final exam dyanamic modeling system (queue) ihwan ghazali - jp1

8/7/2019 Final Exam Dyanamic Modeling System (Queue) Ihwan Ghazali - JP1

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DYNAMIC MODELINGSYSTEM QUEUETake home Final Exam IHWAN GHAZALI ST.


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Ihwan Ghazali (Joint Program Class UGM ITB Uka German)

INTRODUCTION

Queue is a normal occurrence that is found in everyday life, such as people queue

in front of ticket counters at a show, eat at home, in the supermarket cashier, bank, and

others. In manufacturing, the queue is often the case, for example, when the raw materials

must be queued to enter the factory floor or half-finished goods must be queued to enter

the production process further. Queue can be seen in the other traffic light, cars queue for

incoming ships in the harbor, truck-haul trucks that are waiting, and others. People or

goods (hereinafter referred customer) generally must be queued to get a "service" because

of the limited service facilities.

In fact, often must be queued customer too long, so spend the time and "cost of

waiting". Not rare among them choose to go out because the system would not queued

too long. To avoid this the number of service facilities (server) may be. However, the

amount is too much also raises a new problem, namely the cost of the procurement

server. Not to mention the risk delay servers on hours customer a certain amount of time

a little, while the cost for the server continues to exist. Therefore, the model required a

queue system, where the model is expected to be designed a queuing system a more

efficient, especially in terms of cost. Destination queue is a basic model to minimize costs

include direct costs and the cost of providing a server that does not directly arise because

customer have to wait to be serviced.

2. Basic Model Structure Queue

In analyzing the queue, the three main components, namely:

a. Arrival or input system

b. The Queue

c. Service facilities

The three components are illustrated in the image below:


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The sistem can be describe like this follow :

Qin : rate of customer entry to the restaurant (people/min)

Qserved : rate of served customer (people/min)

Qout : rate of unsatisfy customer (people/min)

Coperator : Operator capability to serve customer (people/meter)

Input

Output


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L : length of queue (meter)

T : time (min)

NQueue : people queueing (people)

: density of queue (people/ meter)

K : constant of unsatisfied consumer walkout per length of queue (people/ meter)

Base Equation:

+= disgenoutinacc mmmmm

In this case the gnereation side is not avaible because no genereation in queue

method.

..OWservedinserving QQQQ =

..OWservedinoperator QQQdt

dLC = ; KLQ OW =..

KLQQdt

dLC servedinoperator =

(

operator

servedin

C

KLQQ

dt

dL =

operator

in

operator

served

operator C

Q

C

QL

C

K

dt

dL=++

Assumtion that the capability of operator is constant

Where:L

NQUEUE= , Then

QUEUENL =

operator

in

operator

servedQUEUE

operator

QUEUE

C

Q

C

QN

C

KN

dt

d=++

Finally:

operator

in

operator

served

QUEUE

operator

QUEUE

C

Q

C

QN

C

K

dt

dN =++


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A number of arrival

A number Of served

Time

Anu

mberOfArrival

to know about kind of graphical from the equation, I use some treatment of arrival :

1. Random Arrival

2. Sinous Arrival

3. Ramp Arrival

4. Pulse Arrival

Random Model

Its mean that the arrival is used radom Quantity.

Random Quantity (Qin)


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AnumberOfArrival

Time

Anumber of arrival

A number Of serve

SIN MODEL

Time

AnumberOfArrival

Anumber of arrival

A number Of served

RAMP MODEL

PULSE MODEL


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Time

AnumberOfArrival

Anumber of arrival

A number Of served


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Example case solve Using By Arena1. Observation of time arrival of costumer

From The observation of time in operator in indomaret glagahsari can be taken like data :

Tabel 1. Data waktu antar kedatangan Cutomer

Furthermore can be made interval of random number to make time between arrival of

customer .

