4 manual simulation

Kleber Barcia V.

Chapter 4

Manual Simulation

Manual simulation of discrete

events

Kleber Barcia V.

Chapter 4

2

Important concepts ...

System

Model

System state

Entity

Attributes

Event

Activities

A list is a collection of permanent or temporary entities sorted under a certain logic. Example: Customer ordered under FIFO queue.

An event notice is the record of an event occurring or will occur in the future associated with the data necessary for the execution of the event.

Kleber Barcia V.

Chapter 4

3

Important concepts ...

A event list is a list of event notices for future events sorted based on time of occurrence. Also known as Future Event List (FEL).

An activity is typically a service time or interarrival time.

The duration of an activity can be specified in three different ways:

1. Deterministic (5 minutes)

2. Statistical (as random numbers 2, 5, 7 with equal probability)

3. As a function depending on the variables of the system (the loading time of a vessel as a function of loading rate ton/hr)

Rev. 1

Kleber Barcia V.

Chapter 4

4

Example 1: Queue system with two servers

A computer technical support center is staffed by two people, Abel and

Baker, who take calls and try to answer questions and solve computer

problems. The time between calls ranges from 1 to 4 min. Service time

varies depending on the employee between 2 to 6 min. Abel is more

experienced and can provide service faster than Baker. Abel has

priority to serving customers.

The discrete event model has the following components:

System State

LQ (t) = Number of callers waiting to be served at time t

LA (t) = 0 or 1 indicating that Abel is idle or busy at time t

LB (t) = 0 or 1 indicating that Baker is idle or busy at time t

Entities

Neither clients nor servers are represented explicitly in the model

Kleber Barcia V.

Chapter 4

5

Example 1: Queue system with two servers

Events

Events of arrival

The completion of service by Abel

The completion of service by Baker

Activities

Interarrival time defined in the simulation table

Abel service time defined in the simulation table

Baker service time defined in the simulation table

Delay

The customer waiting in queue until Abel and Baker are available to

address them

Kleber Barcia V.

Chapter 4

6

The Event Scheduling/Time Advance Algorithm

It is the mechanism that ensures that all events occurring in the

chronological order in which advances the simulation time. It is

based on the list of future events (FEL)

Example 2: Single Server Queue

A shop has one dependent. Customers arrive randomly at

intervals of 1-8 min. with an equal chance of occurrence. The

service time varies from 1-6 min. with a given probability.

Find the total time the server is busy (B) and the number of

customers waiting in queue (MQ) in a simulation of 60 min.


Kleber Barcia V.

Chapter 4

7


System State

LQ (t) = number of customers waiting in queue at time t

LS (t) = number of customers being served at time t

Entities

Customers are not explicitly represented in the model

Events

Arrivals (A)

Outputs (D)

Stopping event (E) scheduled to occur at time 60

Kleber Barcia V.

Chapter 4

8


Future Event List

(A, t) Arrival Client will happen at some future time t

(D, t) out of the client that will occur at a future time t

(E, t) Stop the simulation will happen in time 60

Activities

Interarrival time

Service time

Delay

While the customer waits in queue

Interarrival time 8 6 1 8 3 8

Service time 4 1 4 3 2 4

Kleber Barcia V.

Chapter 4

9

Example 2: Single Server Queue Simulation Table

System State Cumulative

Statistics

Clock LQ(t) LS(t) Future Event List Comment B MQ

0 0 1 (D,4) (A,8) (E,60) First A occurs 0 0

(a*=8) Schedule next A

(s*=4) Schedule first D

4 0 0 (A,8) (E,60) First D occurs: (D,4) 4 0

8 0 1 (D,9) (A,14) (E,60) Second A occurs:(A,8) 4 0

(a*=6) Schedule next A

(s*=1) Schedule next D

9 0 0 (A,14) (E,60) Second D occurs:(D,9) 5 0

14 0 1 (A,15) (D,18) (E,60) Third A occurs:(A,14) 5 0


15 1 1 (D,18) (A,23) (E,60) Fourth A occurs:(A,15) 6 1

(Customer delayed)

18 0 1 (D,21) (A,23) (E,60) Third D occurs: (D,18) 9 1


21 0 0 (A,23) (E,60) Fourth D occurs:(D,21) 12 1

a * = Interarrival time s * = service time Rev. 1

Kleber Barcia V.

