Modeling and simulation of queuing system to improve service quality at commercial bank of Ethiopia

Abstract This study aims to develop a queuing model at the Commercial Bank of Ethiopia to improve the service quality perceived by customers using a simulation tool. Performance variables that were considered when developing this model are the average waiting time for a client to get service, customer arrival rates, and service time. After the identification of the problem, the service quality of the bank is assessed using a questionnaire that was prepared in SERVQUAL format. The filled-out and returned questionnaires were analyzed using SPSS, and the results show that the service quality of the bank was deemed very low. The recorded data was then ultimately used as a basis for the determination of arrival, service rates, and the distribution function in the simulation input analyzer. The distribution function determined was used as an input for the development of the existing queue model, and based on that, scientific scenarios are adopted from scientific research and further observations at the bank are added to show enhancement of the existing model. The study used four scenarios to test the response group, and one scenario was selected as the best. This has been identified by adding a server to the counters where there is less utilization, that is, servers four and five. As a result, the waiting time has been minimized by 20 minutes under server four and by 83.4 minutes under server five. Also, the number of customers served per day can be increased from 1048 to 1168, which is 11.45% improvement.


Introduction
Banks have been used in Ethiopia since 1924.However, over the past 20 years, the number of accounts opened by users has increased more than 20-fold, reaching as high as 20 million.Despite this, adult account ownership in Ethiopia is still low compared to neighboring nations (Seid et al., 2020).This makes it a wild new world for banks because of the demand.Simply offering services is not always enough to succeed in the market.To maintain success in the financial industry, services must be of the highest quality, easily accessible, and tailored to meet clients' needs quickly and efficiently.However, long lineups or queues are frequently noticed when banks provide service in Ethiopia as a result of the exponential growth in bank users.
Queuing, also known as waiting in line, is a common occurrence in everyday life; for example, banks have customers in line to receive teller assistance, automobiles queue up for re-filling, and employees queue up to use a machine to complete their tasks.Samanta et al. (2007) State that queues occur when consumers (humans or objects) in need of service must wait because there are more of them than there are servers available; or the facility is inefficient, or it takes longer than necessary to serve a client.
Service quality has been the main agenda for many firms, and therefore, it has become a critical component and a concern for both customers and enterprises.Banks are among the enterprises where customer satisfaction is a critical success factor and a major source of competitiveness.One technique for achieving customer satisfaction is to provide ease of access, which includes the location of the service facility, its hours of operation, and the shortest waiting time for service.According to Kabamba and Mbujimayi (2019) the biggest reason for frustration is long waiting times.When the client enters a system to obtain a service and then departs the premises after being serviced, the issue of queuing must be addressed.
Thus, it was found important for the management to devise formulas and techniques that would cut waiting time and produce satisfied customers without spending more money.André et al., argues that delaying the collection of a resource creates an opportunity cost in the sense that during the waiting time, the benefits otherwise generated by the increment in the capital are lost.These forfeited benefits are waiting for costs per se and are independent of collection risks.
As a result, various approaches have been implemented to improve service quality and, ultimately, customer satisfaction.In a study conducted by Kumasey (2014), a correlational and qualitative approach was employed to examine the relationship between service quality and customer satisfaction in the Ghanaian public service.The results indicated a significant and positive correlation between service quality and customer satisfaction.Additionally, the study found that customer perception was also positively linked with customer satisfaction Meanwhile Madadi et al. (2013) investigated and suggested the best configuration for a bank using a simulation model.The average waiting time and server utilization significantly improved with the suggested setup.Kazeem (2021) found that the majority of bank customers were dissatisfied with the waiting time before being attended to.Based on this discovery, the study recommended an effective and efficient application of queuing theory, which can be particularly useful in banks with high-volume out-of-customer workloads and/or those that offer multiple points of service.
Queuing theory is a strong management technique that is frequently underutilized, particularly in the service sector where there is a high waiting time.When used correctly, this powerful management tool may provide astonishing outcomes.It can also be described as the study of waiting in all these various situations.It represents the numerous kinds of queuing systems that emerge in practice using queuing models.The models enable finding an appropriate balance between the cost of service and the amount of waiting (Aronu et al., 2021).A queuing model often depicts both the stochastic nature of the demands and the physical architecture of the system by describing the number and placement of the servers that serve the customers as well as the unpredictability of both the arrival process and the service process.The elements of a queue are arrivals that need service of some kind, service facilities that take care of the arrivals, and a place where the arrivals wait until they can be served.
One of the most important participants in the financial system is the banking system (Khan et al., 2020).Banks are used for cash flows and modern money movement, and the Commercial Bank of Ethiopia, the most utilized bank with numerous branches dispersed around the country, has many clients.As a result, client demand has outstripped the bank's capacity.This has made waiting in line at the commercial bank of Ethiopia, not an unusual occurrence.According to the data reviewed and gathered for this study, the average customer spends 28 minutes or more receiving a service from the bank.The reaction from customers shown in the survey conducted for this study indicates that customers have been extremely dissatisfied with the service they receive from the bank.This has resulted in a risk that customers of the bank have been spending an excessive amount of time waiting in line to get service, and this issue will not only reduce customer pleasure but also has apparent financial consequences ranging from the time wasted while waiting in line to frustrated and displeased customers, which causes the company to lose money by losing customers to rivals.Therefore, the goal of this research is to investigate the key causes of lineups and build a queueing model and simulate queuing system to improve service quality at a commercial bank in Ethiopia this helps to improve the excessive lines observed at the bank while balancing management expenses and providing a pleasant service to clients by measuring the expected queue length, service, and arrival rate using Poisson's distribution ratio.

