Simulation Basics (1)

7/30/2019 Simulation Basics (1)

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Dr. Pramod. M1


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A set of integrated resources (machinery, labourer,

equipment, information, and tools) that process raw

material as input and produce final products as

outputs.

Its Purpose:

Meet customer requirements

Add Value

At Minimum cost High Quality and Reliable

Environmentally Friendly

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The responsibilities of management are: Establish priorities

Utilise resources

Monitor Performance

Measure Performance

Improve productivity (yield) and efficiency(input/output)

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Production Machines, tools, fixtures, and other

hardware equipment

Material Handling Systems

Loading and unloading (batch control)

Positioning (manual, automated)

Transporting (conveyors, transporters)

Temporary storage (buffers)

Computer Control Systems (SCADA, Robotics,Scheduling, Safety Monitoring, Quality, )

Human Resources

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Types of operations

Number of workstations and system layout

Product variety

Level of automation

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Processing operations: Working on individual parts

(e.g. metal sheets, rolling, machining, drilling,

treating, painting, etc.)

Assembly operations: combining and putting parts

together e.g. (mounting gearbox, engines dressing,

Trimming shops in car factories, etc.)

Type of parts and products: The specification of the

material and also the method of processing the part

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Key factorin classification scheme

Determines main performance factors such as

capacity, capability, efficiency, productivity,utilisation, cost per unit, and maintainability

Determines the complexity of operations

Arrangement of workstations is called System

Layout

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Type I: Single Station where (n = 1) Type II: Multiple Stations with fixed routings

where (n > 1)

Type III: Multiple Stations with variable routing

where (n >1)

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Characteristics Product Process Group (Cell) Fixed Pos.

Throughput time Low High Low Medium

WIP Low High Low Medium

Skill Levels Choice High Med-High Mixed

Product Flexibility Low High Med-High High

Demand Flexibility Medium High Medium Medium

Machine Utilisation High Med-Low Med-High Medium

Operator Utilisation High High High Medium

Production cost/unit Low High Low High

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First Law (Littles Law): in a steady state system,WIP = Production Rate x Throughput Time

Second Law: Matter is conserved

Raw material enter the system (input) and finished products exitthe system (output). Any remaining or rejected parts need to beaccounted for.Therefore the summation of entry should be equal:-Total Material

Entry (input) = Finished Parts (output) + Removed Material +

Disposed Material + Recycled Material

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Third Law: The larger the system the less reliableit is

Fourth Law: Objects decay

Both hardware and software objects decay over time,they need maintenance and replacement

Fifth Law: Exponential growth in complexityComplexity increases with a larger rate when

components are added to the system.

Sixth Law: Technology advances

Natural evolution to better material, processes andinformation

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Principles of Manufacturing Systems


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Seventh Law: System components appear to behaverandomlyEvents can not be precisely predicted and this needs to be observed in anysystem design, development and analysis

Eighth Law: Limits of human rationalityHuman beings have limitations, this should be accounted for in any systemanalysis

Ninth Law: Combining, Simplifying, and Eliminating

save Time, Money and EffortKISS concept Good models are abstract, straight to the point, accurateand specified objectives.

Over complication is Lethal

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Simulation is a powerful tool for modeling and

analysis of complex systems.

Many real life problems are difficult to study via

analytical methods. But simulation model can be

constructed and run for all types of problems to

generate information on the system performance-

How well the system performs for a set of parameters How to optimize the system

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Used mainly as a decision making tool

Until 1980s , simulation was costly and time

consuming but with the advent of PC and

powerful hardware- fast, low cost, interactive,

visualization and animation oriented simulation

was possible

Arena general purpose visual simulation

environment

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Simplified representation of a system under study

Experiment with the system with a set of goal like

improve system design, cost benefit analysis,

sensitivity analysis

Representation describes system structure while

histories generated describes system behavior.

Model- simplified representation of a complex system

to capture behavioral aspects interested to the analyst

to gain insight into the behavior of the system--

abstraction & simplification16


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Evaluating a systems performance under ordinaryand unusual scenarios

Predicting performance of experimental system

design

Ranking multiple design and their trade offs

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Worldview is a philosophy-----two types : developer

WV and user WV

Developer WV----discrete event simulation

paradigm, model possesses a state at any point in time and the state

remains unchanged unless a simulation event occurs thenthe model undergoes transition.