Chapter 4

10

Example 3: Extension of Example 2

Suppose that in the previous example is required to estimate the average time that the customer spends in the system and proportion of customers who spend 4 or more minutes in the system.

To perform this calculation the system is expanded with the following components:

Entities

(Ci, t) represents the client Ci at a time t. Customers are explicitly represented in the model.

Future Event List

(A, t, Ci) represents the arrival of client Ci at a future time t

(D, t, Cj) represents the output of Cj client at a future time t

Three new statistics should be calculated:

Rev. 1

Kleber Barcia V.

Chapter 4

11

Example 3: Extension of Example 2

S = the sum of the time customers spend in the system

F = The amount of customers who spend 4 or more minutes being attended

ND = The number of customers leaving the system

Considering the simulation table, the average time the customer spends in the system is:

S/ND = 15/4 = 3.75 minutes

The proportion of customers who spend 4 or more minutes in the system is:

F/ND = = 0.75

Rev. 1

Kleber Barcia V.

Chapter 4

12

Example 3: Extension of example 2 Simulation Table

System State List Future Event

Cumulative

Statistic

Clock LQ(t) LS(t) CHECKOUT LINE List S ND F

0 0 1 (C1,0) (D,4,C1) (A,8,C2) (E,60) 0 0 0

4 0 0 (A,8,C2) (E,60) 4 1 1

8 0 1 (C2,8) (D,9,C2) (A,14,C3) (E,60) 4 1 1

9 0 0 (A,14,C3) (E,60) 5 2 1

14 0 1 (C3,14) (A,15,C4) (D,18,C3) (E,60) 5 2 1

15 1 1 (C3,14)(C4,15) (D,18,C3) (A,23,C5) (E,60) 5 2 1

18 0 1 (C4,15) (D,21,C4) (A,23,C5) (E,60) 9 3 2

21 0 0 (A,23,C5) (E,60) 15 4 3

Kleber Barcia V.

Chapter 4

13

Example 4: Dump Trucks (DT)

Six dump trucks are used to transport coal from the entrance of a

mine to a train transport. Each truck is loaded in two loading areas.

After loaded, the truck is moved to the weighing section. The system

works on the FIFO system. The travel time between the loading area

and weighing is negligible. After weighing, the trucks travel, unload

and return to the loading queue.

Estimate the loader and scale utilizations (percentage of time busy)

Kleber Barcia V.

Chapter 4

14


Loading

time Probability

Cumulative

Probability

Random

Digits

5 0.30 0.30 1-3

10 0.50 0.8 4-8

15 0.20 1.00 9-0

Weighing

Time Probability

Cumulative

Probability

Random

Digits

12 0.70 0.70 1-7

16 0.30 1.00 8-0

Travel

Time Probability

Cumulative

Probability

Random

Digits

40 0.40 0.40 1-4

60 0.30 0.70 5-7

80 0.20 0.90 8-9

100 0.10 1.00 0

Distribution of weighing time for trucks

Distribution of loading time for trucks

Distribution of travel time for trucks

Kleber Barcia V.

Chapter 4

15



System State

LQ (t) = Number of trucks waiting in line to load

L (t) = Number of trucks loading (0, 1, or 2)

WQ (t) = Number of trucks waiting in line to weigh

W (t) = Number of trucks weighing (0 or 1)

Entities

The six dump trucks (DT1, DT2, DT3, DT4, DT5 and DT6), are not represented explicitly in the model

Future Event List

(ALQ, t, DTi) Dti arrives at loader queue ALQ at time t

(EL, t, DTi) Dti ends loading EL at time t

(EW, t, DTi) DTi ends weighting EW at time t

Kleber Barcia V.

