Average Number Of Customers Research Articles

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 POTENTIAL OF ORNAMENTAL FISHES IN KATHMANDU

Ornamental fishes are the peaceful, generally attractive fishes used for aesthetic, decorative, recreational and therapeutic purposes and a thriving industry supporting millions of people throughout the world. This study was conducted to learn about the status, sources, challenges and potential of ornamental fishes in Kathmandu (Nepal). Interviews were conducted with the major ornamental fish suppliers, traders and owners of aquarium shops and production farms to extract necessary information along with direct visits to the concerned places. Several secondary sources like published and unpublished reports, journals, books, photo books and pictorials were also used for data collection and analysis. The average number of customers per day in the studied shops was found to be 10-15 people in most of the shops. An increasing trend of customer flow was noticed in most of the shops in recent years. The average estimated profit margin was found to be 20-30%. Government support is recommended to tackle the major existing challenges including high mortality and maintenance issues of fishes. The increase in the number of shops, flow of customers and good profit margin shows the blooming status of the ornamental fish industry and helps to provide insights for the future of the industry.

Influence of public sensitisation and awareness on service delivery of land registries in the Rift Valley Region, Kenya

This study sought to address the gap in the understanding of the extent to which public awareness influences service delivery in the context of land reform in the Rift Valley Region in Kenya. The study used descriptive analysis in the research design. The study findings were generated using both descriptive and inferential statistical analyses. The target population comprised both the staff working in various departments in all three land registries and an average number of customers who visited the land offices from the three land registries on a weekly basis. The study also targeted a special group of clients from land-related agencies. The target population for this study was 179 staff in the Ministry of Lands, targeted citizens and special clients from land-related agencies, Rift Valley region. Slovin’s formula was used to attain a sample size of 140 respondents. The study employed purposive sampling and stratified random sampling techniques. Questionnaires were used in data collection, which was analysed using SPSS (Version 29.0) and presented using means, standard deviations and tables. The study found that public sensitisation and awareness have a statistically significant influence on the service delivery of land registries in the Rift Valley Region, Kenya (p<0.05). This study recommends that land registries in the Rift Valley region invest more in public awareness campaigns to get the public in a more representative role so that they are more aware of their land rights and feel more involved when it comes to land issues.

Vessels Arrival Process and its Application to the SHIP/M/infty Queue

In modeling of port dynamics it seems reasonable to assume that the ships arrive on a somewhat scheduled basis and that there is a constant lay period during which, in a uniform way, each vessel can arrive at the port. In the present paper, we study the counting process N(t) which represents the number of scheduled vessels arriving during the time interval (0, t], t>0. Specifically, we provide the explicit expressions of the probability generating function, the probability distribution and the expected value of N(t). In some cases of interest, we also obtain the probability law of the stationary counting process representing the number of arrivals in a time interval of length t when the initial time is an arbitrarily chosen instant. This leads to various results concerning the autocorrelations of the random variables X_i, iin mathbb {Z}, which give the actual interarrival time between the (i-1)-th and the i-th vessel arrival. Finally, we provide an application to a stochastic model for the queueing behavior at the port, given by a queueing system characterized by stationary interarrival times X_i, exponential service times and an infinite number of servers. In this case, some results on the average number of customers and on the probability of an empty queue are disclosed.

Optimisation of Queueing Efficiency and Performance of Nigeria Commercial Banks

The objective of this research is to carry out an optimisation of the comparative analysis of the queuing efficiency of commercial banks using the TORA Optimisation Approach. Based on a sample size of four commercial banks of the top two performing banks and least two performing banks in Lagos State Nigeria, the research adopted the output from the Tora Optimisation Software to show the performance of each of the banks based on queuing efficiency. The variables measured include arrival rate ( λ ) and service rate ( µ ). They were analysed for synchronised efficiency in customer satisfaction as relating to the queuing efficiency of each of the banks which were compared among commercial banks using number of queuing efficiency performances such as; the average number of customers on queue and in the system, average time each customer spends on queue and in the system and the probability of the system being idle. The results showed that Bank A had the highest traffic intensity with its customer arrival rate not being matched with faster service delivery rate by bank officials. Banks peak period with high influx of customers was 10:30 to 11:30am and between 12:30pm to 1:30pm daily is off peak period. The research made recommendation on how the queuing efficiency of each banks, can be improved upon due to its concern to most customers. Keywords: Queuing Efficiency, Peak period, Traffic Intensity, Queuing system, Arrival Rate, Service Rate