Model evolution is controlled by a clock and an event list,each event is a code which can change the state variableand schedule other events

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Problem analysis and information collection-

identification of input, performance measures,

relationship among parameters, constraints, flow

diagrams and trees...

Data collection-

estimate model input parameters and assumptions

Model construction- either using computer language or using special

simulation environment like arena

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Model verification-

make sure that the model is correctly constructed as

per specification

Model validation-

fit of the model to empirical data. Good fit means

performance measure predicted by the model match

or agree reasonably with those in real life systems

Designing and conducting simulation runs

Output analysis & Final recommendation

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Discrete event simulation Probability and statistics

Random number generation

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Provides an integrated framework for building

simulation models in a wide variety of

applications. It integrates all the functions needed

for a successful simulation including:

1. Animation

2. analysis of inputs and outputs data

3. model verificationinto one comprehensive environment.

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Consists of modular templates build around SIMAN

language constructs and visual front end SIMAN consists of two classes of objects- blocks and

elements

Blocks are logical constructs that represent operations(SEIZE/ RELEASE)

Elements are objects that represent a facility

(RESOURCES, QUEUES, TALLIES....)

Arena fundamental modeling component is the

modules which is a high level construct consisting of

many SIMAN blocks and elements.

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a unique collection of small example models that

demonstrate a variety of modeling techniques and

situations commonly encountered using Arena.

SMARTs have been specifically designed for use as

a training or reference tool to assist you in your

model-building efforts .

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Entities : In every simulation model entities are

objects under a particular process, and they move

along the system.

Example: manufacturing raw material and products, banks

customers, hospitals patients are the entities.

In a typical Simulation project there can be one or

many different types of entities.

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Attributes : Are the characteristics of each entity

and represent values associated with individual

entities. In a typical system we can define as many attributes as we

need for the entities. Example: length, or weight, or patients the type of the

disease.

Stations : Stations are boundaries where

processing occurs in a system. Example: Production line a process is performed by a station

i.e. drilling, milling, filling, etc. And in offices these boundariescould be departments.

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Transporters : Entities move in the system via

transporters.

Transporters can be used to represent material handling or

transfer of devices.

Some examples for transporters are; AGVs, trucks, forks,

cranks, carts, etc

Conveyors : Conveyors are devices that move

entities form one station to another in one direction.

Such as escalators and horizontal conveyors.

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Variables : Represent values that describe the

characteristics of the system. These values are available to

all entities.

Used for many different kinds of things

Travel time between all station pairs Number of parts in system (Work-in Process)

Simulation clock (built-in Arena variable)

Name, value of which theres only one copy for the whole model

Not tied to entities

Entities can access, change variables

Some built-in by Arena, you can define others

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Consider a single WS with an m/c of infinite buffer.

jobs arrive randomly and wait in buffer if the m/c isbusy. The IAT are expo(30)min while PT are

expo(24)min. (M/M/1 Queue). System simulated for

10000 hrs Data:-

IAT are expo(30)min

PT are expo(24)min

Simulation run time-10000 hrs

Compare with theoretical results, estimate avg job

delay in Q, avg no in Q and m/c utilization

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Result:- (insufficient ) no of observations insufficient for adequate

statistical confidence.

Number busy- no of busy units of a resource

Number schedule- resource capacity

Inst utilization-utilization per resource unit= number busy/number

scheduled

For M/M/1- m/c utilization ==/ Where = job arrival rate = 1/30,

And = job processing rate= 1/24

= 0.8 (0.81 obtained through simulation)

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Consider a manufacturing network of two workstations

in series, consisting of an assembly workstationfollowed by a painting workstation, where jobs arrive

at the assembly station with exponentially distributed

inter-arrival times of mean 5 hours.

the assembly process always has all the raw materials

necessary to carry out the assembly operation the

assembly time is uniformly distributed between 2 and 6

hours

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after the process is completed, a quality control test is

performed, and past data reveal that 15% of the jobs

fail the test and go back to the assembly operation for

rework jobs that pass the test proceed to the painting

operation that takes 3 hours for each unit.