Queuing theory
The research of a Danish engineer by the name of A. K. Erlang served as the foundation for queuing theory.Erlang tested varying telephone traffic demand in 1909.He published a study addressing the delays in automatic dialing equipment eight years later.
At the end of World War II, Erlang's early work was extended to more general problems and business applications of waiting lines.Mehri et al. (2008) Queuing theory covers all aspects of the process of waiting in line to be serviced, including the arrival process, the service process, the number of servers, the number of system locations, and the number of customers-which may be individuals, data packets, or automobiles (Basak & Choudhury, 2021).It demonstrates and models the situation of waiting in lines.Queues occur when the need for services is greater than its supplies, which is sometimes unavoidable in the everyday workings of life (Ailobhio et al., 2021).queuing theory is the mathematical study of waiting lines or the act of joining a line (queues).In queuing theory, a model is constructed to enable the calculation of queue lengths and waiting periods.
The theory has a wide range of useful applications, such as traffic flow (vehicles, aircraft, communication), scheduling (patients in hospitals, tasks on machines, computer programs), and facility design (banks, post offices, fast-food restaurants).Queuing theory can sometimes assist us to avoid these queues, which we encounter in a variety of ways nowadays (Augustine, 2013).According to Yusuf et al. (2015), in a bank, queuing theory can be applied to assess a multitude of factors such as registration fill time, customer waiting time, customer counseling time, and receptionist and technician staffing levels.In the Department of Veterans Affairs (VA), Department of Defense (DoD), university health systems, and managed care organizations, receptionists may find it particularly useful to apply queuing theory because of their high volume of outbound customers and/or the fact that they offer multiple points of service.

Queuing models
A queuing model is a mathematical representation of a queuing system that includes certain presumptions on the discipline and organization of the queue, the number and type of servers, the arrival and service procedures, and their probabilistic character.There are formulae available for these models as well as many others that enable the quick computation of several performance measurements that may be used to aid in the design of a new service system or improve an existing one (Green, 1995).One of the challenges for banks is reducing customer wait times.Queuing models should be implemented by banks to stay competitive.Banks may benefit from using queuing technologies to reduce wait times through effective queue management that increases profits (Aronu et al., 2021).Oladipo (2017) queuing theory modeling is categorized using special (or standard) notations in the form of (a/b/c) as described by D.G. Kendall The Kendell notation later received the d and e symbols from A.M. Lee.The typical format followed in the literature on queuing theory to describe queuing models is GI= General probability distribution normal or uniform for the inter-arrival time.
EK = Erlang-k distribution for inter-arrival or service time with parameter k (i.e., if k = 1, Erlang is equivalent to exponential, and if k = ∞, Erlang is equivalent to deterministic).

Queuing disciplines
When a customer arrives, they must get in line if all servers are already occupied.Though lines of people or objects standing in a queue are common, queues can also be intangible, such as when a phone call is placed on hold.The queue discipline is the policy that governs when customers in a line will be served (Green, 1995).Figure 1 illustrates an example of queue discipline.
This relates to the order in which products were serviced, or the priority rule by which clients are handled.There are two main categories, which contain the following queue disciplines (Augustine, 2013).(source (Ailobhio et al., 2021)).
(i) FIFO (First In-First Out): This method enables the system to prioritize serving the first item to enter the system (items at the front of the queue).Because it is regarded as being more equitable than the other kinds of regulations, it is the discipline that is used the most commonly.
(ii) LIFO (Last In-First Out): In this case, the item at the end of the queue or the one that first enters the system gets served (Augustine, 2013).

