AN AUTOMATIC PRIORITY QUEUEING MODEL FOR BANKING SYSTEM

ISSN 2277-2685 IJESR/April 2016/ Vol-6/Issue-4/82-88 Tabi Nandan Joshi et. al., / International Journal of Engineering & Science Research AN AUTOMATIC PRIORITY QUEUEING MODEL FOR BANKING SYSTEM ABSTRACT Dr. V. K. Gupta 1, Dr. S. K. Tiwari 2, Tabi Nandan Joshi* 3 1 Prof. & Head, Department of Mathematics, Govt. Madhav Science College, Ujjain, India. 2 Reader, School of Studies in Mathematics, Vikram University, Ujjain, India. 3 School of Studies in Mathematics, Vikram University, Ujjain, India. Waiting line and service system are important part of the business world. This paper focuses mainly on banks lines system. The banks are trying to improve customer satisfaction by offering better service. Businesses are always looking for ways to improve customer satisfaction so that they can attract new customers and retain old ones. In order to accomplish this, banks would like to reduce the average time customers spend waiting for services. Our model give efficient method to reduce average customer waiting times and average queue length within the requirements. Keywords: Queueing System; Scheduling Algorithm; Priority; Average waiting time; Idle Time. INTRODUCTION The waiting queues of the customer develop because the service to a customer may not be delivered immediately as the customer reaches the service facility [5]. One of the important classes of queuing systems that we all encounter in our daily lives is business service systems, where customers receive service from commercial organizations. Many organizations involve person-to-person service at a fixed location, such as a petrol pump, cafeteria, barber shop and banks. Many banks have done immense effort to increase the service efficiency, which gives customer satisfaction but the most of them are facing a serious problem of waiting line of customers. In bank, the waiting line of customers appears due to low efficiency of the queuing system, low service rate of the system. Lack of satisfactory service facility would cause the waiting line of customers to be formed. The only technique is that the service demand can be met with ease is to increase the service capacity and increasing the efficiency of the existing capacity to a higher level. In the following, to solve the problem of the long waiting lines of the customer is studied by means of the queuing theory, the determination to reduce the time of customers waiting is obtained to achieve the goal of people oriented and the greatest effectiveness of the banks. The aim of this paper is to decrease the customer waiting time and also to analyze the queue to take the decision about how to pick a customer for service. Therefore the research is focused on analyzing the queues to optimize their operations and to reduce waiting time for customers [4,6,8]. Queueing System The study of waiting lines, called queuing theory, is one of the oldest and most widely used quantitative analysis techniques. The queueing theory or waiting lines owes its development to A. K. Erlang in 1903. Queue is the common activity that customer have to go through to avail thee desire service, which could be processed or distributed one at a time. Queues, another term for waiting lines, may also take the form of machines waiting to be repaired, trucks in line to be unloaded, or airplanes lined up on a runway waiting for permission to take off [5]. Waiting lines are an everyday occurrence, affective people shopping for groceries buying gasoline, making a bank deposit, or waiting on the internet for the first available railway reservation. The three basic components of a queuing process are arrivals, the actual waiting line and service facilities. Characteristics of a Queuing System: The three important part of queuing system are: (1) the arrival or inputs to the system also called as the calling population, *Corresponding Author www.ijesr.org 82