We are interested in simulating the system for 100,000

hours estimating process utilizations, average job

waiting times and average job flow times (the elapsed

time for a job from start to finish)

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Data- IAT=Expo(5)hr PT

assembly=Unif(2,6)hr QC=85% True, 15% false --

---rework PT paint= 3 hrs

Simulation time=100000hrs Attributes=Tnow, total

rework Record= flow time=

time between jobdeparture from paintand arrival time atassembly, reworks / job

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time between arrival of successive batch is expo

(30)min. Upon arrival at the prep area it is separated

into 4 units which are processed individually from here.

The processing at the prep area follows TRIA (3,5,10).

The part is then sent to the sealer.

At the sealer , the case is sealed and tested, the total

time for these operations depends on the part type;

TRIA (1,3,4)for part a and WEIB(2.5,5.3) for Part B.

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91 % of the parts pass inspection and are transferred

directly to the shipping dept.

The remaining parts are transferred to the rework area

where they are disassembled, repaired cleaned

assembled and retested. 80 % of the parts are salvaged

and passed on to the shipping dept and the rest is

thrown out as scrap. time for rework follows expo

(45)min independent of the part type. The system is

run for 4 8 hr shifts or 1920 min

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Travelers arrive at the main entrance door of an airline

terminal according to an EXPO Interarrival time ofmean 1.6 min, with the first arrival at time 0.

The travel time from entrance to check in is UNIF

distributed between 2 and 3 min. at the check incounter travelers wait in a single line until one of the

five agents is available to serve them.

Check in time follows a WEINB distribution with

parameters (7.76, 3.91). upon completion of their check

in they are free to travel to their gates., simulation run

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Data IAT passengers= EXPO(1.6)min

Travel time to check in=UNIF (2,3)min Check in time =WIENB(7.76,3.91) min Simulation run time =16 hrs First arrival time =0 min

Find:- avg time in system, no of passengers completing check

in and avg length of check in Q

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The emergency room of a small hospital operates

around the clock. It is staffed by three receptionists at

the reception office, and two doctors on the premises,

assisted by two nurses. However, one additional doctor

is on call at all times; this doctor is summoned when the

patient workload up-crosses some threshold, and is

dismissed when the number of patients to be examinedgoes down to zero, possibly to be summoned again

later.

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Patients arrive at the emergency room according to a

Poisson process with mean interarrival time of 10 minutes.

An incoming patient is first checked into the emergency

room by a receptionist at the reception office. Check-in

time is uniform between 6 and 12 minutes. Since critically ill

patients get treatment priority over noncritical ones, each

patient first undergoes triage in the sense that a doctordetermines the criticality level of the incoming patient in

FIFO order.

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The time spent to reach the treatment room is uniform

between 1 and 3 minutes and the treatment time by a

nurse is uniform between 3 and 10 minutes.

Once treated by a nurse, a noncritical patient waits FIFO

for a doctor to approve the treatment, which takes a

uniform time between 5 to 10 minutes., all patients wait

FIFO for an available doctor, but critical patients aregiven priority over noncritical ones.

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Following treatment by a doctor, all patients are

checked out FIFO at the reception office, which takes

a uniform time between 10 and 20 minutes, following

which the patients leave the emergency room.

To estimate the requisite statistics, the hospital

emergency room was simulated for a period of 1 year.

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Model:- 2 segment ER segment, on call doc segment

Data:- receptionist=3, doc=2, on call doc= 1, nurse= 2

IAT patient=Poisson(10)min

Check in time Patients=unif(6,12)min Triage Time= tri(3,5,15)min

Critical patients =40%

Treatment time for P crit=unif(20,30)min

Travel time for p non cri= unif(1,3)min

Treatment time for p non cri=unif(3,10)min

Waiting time for all patient= unif (5,10)min

Check out time for all patient= unif (10,20)min

Simulation length= 1 year

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Modeling Production Lines :-resource allocation

problems- workload allocation and buffer capacity,

productivity improvement measures, Modeling

Machine Failures.

Modeling Transportation Systems:-Designing new

traffic routes and alternate routes to satisfy demand

for additional road capacity, or eliminating bottlenecks

and congestion points in existing routes, Designingtraffic patterns on the factory floor, Designing port

facilities and material handling systems.

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Modeling Computer Information Systems:-

Modeling Supply Chain Systems:-Customer service

levels, Average inventory levels and backorder

levels, Rate and quantity of lost sales, Inventory

management segment, Demand management

segment.