Service quality
Service quality is a critical factor in achieving customer satisfaction and loyalty in service-oriented businesses.Several studies have investigated the impact of service quality on customer satisfaction and loyalty in various industries.Madadi et al. (2013) service quality is a crucial core competency for banks, and they place significant emphasis on it.The length of queues and the duration of waiting times are two crucial factors that significantly affect customers' perception of service quality in banks.
The banking industry is one of the most competitive service-oriented industries, and service quality is considered a critical factor in achieving customer satisfaction and loyalty.Several studies have investigated the impact of service quality on customer satisfaction and loyalty in the banking industry.
In a study conducted by Zia (2022) in Saudi Arabia, service quality was found to be a significant predictor of customer satisfaction and loyalty.The study utilized a survey to collect data from bank customers, and the results indicated that reliability, responsiveness, and empathy were the most critical dimensions of service quality that influenced customer satisfaction and loyalty.
Similarly, in a study conducted by Nguyen and Nguyen (2021) on the Vietnamese banking industry, service quality was found to have a significant impact on customer satisfaction and loyalty.The study used a survey to collect data from bank customers, and the results indicated that tangibles, reliability, and responsiveness were the most critical dimensions of service quality that influenced customer satisfaction and loyalty.
In another study conducted by Haddad et al. (2019) in Jordan, service quality was found to be positively related to customer satisfaction in the banking industry.The study utilized a survey to collect data from bank customers, and the results indicated that tangibles, reliability, and empathy were the most critical dimensions of service quality that influenced customer satisfaction.
Another study by Tan et al. (2016) examined the relationship between service quality and customer satisfaction in the Malaysian banking industry.The study found that service quality significantly influenced customer satisfaction, and reliability, responsiveness, and empathy were the most critical dimensions of service quality that impacted customer satisfaction.Amirzadeh and Shoorvarzy (2009) examined the quality elements of services in banks by the SERVQUAL instrument.The research was conducted among bank customers.The questionnaire was used to collect the necessary data.This work attempts to apply a fuzzy approach to service quality, where consumers' evaluations of service quality are typically stated subjectively in ambiguous linguistic terms.According to the study's findings, "short and appropriate queues" and "confident and reliable employees" are the most crucial quality elements in bank service.

Simulation modeling for queuing problem
According to Kumasey (2014) the fulfillment of human needs is a significant goal that businesses work toward.The goal of the study was to look at customer satisfaction and service quality in Ghana's public sector.Data from 304 participants was gathered via a questionnaire by the researcher, utilizing a correlational study design and a strictly quantitative research methodology.Using the Pearson product-moment correlation test, the hypotheses were evaluated.The outcome demonstrated a strong and favorable relationship between customer satisfaction and service quality.Customer expectations and perceptions are also strongly and favorably connected to customer satisfaction.Aronu et al. (2021) revealed that the traffic intensity of the queue model decreases as the number of cashiers increases.The distribution of the inactive server count revealed that as there are more servers, there are also more inactive servers.The findings indicate that the total cost of the bank's service increases as the number of servers increases.Additionally, the examination of the total cost of waiting discovered that when the number of cashiers increases, the overall cost of waiting decreases.An increase in the number of servers (cashiers) has been found to increase the total operating cost.Wang et al. (2009) used integrated data processing system (IDS) Scheer integrated architectural information system (ARIS) and Rockwell Arena software to design a simulation model that represented patients arriving at a particular emergency care center.Process bottlenecks have been identified, and the best allocation of resources and personnel possible has been made without disrupting the current system.To reduce waiting time in emergency conditions, doctors' efficiency improvement and rapid pass process are proposed and tested as alternative solutions.By constructing computer-based simulation models, Madadi et al. (2013) suggested the best possible configuration for the bank.The simulation model proved its capacity to investigate various configuration alternatives without imposing the cost of physical changes, leading to the selection of the best solution at a significantly lower cost.Investigation of various service configurations the computer-based simulation model was created based on the data and conceptual model associated with the current configuration of the bank.

Hypothesis
After the carful investigation of literature, the following hypothesis has been developed.

Null Hypothesis (H0):
The current system of serving customers in the bank is operating efficiently and effectively, and there is no significant difference between the observed and expected customer waiting times.

Alternative Hypothesis (Ha):
The current system of serving customers in the bank is not operating efficiently and effectively, and there is a significant difference between the observed and expected customer waiting times.

Methodology
The methodology part includes the research design, the study's demographic, the sampling design and sample size to be utilized, the data, data collection methods, and data analysis procedure.

