Analysis of queue change of visitors and performace system in the Department of Population and Civil Regristation of Semarang City

The Population and Civil Registry Office in Semarang city is one of the public service units. In the public service sector, visitor / customer satisfaction is very important. It can be identified by the length of the queue, the longer visitors queue this results in visitor dissatisfaction with the service. Queue analysis is one of the methods in statistics to determine the distribution of queuing systems that occur within a system. In this study, a queuing analysis as divided into two periods. The first period lasts from 2-13 March 2015, while the second period lasts November 16th to December 20th 2019. The variables used are the number of visitors and the service time at each counter in intervals of 30 minutes. The results obtained are changes in the distribution and queuing model that is at counter 5/6 and counter 10. The queuing model obtained at the second perideo for the number of visitors and the time of service with a General distribution. The average number of visitors who come in 30 minute intervals in the second period is more than the first period, this indicates an increase in visitors. The opportunity for service units is still small, the waiting time in the queue is getting smaller. This shows that the performance of the queuing system at the Semarang Population and Civil Registry Office is getting better.


Introduction
Queuing is a common thing and often happens in everyday life. Most people consciously or unconsciously, have experienced a queue situation or often referred to as a waiting situation. The queue process is a process related to the arrival of a customer at a service facility, then waits in line or queue if it has not received service and finally leaves the

The Queuing System
According to Kakiay (2004) [3], a queue is a waiting line of a number of customers who require service from one or more service facilities. A queuing process is a process associated with the arrival of a number of customers at a service facility, then waits in a queue line if it cannot be served, and finally leaves the service facility after being served. While the queuing system is a set consisting of customers, servants, and a rule that regulates service to customers. There are several important factors that are closely related to the queuing system. The factors that influence the queue and service lines are the distribution of arrival, the distribution of time services, the facility of services, service discipline, the measure of queue, source of calling. According to Taha (1996) [4], Kendall's notation is used to detail the characteristics of a queue. Appropriate notation for summarizing the main characteristics of parallel queues has been universally standardized in the following format: (a / b / c) : (d / e / f ) a : arrival distribution; b : the distribution of time services; c : the facility of services (for c = 1, 2, 3, … ∞); d : service discipline (FIFO, LIFO, SIRO, and priority of services); e : The size of the system in the queue or the maximum number allowed in the system (finite or infinite); f : Number of customers who want to enter the system as a source (finite or infinite); Steady state conditions are met if the value of the level of usefulness (ρ) <1 means the average rate of arrival of visitors to the death counter is smaller than the average rate of service. This can also be interpreted that a condition where the number of visitors who come are still able to be served effectively and vice versa if the arrival rate of visitors is too much so that the server is not able to serve all of them there will be a buildup of visitors queue.For example λ is the average number of customers who come to the service per unit of time and µ is the average number of customers that have been served per unit of time, then [5]. (1)

Poisson Process
According to Gross and Harris (1998) [6], the process of number of arrivals is considered {N (t), t ≥ 0}, where N is denoted the number of arrivals that occur until time t, with N (0) = 0, which follows the three assumptions as follows: 1. The probability of one arrival occurring between time t and is equal to . It can be written that Pn = {arrivals occur between t and } = , where λ is a constant that is independent of N (t), is an added time element, and is denoted as the number of arrivals that can be ignored when compared with , with 2. Pn (t) {more than one arrival between t and } is very small or can be said to be ignored = 3. The number of arrivals at successive intervals is fixed / independent, which means that the process has free additions.

The testing of Fit Distribution
According Daniel (1989) [7], there are tho method that used to fit test distribution of observatioan such as Kolmogorov-Smirnov and Chi Quadrat testing. The procedure of Kolmogorov-Smirnov testing as follow as: Hypothesis of testing H0 : The distribution of observation is equivalent with Poisson distribution H1 : The distribution of observation is Not equivalent with Poisson distribution with significant level , and the test of statistics is D = sup |S(n) -F0(n)| (2) Criteria of testing is H0 rejected for > Dtable (D*α/2, n)or the value of significant less than significant level where Dtable (D*α/2, n) is Kolmogorov-Smirnov's The distribution of observation is Not equivalent with Poisson distribution with significant level , and the test of statistics is: (3) where is observation value i-th; and the expected value of observation i-th, for Criteria of testing is H0 rejected for # ≥ %,' # dengan v = r-1-g, g is the number of coloumn; r is the number of row.

(M/G/1) : (GD/∞/∞) queue model
The (M/G/1):(GD/ model called to The Pollaczek-Khintchine (P-K) is a formula that will be obtained in a single service situation that fulfills the following three assumptions [8]: 1. Poisson arrival with an average arrival . 2. Distribution of general or general service time with average service expectations is . (4) 3. Steady state with = E{t} < 1 or .
In the P-K formula, a system performance measurement is obtained for (M/G/1): (GD/∞/∞) model as follow as: 1. Estimated number of customers in the system: 2. The estimated number of customers in the queue: Lq = Ls -E{t} 3. Estimated time in the system:Ws = 4. The estimated waiting time in the queue:Wq =

(M/M/c) : (GD/∞/∞) queue model
In the queuing model the customer arrives with an average arrival rate is λ and maximum c customers who can be served together. By example and , probability values for 0 customers can be written [9]: System performance measurement for (M/M/c):(GD/∞/∞) model as follow as: 1. Average waiting in queue: (7) 2. Average number of customers waiting in the system: (8) 3. Average time customers wait in a queue: = (9) 4. Average time customers wait in the system: (10)

(G/G/c) : (GD/∞/∞) queue model
The system performance measures in this General model follow the performance measures in the M / M / c model, except for the calculation of the estimated number of customers in the queue (Lq) as follows [10]: (11) with v(t) is a variant of service time; v(t') is a variant of interarrival times.

