Service efficiency evaluation of automatic teller machines a study of Taiwan financial institutions with the application of queuing theory

Transcription

1 Service efficiency evaluation of automatic teller machines a study of Taiwan financial institutions with the application of queuing theory Pei-Chun Lin Department of Transportation and Communication Science National Cheng Kung University 1, University Road, Taiwan 701 Taiwan R.O.C. Ann Shawing Yang Department of International Business and Trade Shu Te University Kaoshiung 824 Taiwan R.O.C. Abstract This study examines the service efficiency of 26 banking institutions in Taiwan (including the postal banking services) through the application of queuing theory by evaluating service efficiency of ATMs functions composed of cash withdrawal, fund transferring, password alternations and balance inquiry. Firstly, we apply design of experiment to collect the service times of four major ATMs functions and use goodness of fit to test the distribution of collected data. Then, the fitted queuing model is utilized to calculate average number of customers presented in the queuing system, average number of people waiting in the queue, average time a customer spends in the system and average time a customer spends in queue for evaluating the service efficiency of ATMs. Data was collected on field from July to August Study results found the most efficient banks and least efficient banks. This study also suggest some bank should add more ATMs to reduce customer waiting time and conclude some banks have installed too many ATMs for their current users. Keywords : Automatic Teller Machines (ATMs), queuing theory, service efficiency. peichunl@mail.ncku.edu.tw annyang@mail.stu.edu.tw Journal of Statistics & Management Systems Vol. 9 (2006), No. 3, pp c Taru Publications

2 556 P. C. LIN AND A. S. YANG 1. Introduction An Automatic Teller Machine (ATM) is an electronic device, which allows a bank s customers to make cash withdrawals and check their account balances at any time without the need for a human teller. Many ATMs also allow cash and check deposits. In modern ATMs, customers authenticate themselves by using a plastic card with magnetic stripes which encodes the customer s account number. A numeric password called PIN (Personal Identification Number) could, in some cases, change when using the machine. If the number is entered incorrectly several times consecutively, most ATMs will retain the card as a security precaution to prevent an unauthorized user from working out the PIN by pure guesswork. Survey finds customer service is watched closely and ATMs are just about everywhere (Anonymous (1989)). The Bureau of Monetary Affairs (BOMA) under the Financial Supervisory Commission in Taiwan has endowed missions to regulate the rapidly expanded banking industry since 1990s. The statistics of BOMA as of April 2005 show the total number of ATMs in Taiwan area amount to 21, 985 units and total number of cash card amount to 120, 675, 033 cards. Number of ATM transactions in April 2005 is 57, 232, 016 and the average number of ATMs usage is 2.5 times per citizen. More and more customers perceive ATMs as self-service, fast, efficient and available 24 hours, 365 days a year (American Bankers Association (1990)). The high utilization rate of ATMs in financial institutions has inevitably caused the phenomenon of waiting especially during peak hours. While the ATMs remain their current volume of service facility, customers are forced to extend queuing time or switch to human teller services, which increase transaction cost. Although to add more ATMs may relief the waiting problem, idle service facility could as well cause low utilization rate and result in a waste of facility cost. In Taiwan, liberalization and internationalization have become primary policies for banking industry. According to the Taiwan Russel EMPulse report in April 2005 (Russell EMPulse (2005)), Taiwan simply has too many banks for its 23 million citizens. The sheer number of banks has created a hypercompetitive banking environment in which profitability and returns are low. To intensify customer service, service quality and create competitive edge becomes an enviable goal for banks to reach. This paper is organized as follows. Section 2 presents the queuing theory applied in this study and some related literatures, followed by