Research design
Research design is the conceptual framework within which research is conducted; it constitutes the blueprint for the collection, measurement, and analysis of data.As such, the design includes an outline of what the researcher will do, from writing the hypothesis and its operational implications to the final analysis of data (Kothari, 2004).
This study aims to bring down the long queue time often noticed at the commercial bank of Ethiopia by developing a simulation and mathematical model and taking personal factors about the satisfaction and dissatisfaction of customers with the current process through a descriptive survey that follows the SERVQUAL format.In addition to that, the study gathers quantitative data through various approaches, such as observation, survey, interview, and measurement.

Data collection methods
Data was collected through the administration of questionnaires to the respondents.Also, observation and measurement has been taken using a stopwatch to record the arrival and service time of the customers.The study instilled quantitative approaches to data-collection methods.An explanation was given to both the respondents and how the questionnaire should be filled out.The questionnaires distributed were issued to customers at the commercial bank of Ethiopia's Gondar, Maraki branch.The customers had a full right to say no to filling out the survey.
Primary data is information gathered by researchers directly from primary sources, such as interviews, questionnaires, surveys, and experiments.Primary data is often acquired from the source-where the data originated-and is regarded as the best type of data in research.

Observation
Direct observations took place alongside the measurement of time for two weeks non-inclusive of Sundays.To observe the whole procedure and gather different data including the number of customers the bank gives service to, the services the bank provides, problems in service delivery, the number of servers, the needs of customers, and checking if customers were satisfied or not.All the information that was noticed was copied down on a notebook and it is used in developing the conceptual frameworks of this study.Service time and arrival time of customers was determined every day during the two weeks of data collection by a stopwatch using a mobile phone.The arrival time of customers, and service time was independently recorded and copied down on a notebook.

Interview
Information was gathered by asking different questions from individuals including the servers, customers, and managers.The why, what, how, when, and rating technique was applied in the questions to obtain people's perception of the service quality provided by the bank and their opinions on how the queue time would be fixed.

Questionnaire
The study contained a list of questions used to gather data from different respondents about their opinions and experiences that will be useful to rate the service in an expected and precepted manner.The questionnaire was based on the SERVQUAL model that further divides the questions into five based on responsiveness, assurance, reliability, tangibility, and empathy.For better understanding, the questionnaire is designed into three parts.The demographic information of the respondents was taken into account in the questionnaire's first section.The questions were designed with multiple-choice selections for convenience.The second part of the questionnaire required the respondent to rate the quality of service they expected from the bank their choice was classified into a five pre-defined level scale-"Strongly Disagree", "Disagree", "Neutral", "Agree" and "Strongly Agree".The final part of the questionnaire also applies the same concept used in the second part of the questionnaire, but it asks the respondents to rate the precepted or obtained quality of service from the bank.The questionnaire was designed in the Amharic language for an unprecedented scale amount of convenience and communication with respondents.

Research approach
In this study the quantitative method has been employed because to address the issue well and get best outcome for the study.In the numerical recorded data like the number of customers in the waiting line and system, time a customer spent in the waiting line and system, the number of customers that the office can hold and the number of servers or employees working in the customer service are all included in quantitative data collection.This research study adopts a quantitative emphasis to find correlational relationships between variables that affect service quality and was facilitated by the use of primary data.The quantitative rating obtained from customers through the Likert scale is further analyzed by SPSS software.The study also uses quantitative data on the arrival rate, service rate, and queue time of the customers in the waiting line, and the total system is measured with a stopwatch.The data gathered from the stopwatch is distributed and a simulation model is developed using Rockwell Arena software.

Sample size and sampling technique
Sample size refers to the number of objects that must be chosen from the entire universe to make up a sample (Kothari, 2004).The formula and methodology that are used to determine sample size in this study are adopted from previous studies of formulas and censuses for a small population that used formulas to determine the sample size.According to Israel (1992) in addition to the purpose of the study and population size, the level of precision, level of confidence or risk, and the degree of variability in the attributes needs to be measured.In this study, the sample size determination adopts Yamane's formula, which considers a confidence interval of 95% (it holds that 95 out of 100 samples will hold a true value).
Through the unstructured interview conducted at the branch, the employees stated that on average, 600 people get service from the branch, and the population size of this study is 600 people on average.
Where: n is the sample size N is the population size e is the level of precision (applying 95% confidence interval which will be 0.05) Thus, based on this formula the sample size studied for this study will be: Therefore, the sample size for this study to distribute questionnaires is 240 people.
This study used probability sampling, also known as random sampling.The researchers employed simple random sampling to distribute the questionnaire at Gondar's Maraki branch.This method was chosen because it ensures that each member of the population has an equal chance of being selected for the sample.Probability samples are widely used in modern survey research because they allow the researcher to control the margin of error.Random sampling is considered the best technique for selecting a representative sample because it ensures the law of statistical regularity that a sample selected at random will generally have the same composition as the population.All other things being equal, well-designed and executed probability sampling produces unbiased estimates (Rasinski & Griffith, 2004).