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The manufacturing facility is a production line composed

of manufacturing stages consisting of workstations with

intervening buffers to hold product flowing along the line.

push regime:- where little attention is given to the

finished-product inventory

pull regime:- where the process only produces in response

to specific demands

storage limitations in workstations give rise to a

bottleneck phenomenon, involving both blocking and

starvation


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Space limitations in a downstream workstation can,

therefore, cause stoppages at upstream

workstations a phenomenon known as blocking.

some workstations may experience idleness due tolack of job flow from upstream workstations. This

phenomenon is called starvation

starvation tends to propagate forward to

successive workstations located downstream in the

production line.


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Blocking and starvation are, in fact, the flip sides of

a common phenomenon and tend to occur

togethera bottleneck workstation

MODELS OF PRODUCTION LINES

Productivity losses are potentially incurred

whenever machines are idle (blocked or starved)

due to machine failures or bottlenecks originatingfrom excessive accumulation of inventories

between workstations.


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Design problems in production lines are primarily

resource allocation problems. workload allocation and buffer capacity allocation for a given set of

workstations with associated processing times

Performance analysis of production lines strives to

evaluate their performance measures as function of a

set of system parameters. The most commonly used

performance measures follow: Throughput, Average inventory levels in buffers Downtime probabilities Blocking probabilities at bottleneck workstations Average system flow times (also called manufacturing lead times)


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Consider a generic packaging line for some product,

such as a pharmaceutical plant producing a

packaged medicinal product, or a food processing

plant producing packaged foods or beverages.

The line consists of workstations that perform the

processes of filling, capping, labeling, sealing, and

carton packing. Individual product units will be

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We make the following assumptions:

The filling workstation always has material in frontof it, so that it never starves. 2. The buffer space

between workstations can hold at most five units. 3.

A workstation gets blocked if there is no space in

the immediate downstream buffer (manufacturing

blocking).4. The processing times for filling,

capping, labeling, sealing, and carton packing are

6.5, 5, 8, 5, and 6 seconds, respectively.


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Note that these assumptions render our packaging

line a push-regime production. line. To keep matters

simple, no randomness has been introduced into the

system, that is, our packaging line is deterministic. It is

worthwhile to elaborate and analyze the behavior of

the packaging line understudy.

The first workstation (filling) drives the system in

that it feeds all downstream workstations with units.


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Clearly, one of the workstations in the line is the

slowest . The throughput of that workstation thencoincides with the throughput of the entire packaging

line.

Furthermore, workstations upstream of the slowest

one will experience excessive buildup of WIP inventory

in their buffers. In contrast, workstations downstream

of the slowest one will always have lightly occupied or

empty WIP inventory buffers.


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machine failures of various kinds constitute an

important source of idleness and variability . efficient

operation requires that downtimes be minimized, since

these represent loss of production time.

Failures that occur while machines are actually

processing jobs are called operation dependent and the

new breed of highly computerized machines may fail atany time, regardless of machine status. Such failures

are called operation independent


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Suppose that Filling Process in the packaging line

model of fails randomly and that it needs an

adjustment after every 250 departures from the

workstation.

Assume that uptimes are exponentially distributed

with a mean of 50 hours, while repair times are

uniformly distributed between 1.5 hours to 3 hours.

Also, the aforementioned adjustment time is uniformly

distributed between 10 minutes to 25 minutes.


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Assume further that Packing Process can also experience

random mechanical failures, and downtimes are triangularly

distributed with a minimum of 75 minutes, a maximum of 2

hours, and a mode at 90 minutes.

The corresponding uptimes are exponentially distributed

with a mean of 25 hours. Finally, assume that random failures

occur only while the machines are busy (operation-

dependent failures).

We shall refer to the modified packaging line model as the

failure-modified model


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how failures in the failure-modified model are

specified in a dialog spreadsheet for the Failure

module from the Advanced Process template

panel. Arena provides a mechanism for defining

resource states and for linking them to failures/

stoppages in the form of the StateSet spreadsheet

module from the Advanced Process template

panel.


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Monte Carlo simulation is an invaluable tool for

studying transportation systemsand solving their

attendant problems

Some common examples are listed below: Designing new traffic routes and alternate routes to satisfy

demand for additional road capacity, or eliminatingbottlenecks and congestion points in existing routes byappropriate placement of traffic lights and tollbooths.