3 AUTOMATIC TELLER MACHINES 557 methodology and data collected in Section 3. Sections 4 and 5 contains the empirical results and conclusions, respectively. 2. Related literatures D. G. Kendall in 1951 (Kendall (1951)) proposed a standard notation for classifying queuing systems into different types. The Kendall classification of queuing systems (1953) exists in several modifications. The most comprehensive classification uses 6 symbols a/b/c/d/e/ f. The first characteristic specifies the nature of the arrival process. M is the standard abbreviation used to specify interarrival times are independent, identically distributed (iid) random variables having an exponential distribution; GI specifies interarrival times are iid and governed by some general distribution. The second characteristic specifies the nature of the service times. M is also the standard abbreviation used to specify service times are iid and exponentially distributed; G represents service times are iid and follow some general distribution. The third characteristic is the number of parallel servers. The fourth characteristic describes the queue discipline, where FCFS represents first come, first served and GD represents general queue discipline. The fifth characteristic specifies the maximum allowable number of customers in the system. The sixth characteristic gives the size of the population from which customers are drawn. The birth-death methodology is used to analyze the properties of some specific queuing system such as M/M/1/GD/ /, which has exponential inter-arrival times (the arrival rate per unit time is assumed to be λ) and a single server with exponential service times (each customer s service time is exponential with rate µ). The traffic intensity (ρ) of the queuing system is equivalent to λ µ. Table 1 lists several quantities of interest assuming that the steady state has been reached for the M/M/1/GD/ / queuing system. We also consider banks employ multiple serves and serves work in parallel. Servers are in parallel if all servers provide the same type of service and a customer need only pass through one server to complete service. The average measures of performance of the steady state are listed in Table 2 for the M/M/s/GD/ / queuing system. Table 3 shows the derived results of the M/M/1/GD/ / queuing system by Pollaczek and Khinchin (Winston (1994)). The formulas list in Table 4 are proposed by Allen-Cunneen (Allen (1990)) and used to approximate the results of the M/M/s/GD/ / queuing system.

4 558 P. C. LIN AND A. S. YANG Table 1 Steady state quantities of M/M/1/GD/ / queuing system Quantity of interest Formula Traffic intensity ρ = λ µ Steady state probability of zero customer will be P o = 1 ρ present Steady state probability on n customers will be present Average number of customers present in the queuing system P n = (1 ρ)ρ n L s = λ (µ λ) λ Average number of people waiting in the queue L q = 2 (µ(µ λ)) Average time a customer spends in the system W s = L λ = 1 Average time a customer spends in queue (µ λ) W q = L q λ = λ (µ(µ λ)) Table 2 Steady state quantities of M/M/s/GD/ / queuing system Quantity of interest Traffic intensity Steady state probability of zero customer will be present Steady state probability on n customers will be present. The stead-state probability that all servers are busy Average number of people waiting in the queue Average number of customers present in the queuing system Average time a customer spends in queue Average time a customer spends in the system Formula ρ = λ sµ 1 P o = s 1 (sρ) i + (sρ)s i=0 i s!(1 ρ) P n = (sρ)n P 0 (n = 1, 2,..., s) n! P n = (sρ)n P 0 s!s n s (n = s, s + 1, s + 2,...) P(n s) = (sρ)s P 0 s!(1 ρ) L q = W q = L q λ P(n s)ρ 1 ρ L s = L q + λ µ = P(n s) sµ λ W s = L P(n s) = λ sµ λ + 1 µ

5 AUTOMATIC TELLER MACHINES 559 Table 3 Steady state quantities of M/M/1/GD/ / queuing system Quantity of interest Formula Traffic intensity ρ = λ µ Service time distribution S need not be exponential 1 µ = E(S), σ 2 = var(s) Average number of people waiting in the queue L q = λ2 σ 2 + ρ 2 2(1 ρ) Average number of customers present in the queuing system Average time a customer spends in queue L s = L q + λ µ W q = L q λ Average time a customer spends in the system W s = W q + 1 µ Table 4 Steady state quantities of M/M/s/GD/ / queuing system Quantity of interest Formula ( ) standard deviation of interarrival time 2 SqCV interarrival time SqCV service time Average number of people waiting in the queue Average number of customers present in the queuing system Average time a customer spends in queue mean interarrival time ( ) standard deviation of interarrival time 2 mean interarrival time W q = L q = λw q L s = λw Erlang S (1 utilization) SqCV interarrival time + SqCV service time 2 1 µ Average time a customer spends in the system W s = W q + 1 µ