Problem identification
The Commercial Bank of Ethiopia faces challenges in delivering high-quality services to its customers due to long waiting times and inefficient queuing systems.The current system is characterized by poor customer satisfaction, high service time variability, and increased waiting times.This has made waiting in line at the commercial bank of Ethiopia, not an unusual occurrence.According to the data reviewed and gathered for this study, the average customer spends 28 minutes or more receiving a service from the bank.Therefore, there is a need to improve the queuing system to enhance service quality and customer satisfaction.

Simulation procedure
This can provide a general simulation procedure that can be used to model and simulate the queuing system at the Commercial Bank of Ethiopia.The simulation steps were adopted from (Mutingi et al., 2015) as follows: Step 1: Problem formulation Step 2: Setting of objectives and overall project plan Step 3: Modelling and conceptualization of the collected data Step 4: Model translation Step 5: If it is verified then it is to be validated, if not then back to the model translation Step 6: After validation the experimental design Step 7: Run analysis would be carried Step 8: Documentation and reporting Step 9: Implementation

Input modeling
The data recorded were analyzed through the input analyzer of Arena software, to determine its distribution which can later be fed to Arena software in developing the simulation model.This is used as a function that describes the relationship between observations in the recorded sample space.The distribution of the inter-arrival time is betta with the expression of-0.001+ 775*Beta (0,0) (Figure 2).The service time distribution for server 1 is Erlang with the expression of 23+ERLA (51.3,2) (Figure 3).For server 2, the service time distribution is Erlang with the expression of 10 +ERLA (52.2,2) (Figure 4).For server 3, the service time distribution is Beta with the expression of 9 + 2.85e + 0.03*BETA (0.837,1.2) (Figure 5).For server 4, the service time distribution is Gamma with  the expression of 29+GAMM (54.9,1.42)(Figure 6), and for server 5, the service time distribution is Gamma with the expression of 29+GAMM (67.6,1.56)(Figure 7).

Model development
The data analysis from the measured data by the stopwatch was done through Microsoft excel and Rockwell Arena software.After the data was collected the collected data was modeled and conceptualized in a manner that can be easily understood and accessed.The data collected was put into excel to determine the average of it which later helped in creating a distribution and a simulation model while minimizing the waiting time by determining a new mathematical and simulation model using a steady-state probabilistic nature.
The simulation model was developed using Arena Rockwell software version 14.The model starts with an arriving customer, and it includes the customer's decision to stay in the queue or leave the queue.Then the customers diverge into multiple queues within the five counters that are available for giving service in the bank the model.The number of servers is about 5. The queue discipline is first come first served (FCFS) basis by any of the server.Taking this into account the following model is developed as indicated in Figure 8.

Model verification and validation
The simulation model shown in Figure 8 represents the current system of commercial banks, and it was thoroughly tested through the simulation software's command window to determine if any errors were present during model execution.The results of this testing are presented in Figure 9, which confirms that the model does not contain any errors.Therefore, we can be confident that our simulation model is accurate and can be used to evaluate the performance of the current system and explore potential improvements.
The Commercial Bank of Ethiopia Maraki branch serves approximately 1045 customers in 9.5 hours.The simulation model also generates an output of 1048 customers after 9.5 hours.The percent error between the actual and estimated values is calculated to be 0.29%, which is a small value and indicates that the estimated value is very close to the actual value.This result confirms the validity of the simulation model and its ability to accurately represent the actual system.