Modelling Customer’s Satisfaction at Portofino Eatery Ado-Ekiti Using Queuing Theory

This study evaluated the queuing system in Portofino Eatery- Bread section with a view to determine its operating characteristics and toimprove customers’ satisfaction during waiting time using the lens of queuing theory. The model of operation was detected to be M/M/smodel while the arrival rate, service rate, utilization rate and waiting time in the queue were derived. Data was collected by directobservation at the Portofino Eatery service facility, Ado – Ekiti. The arrival rate (λ) at Portofino Eatery- Bread section was about 43customers per hour, while the service rate was about 40 customers per hour for each server. The system includes four different servers.The average number of customers in the system in an hour window was 43 customers with a utilization rate of 0.722. This research workconcludes with a discussion on the benefits of performing queuing analysis to a restaurant. In order to avoid congestion and reducecustomer’s waiting time, increase patronage and boost customer’s confidence in Portofino eatery service delivery.

Analysis of the Queuing System for the Indonesian Islamic Bank (BSI) Bengkulu Branch

The purpose of this study is to determine the average level of customer arrivals and the average service time of customers in the queue. The analytical model used in this study is a multi-channel single-phase queuing theory analysis with a mathematical formula. The queuing process is a process related to the arrival of the customer to a queuing system, then waiting in the queue until the waiter selects the customer according to the service discipline, and finally the customer leaves the queuing system after the service is finished. At Bank Syariah Indonesia (BSI) KC Bengkulu S. Parman 1 there are 5 tellers provided to serve customers who will make deposits, withdrawals and cash transfers. Queues that occur at the optimal service level can be obtained by the performance of the queuing system with the calculation results, namely, the average number of customers in the queue (nq) 31.88 customers, customers in the total system 33.08 people, the average time in the queue 0, 000767 and the total system time is 0.034097 or 2 minutes. Thus, customers do not take too long to make transactions. With the number of tellers as many as five people, there is a long waiting time for customers (Wq) in the queue, which is 0.02777 hours or 2 minutes and the average number of customers in the queue (Ls) is 2 people..

The Effect of Online-Based Transportation on Conventional Transportation Revenues in Baubau City

Online-based transportation is a type of transportation that uses a smartphone to store applications in the form of a server that can be used to order transportation equipment in the form of two-wheeled or four-wheeled vehicles. With this online transportation, consumers now no longer have to wait or have to go to wait at the motorcycle taxi stand or at the roadside to wait for a taxi or tell the address because Taxi online already has a coordinate point for a pick-up point for customers. It can even be picked up at home though. In addition, consumers do not need to haggle about fares, because they have been determined based on the distance traveled. Initially, the presence of conventional taxis (Ade Taksi) in Baubau City was 25 units, but over time and coupled with the presence of online transportation, now there are only 8 taxi units that are actively operating. The purpose of this study is to find out how much influence the existence of online-based transportation has on the income of conventional taxi drivers and how people are interested in using conventional taxis after online transportation. Based on the results of research, online transportation has a very negative influence on the income or income of conventional taxi drivers. As evidence, it can be seen from the results of the study that the income of taxi drivers decreased before the presence of online transportation and after the presence of online transportation. The average income earned by conventional taxi drivers is Rp. 4,312,500 and after online transportation of Rp. 3,412,500 and the presence of online-based transportation has a negative impact on the large number of interest in using conventional taxis. This can be proven by the decrease in monthly taxi revenue before the online-based transportation and after the online-based transportation. So that the average number of taxi enthusiasts or customers before the online online-based transportation was 1,170 calls and the average number of customers after the online-based transportation was 927 calls (10.9%). 500 and the presence of online-based transportation has a negative impact on the large number of interest in using conventional taxis. This can be proven by the decrease in monthly taxi revenue before the online-based transportation and after the online-based transportation. So that the average number of taxi enthusiasts or customers before the online online-based transportation was 1,170 calls and the average number of customers after the online-based transportation was 927 calls (10.9%). 500 and the presence of online-based transportation has a negative impact on the large number of interest in using conventional taxis. This can be proven by the decrease in monthly taxi revenue before the online-based transportation and after the online-based transportation. So that the average number of taxi enthusiasts or customers before the online online-based transportation was 1,170 calls and the average number of customers after the online-based transportation was 927 calls (10.9%).