6 560 P. C. LIN AND A. S. YANG Kolesar s study (Kolesar (1984)) determines customer service standards for automatic teller machines of a large retail bank led to the formulation and calibration of a finite waiting room M/M/c/K queuing model. The model suggested that the percentage of lost customers be adopted as the service standard instead of line wait. The new standard was applied against existing transaction reports to identify those congested ATM facilities that could best profit from additional machines and lobby space. The magnitude of the increased business at the upgraded facilities partly confirmed the model s hypothesis that substantial numbers of customers had indeed been balking. In 2004, Wang, Batta and Rump present several models for the location of facilities subject to congestion. Motivated by applications to locating servers in communication networks and automatic teller machines in bank systems, these models are developed for situations in which immobile service facilities are congested by stochastic demand originating from nearby customer locations. They consider this problem from three different perspectives, that of (i) the service provider (wishing to limit costs of setup and operating servers), (ii) the customers (wishing to limit costs of accessing and waiting for service), and (iii) both the service provider and the customers combined. In all cases, a minimum level of service quality is ensured by imposing an upper bound on the server utilization rate at a service facility. 3. Methodology This study firstly applies design of experiment to collect the service times of four major ATMs functions and uses goodness of fit to test the distribution of collected data. Then, the fitted queuing model is utilized to calculate average number of customers presented in the queuing system, average number of people waiting in the queue, average time a customer spends in the system and average time a customer spends for evaluating the service efficiency of ATMs. 3.1 Experimental design This study collects statistical data through volunteer contributions for personal financial and security reasons. Although ATMs are originally

7 AUTOMATIC TELLER MACHINES 561 developed as cash dispensers, they have evolved to include many other bank-related functions. Each volunteer will examine four frequently used functions of ATMs including cash withdrawal, inter-bank transfers, balance inquiries and password alternations for five times resulting thirty statistical data. Each time records only one statistical data to avoid learning effect of volunteers from repeated use of ATMs that may produce bias data. During evaluation, this study considers the following: I. Service time continues to accumulate even occurs during testing. Errors could occur due to wrong input, unfamiliarity, time pressure or interface unclearness. II. ATMs of various financial institutions are tested according to random number. Collected statistical data will calculate in average service rate chart according to alphabetical order of banks. Random number is applied to select the testing order of ATMs to eliminate learning effect. III. Tested ATMs are under normal conditions that all service functions could perform accordingly. Examples are cash dispenses and absence of temporary out of order. IV. Each ATM was measured by cash withdraw card of corresponding bank. Many banks in Taiwan charge fees for non-members to use their ATMs. For consistency, ATM service efficiency analysis avoid utilization of cash withdraw cards from other banks that could affect study credibility. Therefore, each ATM was measured only by cash withdraw card issued by corresponding bank. V. Tested dollar amount is fixed at NT$100 for each cash withdrawal and NT$100 for each fund transfer. VI. Average service efficiency is measured everyday during fixed time periods. In order to avoid processing efficiency variations of ATMs during different time periods that could affect service efficiency analysis result, testing is performed between 7:30 and 9:30 p.m. every afternoon. 3.2 Data collected Figure 1 presents the average arrival rate per hour for the 26 financial institutions located in downtown area of the same city in Taiwan. While the average arrival rate for all banks is between 30 to 40 persons per hour, Bank V and bank C have the highest and lowest average arrival rate at

8 562 P. C. LIN AND A. S. YANG Figure 1 Average arrival rate per hour Figure 2 Time (seconds) required for cash withdraw

9 AUTOMATIC TELLER MACHINES 563 Figure 3 Time (seconds) required for inter-bank transfer Figure 4 Time (seconds) required for balance inquiries

