### I. Introduction

### II. Methods

### 1. Queueing Theory

*L*), the average number of customers in its entire system including the entity being served (

_{q}*L*), the average waiting time in its queue (

_{s}*W*), and the average waiting time in its entire system (

_{q}*W*). The symbols and concepts for a queueing model are presented in Table 1.

_{s}### 2. Our Approach

*W*) as in Table 1. Thus, it is possible to measure the decrease in outpatients' waiting times before and after the introduction of EMR.

_{q}#### 1) Data collection

#### 2) Calculation of arrival rate

#### 3) Calculation of service rate

*t*-test to verify whether there was any difference between the service rates obtained from the digital and observed data (Table 4). Since we were able to conduct observation during just one day, we used digital data for the same day of observation. The differences between the average service rates were 67.47 and 14.9 in the first and second investigations in Hospital A, 12.68 and 25.37 in Hospital B, and 65.66 and 58.06 in Hospital C. We found that there was no statistically significant difference between the service rates obtained from digital and observed data except in the first investigation in Hospital A, where the service rates from the digital and observed data were statistically significantly different with the

*p*-value of 0.001. Although we cannot argue the consistency of the service rates statistically because only six comparison data sets were considered, we may claim that the service rates from the digital and observed data were similar to each other and the service rates obtained from digital data, which were based on huge data sets, were more accurate than the service rates obtained from observed data, which were based on a limited number of data sets.

### III. Results

### IV. Discussion

*t*-test to verify the service rates, we may need more data sets than the six from the three hospitals to argue the statistical significance and generalize our approach. Furthermore, the result of reduction in waiting times might differ according to the size of the hospital. Large hospitals usually provide their services based on appointment, which results in a shorter time for chart delivery, which in turn results in a smaller reduction in waiting times. Hence, extended studies considering hospital size with more data sets are recommended.