Performance Evaluation of the Priority Multi-Server System MMAP/PH/M/N Using Machine Learning Methods

In this paper, we present the results of a study of a priority multi-server queuing system with heterogeneous customers arriving according to a marked Markovian arrival process (MMAP), phase-type service times (PH), and a queue with finite capacity. Priority traffic classes differ in PH distributions of the service time and the probability of joining the queue, which depends on the current length of the queue. If the queue is full, the customer does not enter the system. An analytical model has been developed and studied for a particular case of a queueing system with two priority classes. We present an algorithm for calculating stationary probabilities of the system state, loss probabilities, the average number of customers in the queue, and other performance characteristics for this particular case. For the general case with K priority classes, a new method for assessing the performance characteristics of complex priority systems has been developed, based on a combination of machine learning and simulation methods. We demonstrate the high efficiency of the new method by providing numerical examples.

Stationary system-length distribution of Markovian bulk service queue with modified bulk service rule and dynamic service rates

In this paper, we consider a single server bulk service queue, with modified bulk service rule, say rule, wherein customers are served in batches of maximum batch size K with minimum threshold value L. Further, we allow the customers to enter the service if the server has begun the service and is having less than K customers. In addition, service rates of the batches are taken to be dependent on the size of the batch. Analytic expressions for the joint probability distribution of the number of customers in the queue, and with the server, the marginal probability distribution of the number of customers in the queue, system and with the server is derived. A thorough numerical investigation of the effect of various parameters on the distributions obtained above is done and numerical results are presented in the form of tables and graphs. We also obtain various performance measures (both in closed-form as well as numerically) such as the average number of customers in the queue, system, with the server, etc.

IMPROVING SERVICE QUALITY OF DHABA WITH THE HELP OF QUEUING THEORY

Queuing theory is the mathematics of waiting lines. It is extremely useful in predicting and evaluating system performance. Queuing theory has been used for operations research, manufacturing and systems analysis The common problem arises in almost every famous dhaba is that they lose their customers due to a long wait on the line. Some dhaba provide extra chair for the customer to wait. But after waiting too long they leave. However, waiting chairs alone would not solve a problem when customers withdraw and go to the next dhaba. This causes a lot of loss to our dhaba. 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. Authors obtained the data from a “Gulshan Dhaba” in Hodal, Haryana. in order to derive the arrival rate, service rate, utilization rate, waiting time in queue and the probability of potential customers to balk. The collected data is analysed by using Little’s Theorem and M/M/1 queuing model. The arrival rate at “Gulshan Dhaba”, Hodal during its busiest period of the day is 2 customers per minute (cpm) while the service rate is 2.02 cpm during our study period. The average number of customers in the restaurant is 100 and the utilization period is 0.99.