Methodology Of Research
The data used in this study are primary data, that is data taken from observations and records of visitors at the Semarang City Dispendukcapil office. The study period was divided into two periods, the first period was 2-13 March 2015, while the second period was 16 December to 20 November 2020. The variables used in this study were data on the number of arrivals and service times of visitors at the Semarang City Dispendukcapil office. The steps in conducting research and data analysis are as follows: distribution is accepted, then the distribution follows the Poisson distribution and if the hypothesis is rejected, the arrival distribution is generally distributed. Whereas if the hypothesis for the distribution of services is accepted, then the distribution follows the Exponential distribution and if the hypothesis is rejected, then the distribution of services is publicly distributed. 3. Determine the appropriate queue model. In this case, for each place, namely the counter legalized, counter changes in data, counters of birth, counters of death, divorce / marriage counters, counters counters.

Steady State Size Analysis of Service System Performance
Based on Table 1, there is a change in the number of servers for the birth counter, which in the first period amounted to 3 in the second period to 2 servers. In the table shows that, the value of ρ is less than 1, this shows that the process of antrain in each window shows a steady state. In the first period, the number that was served at most per 30 minutes was the data change counter, while the number that was served the least was the legalized counter. Whereas for the second period, the average amount served at most per 30 minutes is the legalization part, but the average that is served at least is the birth counter. An increase in the average number of arrivals per 30 minutes from the first period to the second period. With c: many servers / number of service facilities; λ = average number of arrivals per 30 minutes; μ = average number served per 30 minutes; and ρ = level of service facility usage with ρ = λ / (c × μ).

Fit Test Distribution of Number of Arrivals and Service Time
Distribution fit testing uses the Kolmogorov Smirnov and Chi Square test. In this study the number of arrivals was tested using Kolmogorov Smirnov. While testing the arrival time using Kolmogorov Smirnov and Chi Square.  Table 2 shows the distribution fit test for the number of arrivals at each counter. There was a change in the distribution of arrivals at counters 5/6 and counters 10. These counters have Poisson distribution in the first period, but as the number of arrivals increased every 30 minutes from the first period to the second period, there was a change to the not Poisson distribution.  Table 3 shows the distribution match test for service time. Based on table 3, there is no change in distribution for service time. The results obtained indicate that the service time is not distributed by Poisson.

Queue Model Systems
Based on the results of the analysis of the steady state size of the performance of the service system and the fit test of the distribution of the number of arrivals and service times of visitors at the Semarang City population and civil registry office, the queuing system model obtained is as follows:

System Performance Measures
From the queuing model obtained, the size of the queuing system performance for the first and second periods. Table 5 and Table 6 show the system performance measures with the statement c is the number of servers / number of service facilities; λ is the average number of arrivals per 30 minutes; μ is the average number served per 30 minutes; Ls is the estimated number of visitors in the system; Lq is the estimated number of visitors in the queue; Ws is the estimated waiting time in the system; Wq is the estimated waiting time in the queue; P0 is the probability that service personnel are unemployed.  Table 5 and Table 6 show the queuing system performance measures for the first and second periods. Based on the table, it can be seen that there is an increase in the average number of arrivals every 30 minutes at each counter, although at counter 4 it can be assumed to be the same. While the average amount served is also increasing from the first period to the second period, it shows that there is speed of service in the system. While the estimated number of visitors in the system in the second period is less than 1, it shows that visitors do not have to wait long to be served. It is also shows the waiting time in the system and the waiting time in the second period is close to zero. It is different from the first period, the number of visitors at Counter 4 tends to accumulate.
There is a queuing system for the first period that the opportunities for unemployed service personnel are very varied, counter 4 has the smallest chance of being unemployed compared to other counters, while counter 5/6 has a very high chance of unemployment. This is certainly different from the second period, where in the second period shows the opportunity to manage it almost evenly around 40-50%. In this analysis shows that the population and civil registration department of the city of Semarang has improved the queue system better. Customers are well served without waiting for a long time.

Conclusion
Queue system at Counter 4 (counter legalized); counters 5/6 (counters of data changes), counters 7, 8, and 9 (counters of birth); counters 10 (counters of death) in the first and second periods are stable because they have a utility value of less than 1. There is a change in the number of servers, namely at counters 7, 8, 9 (birth), which originally amounted to 3 reduced to two. The average number of arrivals in 30 minute intervals is more in the second period compared to the first period. In the first period the most number of arrivals was counter 4, while in the second period the most number of arrivals was at counter 4 and counter 7, 8, 9. However, if you see the distribution of arrivals at each counter is almost the same, ranging from 5-6 visitors every 30 minutes. In the analysis of the two periods it was found that there has been an improvement in services at the Semarang City Occupation and Civil Registry Office. Service time is more efficient, fewer visitors waiting in the queue, so there are fewer visitors waiting in the system.