Results and discussions
In data analysis, the presentation and interpretation of results are covered by creating a queuing model and reducing wait times.This project attempted to raise the quality of service at the Commercial Bank of Ethiopia.The analysis begins by presenting the response rate and demographic profile of the participants under research.The current data was acquired using questionnaires to gauge customer perceptions of the current level of service quality.The survey response indicates the sample size of this study was 240.The questionnaire was distributed to 240 customers.Out of the total of 240 distributed questionnaires, 196 (81.66%) were filled out and returned.The respondents' gender analysis (Figure 10) shows that out of the total 196 respondents, 80 (40.8%) were female and 116 (59.2%) were male.Also, the respondents' age analysis (Figure 11) shows that out of the total 196 respondents, 55 (28.1%) were between the ages of 18-25, 92 of them (46.9%) were between the ages of 26-40, 24 (12.2%) were between the ages of 41-50, 16 (8.2%)were aged between 51-60, and 9 (4.6%) were above the age of 61.The respondents of occupation analysis (Figure 12) shows that out of the total 196 respondents, 40 (20.4%) were students, 70(35.7%)were public servants, 49 (25%) were small business owners, 23 (11.7%) of them were big business owners, 4(2%) were unemployed, and 10(5.1%) had other occupations.And the respondents of the level of education analysis (Figure 13) shows that out of the total 196 respondents, 21(10.7%)had a primary school education, 52(26.5%)had a high school diploma, 50  (25.5%)had a college diploma, 52(26.5%)had an undergraduate degree, and 21(10.7%)had a postgraduate degree.In data analysis, the result presentation and result interpretation are covered by creating a queueing model and reducing wait times.
After analyzing the service quality at the bank, it was found that the average response value from customers indicated that both perceived quality and expected service quality were low.Table 1 shows the difference between the two, further supporting this conclusion.Based on the developed hypothesis, the alternative hypothesis is true: the current system of serving customers  in the bank is not operating efficiently and effectively, and there a significant difference between the observed and expected customer waiting times.
One of the goals of this study is to determine the arrival rate, waiting time, and service time by collecting data from the Maraki branch of Commercial Bank of Ethiopia in Gondar.To achieve this goal, an interview was conducted with a few members of the staff, and it was found that on average, a single server attends to 66 clients during each shift.Using Yamane's technique, the sample size for the study was calculated to be 66 persons per shift.Data was collected from each server until 66 individuals were served per day for 12 consecutive days.
Table 2 shows the analysis of the arrival number of customers.The results indicate that 185 people enter the system per hour, and on average, a customer arrives and enters the system every 1.62 minutes.Table 3 reveals that the average service rate at the CBE Gondar Maraki branch, for all 5 servers combined, is 110 customers per hour.This value represents the average number of customers that can be serviced by the bank per hour, indicating its capacity to serve customers within a given time frame.However, it is noteworthy that the average number of customers arriving per hour is 185, which is significantly higher than the average service rate.This suggests that the bank is unable to meet the demand and that the waiting queue will become infinite if the situation continues.Therefore, it is necessary to identify potential improvements to the system to increase its capacity and reduce the waiting time for customers.Table 4 presents the data on the time customers spend waiting in the system and corresponding number of customers waiting in the queue.The results indicate that customers at counters 5 and 3 experience longer waiting times, with average waiting times of 90 and 80 minutes per shift, respectively.Additionally, the number of customers waiting in the queue is higher at counters 3, 4, and 5. Therefore, making significant changes to these counters could potentially reduce the number of customers waiting in the queue and the time required to receive service.By addressing these areas of the system, the overall customer experience can be improved, and the bank can better meet the demands of its customers.Figure 14 shows the total number of customers seized (number of customers that a business or service provider can accommodate or serve at a given time) during the replication length of the simulation model.The number of customers seized on server one is 110, the number of people seized on server two (Rahel) is 165, the number of people seized on server three (Tewachew) is 222, the number of people seized on server four (Birhan) is 200, the number of people seized on server five (Mengistu) is 256. Figure 15 demonstrates the utilization or resources in the system or the utilization of capacity per resource, as indicated in the chart below.The average operator utilization of server one (Amare) is 40.82%, the average utilization rate of server two (Rahel) is 57.47%, the average utilization rate of server three (Tewachew) is 62.2%, the average utilization rate of server four (Birhan) is 64.54%, and the average utilization rate of server five (Mengistu) is 55.51%.
After running the current queueing simulation model, its major values were able to be discovered, and several findings that were not included within the scope of the study were able to be  discovered to meet the set objectives.The main focus of this study is to determine the average arrival rates, average queue times, and average service times per customer for the commercial bank of Ethiopia's Gondar Maraki branch to propose different scientific scenarios that can reduce the lengthy waiting time experienced by customers when trying to get a service.In this study, four scientific scenarios are proposed, mostly adopted and modified from Amalina and Siburian ( 2021) and observations at the Commercial Bank of Ethiopia.Each of the scenarios and their effects is tested, and the best alternative is chosen to fulfill the general objectives of this study.
To create the scenarios, three control groups were carefully selected based on their records of long customer wait times at the Commercial Bank of Ethiopia.The control groups in this study were comprised of servers with the highest waiting times and queue records, namely server three (Tewachew), server four (Birhan), and server five (Mengistu).Additionally, the replication length of the simulation model was selected as a control group and manipulated in the creation of new scenarios.This was because customers' perceptions of service quality at banks are significantly influenced by queue length and wait time.By selecting appropriate control groups and testing various scenarios, this study aims to improve the customer experience and enhance the effectiveness of the Commercial Bank of Ethiopia's Gondar Maraki branch.Therefore, in the case of the service sector, like a bank, taking several servers who have high waiting times and adding extra time for the service provider is valuable to facilitate and reduce the service time and enhance the number of customers to be served (Madadi et al., 2013).
The response group is another group that is systematically selected to provide feedback on the manipulations made to the control group.This group is carefully chosen to ensure that the feedback received is representative of the wider customer base.In this study, the response group was selected based on the results presented in Table 4, which showed that servers three, four, and five had the longest waiting times.Therefore, servers 1, 2, and 3, along with their waiting times and the number of customers served, were included in the response group.This is because the number of customers served, waiting time, and the number of customers waiting are key performance measures that are used to assess the effectiveness of the system (Kiataramkul, 2019).By including appropriate servers and performance measures in the response group, the study can obtain a comprehensive and representative understanding of the system's performance and customer experience.(1) Existing scenario: The simulation model was based on this situation.This shows how well the bank is currently operating.The existing system of the bank has five servers that work for about 9 hours per day.The other scenarios are created on the basis to improve this scenario.
(2) Scenario I: This model proposes adding one more server within both server four and server five (Tewachew and Birhan).Since there is high waiting time as indicated in the table 4.
(3) Scenario II: This model proposes adding one server within server four (Tewachew) and adding extra 30 minutes of working time to improve the efficiency while performing the job.
(4) Scenario III: This model proposes adding one server for server three and server four (Mengistu and Tewachew).Because, both servers have high waiting time of customers while they provide services.
(5) Scenario Ⅳ: This model proposes adding sever within sever three and sever five (Mengistu and Birhan), where there is high waiting time and waiting number of customer and also adding extra 30 minute to perform their work.
As shown in Tables 5 and 6, the existing system of the bank has a waiting time of 25, 21, and 90 minutes for customers in the queue, and the number of customers who wait in the queue is 10, 8, and 41 under counters 3, 4, and 5, respectively.The system can serve about 1048 customers.
Scenario one: in this scenario, the waiting times of customers in the queue are 5, 2, and 130 minutes.The number of customers who wait in the queue is approximately 2, 1, and 64.The total number of customers to be served is about 1153.Applying scenarios, one helps in reducing the waiting time of customers at counters 3 and 4 and increasing the number of customers going to be served.
Scenario two: In this scenario, the waiting time of a customer is 14, 66, and 160 minutes.The number of customers who wait at the server is approximately 6, 27, and 77.The total number of customers to be served is about 1173.This has slight improvement over the waiting time in counter-3 and has a significant change over the number of customers going to be served.
Scenario three: in this scenario, the waiting time of a customer is about 3, 22, and 5 minutes.The number of customers who wait in the queue is approximately 1, 9, and 2. Additionally, the total number of customers to be served is about 1025.This has a significant improvement in reducing waiting time in the queue and the number of customers in the queue but is less efficient in terms of increasing the number of customers going to be served.Scenario four: in this scenario, the waiting time of a customer is about 26, 2, and 7 minutes.The number of customers who wait in the queue is approximately 11, 1, and 3 under servers 3, 4, and 5 respectively, and the total number of customers to be served is about 1168.Compared to the existing and other scenarios, this has a significant improvement in reducing waiting time, reducing the number of customers in the queue, and increasing the number of customers going to be served.
To summarize and make the description in Table 6 more clear, the Figure 16 below is demonstrated as follows: Therefore, after a careful study of these scenarios and the improvements they made to the overall system, Scenario 4 is recommended to be implemented at the CBE branch because it reduces the waiting times experienced by customers at the servers where high waiting time was recorded.Following a thorough analysis of these cases and the enhancements, they brought to the system as a whole.It is advised that scenario 4 be put into practice at the commercial bank of Ethiopia Maraki branch.As a result, users spend less time waiting at servers where long wait times were reported.
Previous studies have demonstrated the beneficial effects of simulation over analysis and improvement of queuing system in the bank service.Our findings are consistent with previous studies that have used queuing system models to improve service quality in banks.For instance, Mutingi et al. (2015) used simulation model to analyze the effect of various factors on service quality, such as the number of tellers, the arrival rate of customers, and the service time distribution.The results showed that increasing the number of tellers and reducing the service time distribution can improve service quality.Similarly, Amalina and Siburian (2021) had used simulation approach resulted in two scenario improvements, namely adding one additional server and adding one operator in an existing server.The findings revealed that the waiting time and work in progress were reduced when an additional server and an operator were added.Another study, Olu et al. (2022) used a queuing system model to optimize the allocation of resources in a bank, resulting in improved service efficiency and reduced Building on these studies, the present research reduces customer waiting time and increases the number of customers served.Therefore, this study provides strong evidence that simulation is a powerful tool that can reduce waiting time and enhance service output in the service sector.