10 564 P. C. LIN AND A. S. YANG Figure 5 Time (seconds) required for password alternation 70 persons per hour and 5 persons per hour, respectively. Figure 2 presents time required for cash withdraw. The average time spent in cash withdraw is between 30 and 40 seconds. Bank S and Bank X have the longest cash withdraw time at seconds and seconds, respectively. Bank H has the least cash withdraw time at seconds. Figure 3 presents average time spent in inter-bank transfer. Bank Y has the longest average inter-bank transfer time at seconds followed by Bank N at 74 seconds and Bank J at seconds. Bank X has the least inter-bank transfer time at seconds. Differences in average inter-bank transfer time are primary caused by unnecessary operations setup in ATM interface. The maximum operation time is about double of the minimum operation time. Figure 4 presents the time spent in balance inquiry. Bank V has the least average balance inquiry time at seconds followed by Bank K at seconds and Bank D at seconds. Bank A shows the most average balance inquiry time at seconds followed by Bank Q at 34.9 seconds and Bank P at seconds. Figure 5 present average time spent in password alternation. The minimum and maximum average password alternation times are Bank I at seconds and Bank F at seconds with a difference of 20 seconds. Of which, balance inquiry function seems to require minimal time in comparison with three other functions. Statistics of individual banks show inter-bank account transfer requires more time than the three other functions. This is due to operator would repeatedly check the account number of receiver and the amount entries to avoid unnecessary losses.

11 AUTOMATIC TELLER MACHINES Goodness of fit Goodness of fit is used to decide if above statistics come from the population of ATMs users with a specific distribution. The formulas listed in Table 1, Table 2, Table 3 and Table 4 for mapping queuing systems are applied to calculate average number of customers present in the queuing system, average number of people waiting in the queue, average time a customer spends in the system and average time a customer spends in queue for evaluating the service efficiency of ATM. This study applies Kolmogorov-Smirnov test to examine whether those independent observation values originated from any identical probability distribution. Arrivals are defined as non-overlapping time intervals that are independent and for small t (and any value of t), the probability of one arrival occurring between times t and t + t is λ t + o( t), where o( t) refers to any quantity satisfying lim = 0. Also, the probability t 0 o( t) t of no arrival during the interval between t and t + t is 1 λ t + o( t), and the probability of greater than one arrival occurring between t and t + t is o( t). Therefore, inter-arrival times are exponential with parameter λ. Customer arrival are indeed random and adequately represented by a Poisson probability distribution. The mean arrival rate varied, depending on time of day and day of week. However, developing operating characteristic information for the peak or high demand periods is important. An average of the top 6 hourly demands is used to determine the mean arrival rate for each site we observed. Results of the Goodness of fit for service time do not support exponential distribution. However, observed service times showed that the Normal probability distribution provided a reasonable approximation of the service time distribution. Table 5 presents the p-value of testing Normal on service time for each financial institute. We conclude it is suitable to apply the Allen-Cunneen approximation (Allen (1990)) to the M/G/s/GD/ / queuing system. Table 5 P-value of testing Normal on service time Bank P-value A B C (Contd. Table 5)

12 566 P. C. LIN AND A. S. YANG Bank P-value D E F G H I J K L M N O P Q R S T U V W X Y Z Results Service efficiency measured by ATM interface functions including cash withdrawal, fund transferring, password alternation and balance inquiry is firstly ranked from a 1 to 26 scale with 1 representing the most efficient ATM and 26 representing the least efficient ATM for a study sample of 26 financial institutions. Table 6 presents the final ranking of average service time of automatic teller machines. Results evidenced three most efficient banks are Bank 1, Bank D and Bank K and two least efficient banks are Bank Y and Bank N. Figure 6 compares ATM utilization amongst sampled banks. Results evidence minimum utilization rate for Bank C and Bank P due to sparse users and only one ATM server installation, respectively. It is recommended that Bank P could increase one ATM server installation to meet customer demand.