2. Observation time Service

From the observation can be taken the time of data service and interval number of

random as follow :

Tabel 1. Data waktu Pelayanan

Time ofservice

observationfrequency

1 10

2 30

3 20

4 30

5 20

6 10

Sum 120

Interval Arrival(minute) Observationfrequency

0 10

1 20

2 30

3 30

4 20

5 10

Sum 120


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Queue


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Fitting data (arrival)

Distribution Summary

Distribution: BetaExpression: -0.5 + 6 * BETA(2.22, 2.15)

Square Error: 0.001423

Chi Square TestNumber of intervals = 4

Degrees of freedom = 1Test Statistic = 0.516

Corresponding p-value = 0.482

Data Summary

Number of Data Points = 120Min Data Value = 0

Max Data Value = 5Sample Mean = 2.5

Sample Std Dev = 1.39

Histogram Summary

Histogram Range = -0.5 to 5.5Number of Intervals = 6


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FITTING DATA (Server)

Distribution Summary

Distribution: BetaExpression: 0.5 + 6 * BETA(0.158, 0.167)

Square Error: 0.008207

Chi Square TestNumber of intervals = 5

Degrees of freedom = 2Test Statistic = 2.6

Corresponding p-value = 0.282

Data Summary

Number of Data Points = 60

Min Data Value = 1Max Data Value = 6Sample Mean = 3.42

Sample Std Dev = 1.45

Histogram Summary

Histogram Range = 0.5 to 6.5Number of Intervals = 6


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Queues10:05:03PM March 15 2009

Unnamed Project Replications: 1

Replication 1 Time Units:Start Time: Stop Time:0.00 480.00 Minutes

Queue Detail Summary

Time

Waiting Time

Server 1.Queue 5.99

Other

Number Waiting

Server 1.Queue 12.62

Model Filename: Page of1 2Model1


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Category by Replication10:03:32PM March 15,2009

Unnamed Project 1Replications:


Entity

Time

VA Time MaximumMinimumAverage Half Width

Entity 1 (Correlated) 0.00000024 1.00000.4790

NVA Time MaximumMinimumAverage Half Width

Entity 1 0.000000000 0 00

Wait Time MaximumMinimumAverage Half Width

Entity 1 (Correlated) 0 22.70145.9773

Transfer Time MaximumMinimumAverage Half Width

Entity 1 0.000000000 0 00

Other Time MaximumMinimumAverage Half Width

Entity 1 0.000000000 0 00

Total Time MaximumMinimumAverage Half Width

Entity 1 (Correlated) 0.00026611 23.11936.4563

Other

Number In Value

Entity 1 983

Number Out Value

Entity 1 940

WIP MaximumMinimumAverage Half Width

Entity 1 (Correlated) 0 50.000013.5617

Queue

Time



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10:03:32PM March 15, 2009

Unnamed Project 1Replications:


Queue

Time

Waiting Time MaximumMinimumAverage Half Width

Server 1.Queue Correlated 0 22.70145.9935

Other

Number Waiting MaximumMinimumAverage Half Width

Server 1.Queue (Correlated) 0 49.000012.6233

Resource

Usage

Instantaneous Utilization MaximumMinimumAverage Half Width

Resource 1 Correlated 0 1.00000.9384

Number Busy MaximumMinimumAverage Half Width

Resource 1 (Correlated) 0 1.00000.9384

Number Scheduled MaximumMinimumAverage Half Width

Resource 1 (Insufficient) 1.0000 1.00001.0000

Scheduled Utilization Value

Resource 1 0.9384

Total Number Seized Value

Resource 1 941.00

System

OtherNumber Out Value

System 940



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By using the arena we can know about productivity between customer and trader. Like ( waitingtime of operator.

Conclusion

1. In this model have two kinds to solve the model. the first one is using the Matlab. Thissoftware is used to solve the calculation of equation like the above. In queue model the

input of the system is a number of arrival and the process is service by server and the

output is a number has be served.

And the final equation is

operator

in

operator

served

QUEUE

operator

QUEUE

C

Q

C

Q

NC

K

dt

dN =++

We can treath the input (Qin) to change suitable with real condition.(random , ramp, ,

sinus).

2. The second model is used Arena Software.

In this soft ware like the example, we can calculate the real time of process, queue time

(server, and arrival). The distribution can be seen in the fitting the data.

Suggestion :

The process may be have to pay attention more carefully, if the system have a queue, it

mean that have the problem of the system. So we have to decide how the optimal of

operator in the system. It can be influent for efficiency system, but the manager have to

know that if we add the operator it mean that the company have additional cost again. By

using the modeling system of queue, we can determine how the require of operator in thesystem (Optimal Operator). The best answer to solve the queue, i

final exam dyanamic modeling system (queue) ihwan ghazali - jp1

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