Designing traffic patterns on the factory floor, includingtransporters and conveyors, for efficient movement of rawmaterial and product.


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The PickStation module allows entities to select a

destination Station module using a selection

criterion, such as the minimal or maximal queue size,

number of busy resource units, or an arbitraryexpression.

Alternatively, an entity can be endowed with an

itinerary using the Sequence module to specify a

sequence of Station modules


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A Job Shop producing 3 types of Gears; G1, G2, G3. Job

Shop consists of Arrival Dock, Milling , Drilling , Paint

Shop, Polishing Area, Shop Exit

Gear Jobs arrive in batches of 10 units. Their inter-arrival

times are uniformly distributed between 400 and 600

minutes. Of arriving batches, 50% are G1, 30% are G2, 20%

are G3.

Each gear type has different operation sequence. Gears

are transported by Two trucks running at a constant

speed of 100 feet/minute. Each truck can carry only one

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Transport Procedure:

The Transport starts from Arrival Dock When a job is complete at a location, the gear is placed into

an output buffer. A transport request is made for a truck, and the gear waits

for the truck to arrive.

Among the two trucks, the preference will be for the onewhich is closest to the requested location.

The transported job is placed in the input buffer of nextstation.

After all operations, the finished gear departs fromthe job shop via the Shop Exit.

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Assumptions:- Transporter (Truck) speed is same for both loaded and

empty. The freed transporter stays at the destination station until

requested by another station. The Job Shop works for 24 hours a day in 3 shifts at 8 hours

each.

Find:-

Gear flow time

Gear delays at operation location Resource utilization Improvements

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This example illustrates bulk port operations, using the notions

of station, entity routing among stations, entity pick-up and

drop-off by another entity, and the control of entity

movements using logical gating. It concerns a bulk material

port, called Port Tamsar, at which cargo ships arrive and wait

to be loaded with coal for their return journey. Cargo ship

movement in port is governed by tug boats, which need to be

assigned as a requisite resource. The port has a single berth

where the vessels dock, and a single ship loader that loads the

ships.


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A schematic representation of the layout of Port Tamsar

is depicted in Figure 13.2. Port Tamsar operates

continually 24 hours a day and 365 days a year. The

annual coal production plan calls for nominal

deterministic ship arrivals at the rate of one ship every

28 hours. However, ships usually do not arrive on time

due to weather conditions, rough seas, or otherreasons, and consequently, each ship is given a 5-day

grace period commonly referred to as the lay period.

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We assume that ships arrive uniformly in their lay

periods and queue up FIFO (if necessary) at an offshoreanchorage location, whence they are towed into port by

a single tug boat as soon as the berth becomes available.

The tug boat is stationed at a tug station located at a

distance of 30 minutes away from the offshore

anchorage.

Travel between the offshore anchorage and the berth

takes exactly 1 hour.

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We assume that there is an uninterrupted coal supply to

the ship loader at the coal-loading berth, and that ship

loading times are uniformly distributed between 14 and

18 hours.

Once a ship is loaded at the berth, the tug boat tows it

away to the offshore anchorage, whence the boat

departs with its coal for its destination.

Departing vessels are accorded higher priority in seizing

the tug boat.

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An important environmental factor in many port

locations around the world is tidal dynamics. Cargo shipsare usually quite large and need deep waters to get into

and out of port.

Obviously, water depth increases with high tide and

decreases with low tide, where the time between two

consecutive high tides is precisely 12 hours.

We assume that ships can go in and come out of port

only during the middle 4 hours of high tide. Thus, the

tidal window at the port is closed for 8 hours and open

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We wish to simulate Port Tamsar for 1 year (8760

hours) to estimate berth and ship loader utilization,

as well as the expected port time per ship. We

mention parenthetically that although a number of

operating details have been omitted to simplify the

modeling problem, the foregoing description is

quite realistic and applicable to many bulk material

ports and container ports around the world.

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An Arena model of Port Tamsar consists of four

main segments: (1) ship arrivals, (2) tugboat

operations, (3)coal-loading operations at the berth,

and (4) tidal window modulation. These will be

described next in some detail along with

simulation results.