(2) the queue or the waiting line itself, and (3) the service facility. These three components have certain characteristics that must be examined before mathematical queuing models can be developed. Arrival Characteristics The input source that generates arrivals or customers for the service system has three major characteristics. It is important to consider the size of the calling population, the pattern of arrivals at the queuing system, and the behavior of the arrivals. Size of the Calling Population: Population sizes are considered to be either unlimited (essential infinite) or limited (finite). When the number of arrivals on hand at any customers given moment is just a small portion of potential arrivals, the calling population is considered unlimited. Most queuing models assume such an infinite calling population. When this is not the case, modeling becomes much more complex. A queuing system consists of one or more servers that provide service to arriving customers. Figure.1 shows the characteristics of queuing system [3]. The population of customers may be finite (closed systems) or infinite (open systems). QUEUE SERVER DEPARTURE Fig. 1: Characteristics of queuing system The arrival process describes how customers enter into the system. The customers arrive to the service center in a random fashion. Queue represents a certain number of customers waiting for service. The capacity of a queue is either limited or unlimited. Bank is an example of unlimited queue length. The service is an activity requested by a customer, where each service takes a specific time. The scheduling algorithm is used to order the customers and to choose the next customer from the population in the specified queue. The most common scheduling algorithms are [3,7]: a) FCFS (First Come First Serve): The customers are served in the order of their arrival, which is most visibly fair because all customers think of themselves as equal. b) RSS (Random Selection for Service): In this algorithm, customers are selected for service at random, so each customer in the queue has the same probability of being selected for service irrespective of his/her arrival in the service system. c) PRI (Priority Service): The customers are grouped in priority classes according to some external factors. The customer with the highest priority is served first. d) SPF (Shortest Processed First): The algorithm assumes that the service times are known in advance. When several customers are waiting in the queue, the SPF algorithm picks the shortest service time first. Queue Service In queuing system, there are many types of queue models such as [2, 7]: a) SQ (Single Queue): In this model each customer waits till the service point is ready to take him/her for service. b) MQ (Multiple Queues): In this model each customer tries to choose the shortest queue from a number of individual queues. c) DQ (Diffuse Queue): In this model each customer take a ticket from a ticket machine with single or multiple buttons each for specific service. After the customer registers his/her place in the queue by a ticket he/she will monitor the ticket number being served. The customers can not estimate when they will be served. Copyright 2016 Published by IJESR. All rights reserved 83

THE PROPOSED QUEUING SYSTEM MODEL Here present a new technique for queue management technique in banks. Our system is to builds an automatic queue that can test the status of the queuing system such as DQ and choose the appropriate algorithm among more than one scheduling algorithms that already defined in the system such as FCFS and Priority Queue to select the next customer to be served during a specific period of time. Selecting the scheduling algorithm depends on the testing results to achieve the best waiting time for all the available customers that are waiting to be served. To achieve this goal we add additional components to the traditional queuing management system. The suggested queuing system consists of the following components: a) Customer area: In customer area the customer selects a service at the ticket dispenser via regular push buttons, and waits until his/her ticket number shown in a vision and/or audio notice for the number. b) Queuing area: In queuing area the system uses the queuing algorithm that is chosen by the testing area to select one of the waiting customers. c) Testing area: In testing area the system tests the status of the customer according to the existing algorithms and assign customer a particular queue according to priority of specific task. d) Scheduling Algorithms Database area: All the needed scheduling algorithms, the testing result, and the customers numbers, are stored in the scheduling algorithms database area. The testing result and the customer's numbers are saved temporarily and priority will be assign for a specific task. e) Service area: In service area the system serves the customer according to the different services that a bank can give as open an account, transaction, send money, deposit funds, balance, etc. Each service needs a specific time. EXPERIMENTAL WORK Simulations were carried to test the performance of the new proposed system. A database of two standard scheduling algorithms was developed to systematically evaluate the proposed system. For the purpose of illustrations, a comparison between the new system (i. e. Priority based) and the ordinary system (FCFS) that is used usually in most of the banks queuing systems. In the proposed system, two scheduling algorithms are used (FCFS, Prt). For the purpose of calculation and reality a random number generation is used to generate a sequence of customers arrival time and to choose randomly between three different services: open an account, transaction, and balance, with different period of time for each service: 15, 10, and 5 respectively. To test the proposed system we implement two case studies: Special Case: After executing the random generator, a simulation snapshot for the queuing system is generated, the result are 20 customers with different arrival time starting from zero, and different service time as shown in Table1 [1]. After implementing the ordinary queuing system and the proposed queuing system on the above snapshot, the ordinary queuing bank system that uses only FCFS algorithm, as shown in Table 2. The new queuing system calculates the waiting time for each customer [9], then calculates the total waiting time and the average waiting time according to the two algorithms (FCFS, Prt) Copyright 2016 Published by IJESR. All rights reserved 84

