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.

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.

Gross Morphological and Sex Wise Morphometrical Studies on Mandible of Adult Blue Bull (Boselaphus tragocamelus)

2021 ◽  
Author(s):  
S. Sathapathy ◽  
B.S. Dhote ◽  
S.K. Bharti ◽  
I. Singh
Keyword(s):  
Statistical Analysis ◽  
Average Length ◽  
T Test ◽  
Average Thickness ◽  
Legal Cases ◽  
Recorded Data ◽  
Mandibular Notch ◽  
Horizontal Ramus ◽  
Wild Life

Background: The Blue bull (Boselaphus tragocamelus) is one of the biggest antelopes in Asia and is widely distributed in both the forests and adjoining villages with enough green grass.Methods: The present study was carried out on the mandible of six specimens of adult Blue bull (Boselaphus tragocamelus) of either sex. The biometrical parameters were measured by scale, graduated tape and digital Vernier’s caliper. The statistical analysis of the recorded data was done by independent samples t-Test with Systat Software Inc, USA and SPSS 16.0 version software.Result: The mandible of Blue bull consisted of two rami, i.e. horizontal and vertical rami. The two halves of this bone fused incompletely at the mandibular symphysis, situated at the midline. The average length of horizontal ramus of mandible was found to be 24.7±1.02 cm in female, which was significantly less (P less than 0.05) than that of males, where it was recorded as 35.4±1.97 cm. Similarly, the average thickness of vertical ramus at the base was found to be 0.53±0.001 cm in female, which was significantly less (P less than 0.05) than that of males, where it was recorded as 0.80±0.002 cm. The average cranio-caudal length of mandibular notch was found to be 1.32±0.01 cm in female, which was significantly less (P less than 0.05) than that of males, where it was recorded as 1.44±0.02 cm. Most of the biometrical observations on different parameters of mandible of Blue bull were having significantly (P less than 0.05) more values in males than females. Conclusion: Most of the biometrical observations on different parameters of mandible of Blue bull were having significantly (p less than 0.05) more values in males than females. The present gross and biometrical studies would be useful to the wild life professionals for determination of sex of this animal and solving vetero-legal cases related with this species.

The efficiency and heavy traffic properties of the score function method in sensitivity analysis of queueing models

1992 ◽  
Vol 24 (01) ◽  
pp. 172-201 ◽  
Author(s):  
Søren Asmussen ◽  
Reuven Y. Rubinstein
Keyword(s):  
Steady State ◽  
Waiting Time ◽  
Heavy Traffic ◽  
Queueing Network ◽  
Score Function ◽  
Service Rate ◽  
Underlying Distribution ◽  
Control Variate ◽  
Heavy Traffic Limit ◽  
Standard Output

This paper studies computer simulation methods for estimating the sensitivities (gradient, Hessian etc.) of the expected steady-state performance of a queueing model with respect to the vector of parameters of the underlying distribution (an example is the gradient of the expected steady-state waiting time of a customer at a particular node in a queueing network with respect to its service rate). It is shown that such a sensitivity can be represented as the covariance between two processes, the standard output process (say the waiting time process) and what we call the score function process which is based on the score function. Simulation procedures based upon such representations are discussed, and in particular a control variate method is presented. The estimators and the score function process are then studied under heavy traffic conditions. The score function process, when properly normalized, is shown to have a heavy traffic limit involving a certain variant of two-dimensional Brownian motion for which we describe the stationary distribution. From this, heavy traffic (diffusion) approximations for the variance constants in the large sample theory can be computed and are used as a basis for comparing different simulation estimators. Finally, the theory is supported by numerical results.

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)).

scholarly journals Simple and Yet Efficient Estimators for Markovian Multiserver Queues

2018 ◽  
Vol 2018 ◽  
pp. 1-7 ◽  
Author(s):  
Emilio Suyama ◽  
Roberto C. Quinino ◽  
Frederico R. B. Cruz
Keyword(s):  
Maximum Likelihood ◽  
Arrival Rate ◽  
Research Area ◽  
Service Rate ◽  
Traffic Intensity ◽  
Moment Estimator ◽  
Likelihood Estimator ◽  
Future Developments ◽  
Multiserver Queues

Estimators for the parameters of the Markovian multiserver queues are presented, from samples that are the number of clients in the system at arbitrary points and their sojourn times. As estimation in queues is a recognizably difficult inferential problem, this study focuses on the estimators for the arrival rate, the service rate, and the ratio of these two rates, which is known as the traffic intensity. Simulations are performed to verify the quality of the estimations for sample sizes up to 400. This research also relates notable new insights, for example, that the maximum likelihood estimator for the traffic intensity is equivalent to its moment estimator. Some limitations of the results are presented along with a detailed numerical example and topics for future developments in this research area.

scholarly journals Impact of streaming "fast track" emergency department patients