SISTEM PAKAR MENENTUKAN TINGKAT PERAWATAN ATAU KERUSAKAN PADA KENDARAAN BERMOTOR HONDA MATIC DENGAN METODE FORWARD CHAINING

Motorcycles with automatic systems are currently the type of vehicle that are most interested by many riders because they are economical and comfortable. Automatic motorcycles, which are more fuel efficient, seem to be the most desired vehicle by the community today, in 2014 the number of motorcycles in Kupang City was 125,574 and in 2015 there were 139,033 of which were automatic motorcycles. So that intensive care is needed on automatic motorbikes, with intensive care it will make automatic motorbikes more comfortable when riding. Aurora Motor is one of the motorcycle repair shops in Kupang City. In addition to providing service and maintenance services for two-wheeled vehicles, Aurora Motor also sells various kinds of motorcycle parts. The average number of customers who come reaches ± 15 customers per day, which consists of various types of motorcycles with different weights. Currently, the problem at the aurora motorcycle workshop is that there is no system that can quickly identify the damage that occurs to the motorcycle, resulting in the slow process of repairing the motorcycle. it can be concluded that this application has fulfilled its main purpose, which is an application that can help mechanics at aurora motorbike workshops to determine each level of damage and maintenance on a Honda matic motorbike. This application is able to determine the level of maintenance and damage with forward chaining.

ANALYSIS OF SERVICE LEVELS OF THE TIDORE-SOFIFI SPEEDBOAT MODE DURING THE COVID-19 VIRUS PANDEMIC

Speed boat is one of transportation mode to service the Tidore-Sofifi route picking the customers up from Islands Tidore to Halmahera island vice versa clear. Many customers doing a traveling use this mode demands attention to the comfort and safety aspects of the mode user, especially at the Covid-19 pandemic moment. Condition on the ground indicates speedboat mode operating throughout the day, in any the weather picks up people and objects. The purpose of this research analyzes speed boat service level according to rating mode user transportation at the Covid-19 pandemic moment by using analyze method Importance Performance Analysis (IPA). To reach the purpose of this research is done some steps specifically: counting a decrease in the average number of customers per day, map the relationship between the importance and performance of each service indicator according to customer assessment. From the result of the research obtained that during the pandemic Covid-19 number of customers in daily average is carried decreased dramatically to 10,10% numbers of the total customer usually carried up in normal time. The level service from the speedboat transportation Tidore-Sofifi by the IPA method obtained variable has high the interests/expectations however the reality/performance is not good enough, is the availability variable of the first aid kit and availability Hand sanitizer /ACT. While the variable is considered less important by customers, but its performance is good, that is lighting in the night, availability life jacket, and availability rope thrower.

A M/M/1 Queueing Network with Classical Retrial Policy

In this paper we study the M/M/1 queueing model with retrial on network. We derive the steady state probability of customers in the network, the average number of customers in the all the three nodes in the system, the queue length, system length using little’s formula. The particular case is derived (no retrial). The numerical examples are given to test the correctness of the model.

A Single Server Queue with Coxian-2 Service and One-Phase Vacation (M/C-2/M/1 Queue)

In this paper, we study a single server queueing system with Coxian-2 service. In Particular, we study M/C-2/M/1 queue with Coxian-2 service and exponential vacation. We assume that units (customers) arrive at the system one by one in a Poisson process and the server provides one-by-one service based on first in first out (FIFO) rule. We obtained the steady state queue size distributions in terms of the probability generating functions, the average number of customers and their average waiting time in the system as well as in the queue.