Chapter 4

16


List (checkout list)

Loader queue = All trucks waiting to be loading FIFO

Weigh queue = All trucks waiting to be weighed FIFO

Activities

Loading time

Weighing time

Travel time

Delays

Delay at loader queue

Delay at scale

assumptions:

For t = 0, three trucks are at loader queue, two trucks are loading, and one truck is weighing.

Kleber Barcia V.

Chapter 4

17

0 10 20 30 40 50 60 70 80 90 100 110 120 130 140 150

DT1

DT2

DT3

DT4

DT5

DT6

Wait before loading

Loading

Wait before weighing

weighing

traveling

Loading

time 10 5 5 10 15 10 10

Weighing

time 12 12 12 16 12 16

Travel

time 60 100 40 40 80

5 12 24

25 64 72 36 76 52 92 144


SYSTEM ACTIVITIES

Simulation Table Dump Trucks

System State List Cumulative

Statistics Clock Loader Weigh Future Event

t LQ(t) L(t) WQ(t) W(T) Queue Queue List BL BS

0 3 2 0 1 DT4 (EL,5,DT3) 0 0

DT5 (EL,10,DT2)

DT6 (EW,12,DT1)

5 2 2 1 1 DT5 DT3 (EL,10,DT2) 10 5

DT6 (EL,5+5,DT4)

(EW,12,DT1)

10 1 2 2 1 DT6 DT3 (EL,10,DT4) 20 10

DT2 (EW,12,DT1)

(EL,10+10,DT5)

10 0 2 3 1 DT3 (EW,12,DT1) 20 10

DT2 (EL,20,DT5)

DT4 (EL,10+15,DT6)

where:

BL = Total busy time that spent the two loading areas

BS = total busy time that spent the weighing area





12 0 2 2 1 DT2 (EL,20,DT5) 24 12

DT4 (EW,12+12,DT3)

(EL,25,DT6)

(ALQ,12+60,DT1)

20 0 1 3 1 DT2 (EW,24,DT3) 40 20

DT4 (EL,25,DT6)

DT5 (ALQ,72,DT1)

24 0 1 2 1 DT4 (EL,25,DT6) 44 24

DT5 (EW,24+12,DT2)

(ALQ,72,DT1)

ALQ,24+100,DT3)

25 0 0 3 1 DT4 (EW,36,DT2) 45 25

DT5 (ALQ,72,DT1)

DT6 (ALQ,124,DT3)





36 0 0 2 1 DT5 (EW,36+16,DT4) 45 36

DT6 (ALQ,72,DT1)

(ALQ,36+40,DT2)

(ALQ,124,DT3)

52 0 0 1 1 DT6 (EW,52+12,DT5) 45 52

(ALQ,72,DT1)

(ALQ,76,DT2)

(ALQ,52+40,DT4)

(ALQ,124,DT3)

64 0 0 0 1 (ALQ,72,DT1) 45 64

(ALQ,76,DT2)

(EW,64+16,DT6)

(ALQ,92,DT4)

(ALQ,124,DT3)

(ALQ,64+80,DT5)





72 0 1 0 1 (ALQ,76,DT2) 45 72

(EW,80,DT6)

(EL,72+10,DT1)

(ALQ,92,DT4)

(ALQ,124,DT3)

(ALQ,144,DT5)

76 0 2 0 1 (EW,80,DT6) 49 76

(EL,82,DT1)

(EL,76+10,DT2)

(ALQ,92,DT4)

(ALQ,124,DT3)

(ALQ,144,DT5)

where:

BL = Total busy time that spent the two loading areas

BS = total busy time that spent the weighing area

Kleber Barcia V.

Chapter 4

22


Percentage of time busy of the loader area:

(49/2) / 76 = 0.32

Percentage of time busy of the scale area:

76/76 = 1.00

----- HOMEWORK 6 at SIDWeb -----

4 manual simulation

Documents