13 AUTOMATIC TELLER MACHINES 567 Table 6 Ranking of average service time Bank Cash Fund Password Balance Total Final code withdrawal transfer alternation inquiry ranking I D K V E U H G W O S C M X P T Q R F Z L J B A Y N Cash withdrawal is the most utilized ATM function from our observation. Figure 7 presents the average number of customers in queuing system for ATM services. Figure 8 presents the average time per customer spent in queue and system. Results evidence Bank A and Bank Q possess minimum average number of customers in queue. It is observed Bank A has installed four ATMs and Bank Q has installed three ATMs that could achieve the minimal time spent in queue and the least number of customers in queue. Bank P, with only one ATM installation, is evidenced

14 568 P. C. LIN AND A. S. YANG Figure 6 Utilization rate Figure 7 Average number of customer in queue (L q ) and system (L s )

15 AUTOMATIC TELLER MACHINES 569 Figure 8 Average time customer spent in queue (W q ) and system (W s ) with maximum average number of customers and queuing time due to maximum average arrival rate. One ATM is insufficient to meet the peak demand and more than 55% of the customers would have to wait. In addition, Bank A and Bank Q are evidenced with overly low ATM utilizations that could suggest a lesser ATM installation. We take Bank A as an example: onsite observations were conducted to verify the peak arrival rate of 36 customers per hour. From the observed session, the mean service rate per ATM was estimated 90 customers per hour. Four ATMs cause the server utilization as low as Conclusions This empirical study examines the service efficiency of Automatic Teller Machines (ATMs) of 26 financial institutions including the postal banking services in Taiwan. Field observations were conducted in every afternoon during one peak hour from July to August 2004 on ATMs located at banks. Observations were recorded by functions of ATMs that consist of cash withdrawal, fund transferring, password alternation and balance inquiry. First of all, we list the ranking of service efficiency for the 26 chosen site of banks. Lesser final accumulated time required represents better service efficiency while greater final accumulated time represents worse service efficiency of ATMs. Final ranking is made on a grand total of service time of four various functions. Among 26 financial institutes, Bank

16 570 P. C. LIN AND A. S. YANG I, D and K are the three best in average service time require. Secondly, we applied queuing theory and the Allen-Cunnen approximation method to the data collected and calculated important information in the waiting line that are: average number of customers in the waiting line; average number of customers in the system; average time a customer spends in the waiting line; and average time a customer spends in the system. According to above information, we suggest Bank P should add one more ATM to reduce the waiting time of customers and Bank A has installed four ATMs that are too many for its current members. Future suggestions on ATM functions are the inclusion of Hakka and Taiwanese languages as well as cash card, deposit, cash advances and check remittance at the initial interface operating page. Fund transferring should classify account transfers by appointed and un-appointed interbank and cross-bank account banks to protect customers from cash card fraud. References [1] American Bankers Association, Can customers change their ATM perceptions? ABA Banking Journal, Vol. 82 (5) (May 1990), pp [2] American Bankers Association, Banks reveal deposit policies, anonymous, ABA Banking Journal, Vol. 81 (5) (May 1989), pp [3] A. O. Allen, Probability, Statistics and Queuing Theory with Computer Science Application, 2nd edition, Academic, New York, [4] R. EMPulse, Russell EMPulse s Report on Taiwan, [5] D. G. Kendall, Some problems in the theory of queues, Journal of Royal Statistics Society, Series B, Vol. 13 (1951), pp [6] D. G. Kendall, Stochastic processes occurring in the theory of queues and their analysis by the method of the imbedded Markov chain, Annals of Mathematical Statistics, Vol. 24 (3) (1953), pp [7] W. L. Winston, Operations Research: Applications and Algorithms, 3rd edition, Duxbury Press, (1994), pp [8] P. J. Kolesar, Stalking the endangered CAT: a queuing analysis of congestion at automatic teller machines, Interfaces, Vol. 14 (6) (1984), pp [9] Q. Wang, R. Batta and C. M. Rump, Facility location models for immobile serves with stochastic customer demand, Naval Logistics Research, Vol. 51 (1) (2004), pp Received July, 2005