Table 1: 20 customers with different arrival time starting from zero, and different service time Customer Arrival Time Service Time Type of Service C1 0 10 Transaction C2 5 15 Account Opening C3 8 5 Balance C4 15 10 Transaction C5 17 5 Balance C6 19 5 Balance C7 20 10 Transaction C8 25 5 Balance C9 28 5 Balance C10 30 10 Transaction C11 40 15 Account Opening C12 42 5 Balance C13 43 5 Balance C14 44 5 Balance C15 110 15 Account Opening C16 111 10 Transaction C17 112 5 Balance C18 113 5 Balance C19 114 5 Balance C20 115 10 Transaction Algorithm: The minimum average waiting time. CWT i = SSTC i ATC i.. (1) Where: CWT - Customer Waiting Time; SSTC - is Start Serving Time for a Customer ATC - Arrival Time for a Customer; i - The i th Customer number The average waiting time for each group of customers is calculated using equation 2. AWT = ( Σ CWT i ) / TN. (2) Where: AWT - Average Waiting Time; CWT - a Customer Waiting Time TN - total number of customers served; Table 2: Ordinary queuing bank system that uses only FCFS algorithm i - the number of customer Customer Service Arrival Difference C1 05 0 0 C2 10 5 15 C3 25 8 17 C4 30 15 15 C5 40 17 23 C6 45 19 26 C7 50 20 30 C8 60 25 35 C9 65 28 37 C10 70 30 40 C11 80 40 40 C12 95 42 53 C13 100 43 57 C14 105 44 61 C15 110 110 0 C16 125 111 14 C17 135 112 23 C18 140 113 27 C19 145 114 31 C20 150 115 35 The Average waiting time = Total 569 28.45 Copyright 2016 Published by IJESR. All rights reserved 85

Assignment of Priority to a particular task. First we assign the priority to a particular specified task and distribute the waiting customer in different queue (Diffuse Queue) according to their choice of work. Priority 1: Transaction Priority 2: Account Opening Priority 3: Balance Here we present different queue according to the priority for different servers. Priority 1: Transaction: Arrange the customer in a virtual queue in a database. C1 C4 C7 C10 C16 C20 Priority 2: Account Opening: Arrange the customer in a virtual queue in a database. C2 C11 C15 Priority 3: Balance: Arrange the customer in a virtual queue in a database. C3 C5 C6 C8 C9 C12 C13 C14 C17 C18 C19 Applying FCFS algorithm on different Servers Now apply the traditional FCFS method on different assigned priority servers. Server 1 for First Priority work C1 Idle C4 C7 C10 Idle C16 C20 0 10 15 25 35 45 111 121 131 Table 3: Priority 1. For Transaction Customer Service Arrival Difference Idle Time C1 0 0 0 0 - - - - 5 C4 15 15 0 0 C7 25 20 5 0 C10 35 30 5 0 - - - - 66 C16 111 111 0 0 C20 121 115 5 0 Average Waiting Time Total 15 71 = 15/6 = 2.5 Idle Time for Server 1 = 71 Server 2 for Second Priority work Idle C2 Idle C11 Idle C15 5 20 40 55 110 125 Table 4: Priority 2. For Account Opening Average Waiting Time = 0 Idle Time of Server 2 = 80 Customer Service Arrival Difference Idle Time - - - - 5 C2 5 5 0 0 - - - - 20 C11 40 40 0 0 - - - - 55 C15 110 110 0 0 Total 0 80 Copyright 2016 Published by IJESR. All rights reserved 86