Conclusion
In this study, conducted at the Commercial Bank of Ethiopia, a queuing model was developed to reduce customer wait times.During the July observation, there was frequently a lengthy line of dissatisfied customers.In order to investigate this, a SERVQUAL-based questionnaire was developed to assess the bank's service quality, the customers' expectations, and their perception of the bank's service quality.The evaluation of the responses using SPSS revealed that all of the questions had negative values, indicating that the bank did not meet the minimum standards anticipated by the customers.The bank's service quality was determined after examining client expectations and precepts.The sample size for the study was determined to be 66.Therefore, for the duration of the data collection period of 12 days, the arrival time, service time, and wait time for 66 clients per server were recorded.The statistics then indicated that the hourly client arrival rate was 37 and the average wait time for a customer to obtain treatment was 28 minutes, neither of which are negligible amounts of time to consider.A simulation model was built on Arena Rockwell software to keep that time to a minimum.The recorded data was fed into various expressions of the model, and then the model was run for a replication frequency of one and a replication length of 570 minutes, or 9.5 hours.
The model could depict queue times for each server, utilization, and the number of entities coming in and going out.The total number of customers that left the system was 1048.Servers three, four, and five had the highest waiting times of all five servers.So, they were selected as a control for further manipulation of the model to bring a response to the response group, which was mainly the main constituent of the objective of this study; waiting and queue times of the servers that have high waiting times.
The study included different scenarios, some adopted from several kinds of literature, and these scenarios were further tested to see what kind of impact they had on the existing queuing model of the bank.Scenario 4, put forward in this study, has brought waiting times for all three servers to a minimum, and it has been chosen to be practiced at the commercial bank of Ethiopia's Gondar Maraki branch.This scenario minimizes server four by 20 minutes and server five by 83.4 minutes, and the number of customers served has increased from 1048 to 1168.Due to the time constraint, the current study focuses on the commercial bank of Ethiopia.As a result, future researchers can go through it and conduct large-scale data analysis.