2006 ◽  
Vol 30 (4) ◽  
pp. 525 ◽  
Author(s):  
Debra O'Brien ◽  
Aled Williams ◽  
Kerrianne Blondell ◽  
George A Jelinek
Keyword(s):  
Emergency Department ◽  
Length Of Stay ◽  
Waiting Time ◽  
Fast Track ◽  
Average Length ◽  
Waiting Times ◽  
Relative Reduction ◽  
Average Waiting Time ◽  
Discharged Patients ◽  
Track Area

Objective: Fast track systems to stream emergency department (ED) patients with low acuity conditions have been introduced widely, resulting in reduced waiting times and lengths of stay for these patients. We aimed to prospectively assess the impact on patient flows of a fast track system implemented in the emergency department of an Australian tertiary adult teaching hospital which deals with relatively few low acuity patients. Methods: During the 12-week trial period, patients in Australasian Triage Scale (ATS) categories 3, 4 and 5 who were likely to be discharged were identified at triage and assessed and treated in a separate fast track area by ED medical and nursing staff rostered to work exclusively in the area. Results: The fast track area managed 21.6% of all patients presenting during its hours of operation. There was a 20.3% (?18 min; 95%CI, ?26 min to ?10 min) relative reduction in the average waiting time and an 18.0% (?41 min; 95%CI, ?52 min to ?30 min) relative reduction in the average length of stay for all discharged patients compared with the same period the previous year. Compared with the 12-week period before the fast track trial, there was a 3.4% (?2.1 min; 95%CI, ?8 min to 4 min) relative reduction in the average waiting time and a 9.7% (?20 min; 95%CI, ?31 min to ?9 min) relative reduction in the average length of stay for all discharged patients. There was no increase in the average waiting time for admitted patients. This was despite major increases in throughput and access block in the study period. Conclusion: Streaming fast track patients in the emergency department of an Australian tertiary adult teaching hospital can reduce waiting times and length of stay for discharged patients without increasing waiting times for admitted patients, even in an ED with few low acuity patients.

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)).

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.

The virtual waiting time of the GI/G/1 queue in heavy traffic

1971 ◽  
Vol 3 (2) ◽  
pp. 249-268 ◽  
Author(s):  
E. Kyprianou
Keyword(s):  
Markov Chains ◽  
Waiting Time ◽  
Limit Theorems ◽  
Queueing System ◽  
Heavy Traffic ◽  
Waiting Times ◽  
Double Sequence ◽  
Traffic Intensity ◽  
Virtual Waiting Time

Investigations in the theory of heavy traffic were initiated by Kingman ([5], [6] and [7]) in an effort to obtain approximations for stable queues. He considered the Markov chains {Wni} of a sequence {Qi} of stable GI/G/1 queues, where Wni is the waiting time of the nth customer in the ith queueing system, and by making use of Spitzer's identity obtained limit theorems as first n → ∞ and then ρi ↑ 1 as i → ∞. Here &rHi is the traffic intensity of the ith queueing system. After Kingman the theory of heavy traffic was developed by a number of Russians mainly. Prohorov [10] considered the double sequence of waiting times {Wni} and obtained limit theorems in the three cases when n1/2(ρi-1) approaches (i) - ∞, (ii) -δ and (iii) 0 as n → ∞ and i → ∞ simultaneously. The case (i) includes the result of Kingman. Viskov [12] also studied the double sequence {Wni} and obtained limits in the two cases when n1/2(ρi − 1) approaches + δ and + ∞ as n → ∞ and i → ∞ simultaneously.

Ferry Route Level of Service

1997 ◽  
Vol 1608 (1) ◽  
pp. 6-16 ◽  
Author(s):  
Joseph P. Savage
Keyword(s):  
Statistical Analysis ◽  
Waiting Time ◽  
Waiting Times ◽  
Absolute Number ◽  
Service Level ◽  
Washington State ◽  
Point Of View ◽  
Level Of Service ◽  
Transportation Service

Transportation service level measurements have been commonly used and accepted for highway systems, but similar service measures for ferry systems are less common, especially from the users’ point of view. An approach to measuring ferry route level of service is described that allows comparisons among ferry routes and between ferries and alternate modes such as highways (i.e., drive-around choices) and transit. The recommended approach focuses on excess user waiting times (excess delay) by mode (automobile, registered carpool or vanpool, bus, truck, and walk-on passenger), combined with calibrated relationships between volume-to-capacity (V/C) ratio and user delays for forecasting purposes. Data on waiting times for vehicles in the queues were collected on all ferry routes serviced by Washington State Ferries, and an extensive statistical analysis was performed to compute the relationships between V/C ratios and excess waiting times. Excess delay was defined as the waiting time for missed vessel sailings due to overloads, if any, after a ferry patron has arrived at the dock. User delays were expressed in two forms: absolute number of minutes of waiting time, and the number of boat sailings missed before boarding a ferry. The “boat wait” concept was introduced to differentiate between excess delays caused by congestion that prevents a driver from boarding the next ferry, and delays related to the amount of service provided on a route as reflected in the headways between vessels.

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