PENGARUH KUALITAS PELAYANANTERHADAP KEPUASAN KONSUMEN INDOMARET KOTA BUKIT PURWAKARTA

Kehadiran Alfamart dilokasi gerai Indomaret yang telah berdiri, akan menyebabkan perebutan konsumen antara Indomaret dan Alfamart. Kondisi ini terjadi di Indomaret Kota Bukit Purwakarta menyebabkan penurunan jumlah rata-rata konsumen perhari yang berbelanja. Indomaret Kota Bukit tahun 2016, mengalami penurunan yang sangat signifikan sebesar 22,22% dibandingkan dengan rata-rata jumlah konsumen harian tahun 2015. Kondisi terbaru, rata-rata jumlah konsumen harian tahun 2017 (Jan-Apr) juga mengalami penurunan sebesar 1,20% dibandingkan dengan rata-rata omzet harian tahun 2016. Penelitian ini bertujuan untuk mengetahui pengaruh kualitas pelayanan terhadap kepuasan konsumen Indomaret Kota Bukit Purwakarta secara parsial dan simultan. Populasi yang digunakan adalah konsumen Indomaret Kota Bukit Purwakarta dan sampel diambil menggunakan rumus Slovin dengan tingkat kepercayaan 90%. Analisis data menggunakan Regresi Linier Berganda. Hasil penelitian menginformasikan kualitas pelayanan yang meliputi tangible, realibility, responsive, assurance dan empathy berpengaruh terhadap kepuasan secara simultan. Variabel responsive merupakan variabel yang berpengaruh secara parsial dan memiliki pengaruh terbesar terhadap kepuasan konsumen Indomaret Kota Bukit Purwakarta.

Analysis of an retrial queueing system with priority services, working breakdown, Bernoulli vacation, admission control and balking

A single server serves two classes of customers under non-preemptive priority service rule are studied. In addition to this working breakdown, admission control, balking and Bernoulli vacation are also investigated. Here, the customers arrive according to two independent compound Poisson processes and the service is in general distribution. Once the system gets a breakdown, the server proceeds the service at a slower speed for the current customer, after which, the repair will commence. Moreover, the server can not allow all the customers to enter into the system, there is an admission control policy to allow customers. Applying the supplementary variable technique, the Laplace transforms of time-dependent probabilities of system state are determined and further deduced the steady state results. Also, the average number of customers in the corresponding queues and the average waiting times are estimated. Finally, the numerical results are represented.

Prediction of Two-Node Tandem Queue with Feedback Having State and Time Dependent Service Rates

Queuing networks are current area of great research and application interest, in view of their increased applicability in - modelling manufacturing facilities and computer/communication networks, production and assembly lines, hospitals, transport systems, banks and so forth. The present paper develops and analyses a tandem queuing model having two nodes with feedback. Such type of model finds its application in many fields, e.g. telecommunication, inventory, hospitals, traffic control and so on. For example, in hospitals, a patient first visits the doctor and goes through a series of examinations, after which he revisits the doctor for medication. The inter-arrival time is exponentially distributed, whereas the service rate for each node depends on the aggregate of customers in the respective queues and thus follows non-homogeneous Poisson process. After constructing the difference –differential equations, and using PGF technique, we have obtained the joint probability distribution for queue size. Some key measures such as the “average number of customers in queue”, “utilization time of each queue”, “average waiting time in each queue” are computed.

Multi Node Tandem Queuing Model with Binomial Bulk Size Distribution Having Load Dependent Service

In this article we study a multi node tandem queuing model consisting of K-nodes in which the customers arriving in batches to the first queue and after receiving service they will be directed with some node specific probability to join any one of the (K-1) parallel queues which are connected to first queue in series and exit from the system after getting service. It is assumed that the arrival and service completions follow Poisson processes and service rates depend on number of customers in the queue connected to it. Here the bulk arrivals are assumed to be Binomially distributed. Using difference differential equations the joint probability function is derived and performance measures such as average number of customers, waiting time of customer, throughput of each service station, utilization of each server, variance of number of customers in each queue are derived explicitly. A numerical illustration is provided to understand the theoretical results. Sensitivity analysis of the system behavior with regards to the arrival rates and load dependent service distribution parameters is carried out. A comparison between transient and study state behavior is also done .

Effective Servicing of a Busy Base Station using Queuing Models in Cognitive Radio Networks

This paper aims the effective utilization of spectrum using queuing models in cognitive radio. The data from various service providers are obtained and considered for our analysis. Analytical mathematical models based on queuing theory are developed for effectively servicing the arrival calls and improving the service rate. Based on the following parameters, we design a model to service the calls effectively: Average number of customers in the system, Average number of customers in the queue, Average wait in the system and Average wait in queue.