Server 3 for Third Priority work Idle C3 Idle C5 C6 C8 C9 Idle C12 C13 C14 Idle C17 C18 C19 8 13 17 22 27 32 37 42 47 52 57 112 117 122 127 Table 5: Priority 3. For Balance Enquiry Customer Service Arrival Difference Idle Time - - - - 8 C3 8 8 0 0 - - - - 5 C5 17 17 0 0 C6 22 19 3 0 C8 27 25 2 0 C9 32 28 4 0 - - - - - C12 42 42 0 0 C13 47 43 4 0 C14 52 44 8 0 - - - - 55 C17 112 112 0 0 C18 117 113 4 0 C19 122 114 8 0 Total 33 73 Average Waiting Time = 33/11 = 3 Idle Time of Server 3 = 73 Algorithm: The minimum average waiting time using equation (1) and (2). CWT i = SSTC i ATC i Where: CWT - Customer Waiting Time SSTC - is Start Serving Time for a Customer ATC - Arrival Time for a Customer i - The i th Customer number The average waiting time for each group of customers is calculated using equation 2. AWT = ( Σ CWT i ) / TN Where: AWT - Average Waiting Time CWT - a Customer Waiting Time TN - total number of customers served i - the number of customer Idle: Where Idle represents the idle time when the server is free and having customer in the system for a specified task. Total Idle Time = 71 + 80 + 73 = 224 EXPERIMENTAL RESULT With the FCFS procedure for customer service we get from table 2 that, Average waiting time =28.45. which is too high and its result customer balking, hence loss of customer for organization. Copyright 2016 Published by IJESR. All rights reserved 87

By applying different priority assignment queue model with FCFS method we see from Table 3, 4 &5. The Average waiting time for server 1. = 2.5 The Average waiting time for server 2. = 0 The Average waiting time for server 3. = 3 Also from the same we see that the idle time, where there is no customer in the system Idle time for Server 1 = 71 Idle time for Server 2 = 80 Idle time for Server 3 = 73 Total Idle time = 224. Which can be utilize in other pending works. Like to maintain the records etc. CONCLUSION AND FUTURE WORK In a queue system, the balance between dealing with all customers fairly and the performance of the system is very important. Sometimes the performance of the system is more important than dealing with the customers fairly. In this paper, we have presented a new technique for queuing system called automatic queuing system. The proposed technique showed improvements in average waiting time. It will be more effect to add more factors in testing to take the right decision for choosing one of the available scheduling algorithms, such as throughput, utilization, and response time. Also adding more scheduling algorithms to the system database will be useful. Our model give efficient method to reduce average customer wait times and average queue length to within the requirements. REFERENCES [1] Ahmed SA, AL- Jumaily, Huda K.T, AL- Jobori. Automatic Queueing model for Banking Application. International Journal of Advanced Computer Science and Application. 2011; 2(7). [2] Allen A. Probability, statistics, and queuing theory with computer science applications. Academic Press Inc., Second Edition, 1990. [3] Bose KS. An introduction to queuing systems, Springer, 2002. [4] Goluby B, Preston McAfeez R. Firms, queues, and coffee breaks: A flow model of corporate activity with delays. Springer-Verlag, March 2011; 15: 59-89. [5] Hillier FS, Lieberman GJ. Introduction to Operations Research, Tata Mc-Graw Hill, 8th Edition, 2007. [6] Luštšik O. E-banking in estonia: Reasons and benefits of the rapid growth. University of Tartu, kroon and economy 2003; 3: 24-36. [7] Mohamad F. Front desk customer service for queue management system, Master Thesis, University Malaysia Pahang, November, 2007. [8] Mobarek A. E-banking practices and customer satisfaction- a case study in botswana, 20 th Australasian Finance & Banking Conference, 2007. [9] Willig A. A short introduction to queuing theory, Technical University Berlin, Telecommunication Networks Group Sekr. FT 5-2, Berlin, July 21, 1999. Copyright 2016 Published by IJESR. All rights reserved 88