Recommendations
After a thorough analysis of data and observation, the following recommendations are hereby made: • This study suggests the queuing model developed at commercial bank of Ethiopia (CBE) will broaden the chance of development of different scientific scenarios to minimize waiting time at each server for example, the usage of the approach shortest job first (SJF).
• CBE can use an automated queue management system to manage the customer base efficiently.The technology can simplify the service provider's management to control customer flow.
• A crossline might be necessary between servers, and there should be enough seats for everyone; one customer should be at the counter at a time.
• Customers may stay seated and not have to stand in a hectic queue to check whether it is their turn, yet a digital ticket that indicates when they are ready to be served.

Limitation of the study
Queuing systems in commercial banks are often influenced by external factors such as changes in customer behavior, economic conditions, or regulatory requirements.These factors may need to be accounted for in the simulation model and could limit the model's effectiveness in predicting the system's performance.
as follows: {(a/b/c) :(d/e)} Where a= arrival distribution b = service time distribution c = number of servers (service channels) d = the system capacity (queue plus service) e = queue (or service discipline) In place of notation a and b, the following descriptive notations are used for the arrival and service times distribution: M = the inter-arrival time or service-time distribution in the Markovian (or exponential) model.D = Deterministic service subject or inter-arrival time.G = General distribution of service time, i.e., no assumptions are made regarding the sort of distribution with means and variance.

Figure
Figure 1.Graphical illustration of queue discipline.

Figure 2 .
Figure 2. Distribution of the inter-arrival time.

Figure 3 .
Figure 3. Service time distribution for server 1.

Figure 4 .
Figure 4. Service time distribution for server 2.

Figure 5 .
Figure 5. Service time distribution for server 3.

Figure 6 .
Figure 6.Service time distribution for server 4.

Figure 7 .
Figure 7. Service time distribution for server 5.
Figure 8. Arena base existing simulation model.

Figure
Figure 9. Model verification testimony.

Figure
Figure 13.Respondents' level of education analysis.

Figure 14 .
Figure 14.Total number of customers seized customers.

Figure
Figure 15.Scheduled utilization per server.

Figure 16 .
Figure 16.Simulation results of different scenario.