real world is complex and the complexity is due to the uncertainty. The queuing theory by using vague environment is described in this paper. To illustrate, the approach analytical results for M/M/1/8 and M/M/s/8 systems are presented. It optimizes queuing models such that the arrival rate and service rate are vague numbers. This paper results a new approach for queuing models in the vague environment that it can be more effective than deterministic queuing models. A numerical example is illustrated to check the validity of the proposed method.

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