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3

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This example concerns a transportation system

consisting of a toll plaza on the New Jersey Turnpike,and aims to study the queueing delays resulting from

toll collection.

The toll plaza consists of two exact change (EC) lanes,

two cash receipt (CR) lanes, and one easy pass (EZP)

lane. Arriving vehicles are classified into three groups as

follows: 1. Fifty percent of all arriving cars go to EC lanes, and their

normal service time distribution is Norm(4.81, 1.01).

h f ll l d h


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2. Thirty percent of all arriving cars go to CR lanes, and theirservice time distribution is 5 Logn(4.67, 2.26).

3. Twenty percent of all arriving cars go to EZP lanes, and their

service time distribution is 1.18 4.29 Beta(2.27, 3.02).

To simplify matters, we assume that an incoming car

always joins the shortest queue in its category (EC, CR,

or EZP).

We further assume that no jockeying between queues

takes place. That is, once a car joins a queue in front of a

tollbooth, it never switches to another queue.


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Traffic congestion is distinctly non stationary, varying

widely by time of day. As expected, traffic is heavierduring the morning rush hour (6 A.M.9 A.M.) and the

evening rush hour (4 P.M.7 P.M.), and tapers off during

off-peak hours.

Table 13.1 summarizes vehicle interarrival time

distributions over each 24-hour period. The number of

operating cash receipt booths varies over time.

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Since such booths must be manned, and therefore are

expensive to operate, one of them is closed during the

off-peak hours.

Only during morning and evening rush hours do all

cash receipt booths remain open.

Typical performance analysis objectives for the toll

plaza system address the following issues:

What would be the impact of additional traffic on car

delays?

Would adding another booth markedly reduce waiting

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Could some booths be closed during light traffic hours without

appreciably increasing waiting times?

What would be the impact of converting some cash receipt

booths to exact change booths or to easy pass booths?

How would waiting times be reduced if both cash receipt booths

were to be kept open at all times?

Of course, additional issues may be specific to

particular toll plazas under study, but in our case we

wish to address the last issue in the list, using the

performance metrics of average time to pass through

the system and booth utilization.

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The model can be decomposed into the following

segments: creation of car entities from the appropriatedistributions over various time periods, dispatching a

car to the appropriate tollbooth with the shortest

queue, and serving incoming cars.

To this end, we use the Set construct to facilitate

modeling of module sets (model components) with

analogous logic (e.g., multiple tollbooths).


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Simulation Modeling and ArenaJanuary 2009ISBN 978 0 470 09726 7

Charu Chandra, University of Michigan - Dearborn Translations of Simulation with Arena, 3rdEdition
http://www.wiley.com/WileyCDA/WileyTitle/productCd-0470097264.htmlhttp://www.wiley.com/WileyCDA/WileyTitle/productCd-0470097264.htmlhttp://www.wiley.com/WileyCDA/WileyTitle/productCd-0470097264.htmlhttp://www.wiley.com/WileyCDA/WileyTitle/productCd-0470097264.htmlhttp://www.wiley.com/WileyCDA/WileyTitle/productCd-0470097264.htmlhttp://www.wiley.com/WileyCDA/WileyTitle/productCd-0470097264.htmlhttp://www.wiley.com/WileyCDA/WileyTitle/productCd-0470097264.htmlhttp://www.wiley.com/WileyCDA/WileyTitle/productCd-0470097264.htmlhttp://www.wiley.com/WileyCDA/WileyTitle/productCd-0470097264.htmlhttp://www.wiley.com/WileyCDA/WileyTitle/productCd-0470097264.html


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ISBN: 978-0-470-09726-7Manuel D. Rossetti, Associate Professor of IndustrialEngineering, University of Arkansas,Department of Industrial Engineering .Healthcare Operations ManagementMay 2008ISBN 13: 978-1-56793-288-1Daniel B. McLaughlin, DirectorCenter for BusinessExcellence in the Opus College of Business at theUniversity of St. ThomasJulie M. Hays, PhDSimulation Modeling and Analysis with Arena

Academic PressISBN-13: 978-0-12-370523-5Tayfur Altiok, Professor, Department of IndustrialEngineering, Rutgers University [email protected] Melamed, Professor, Department ofManagement Science and Information ystems,Rutgers University [email protected] Process Analysis and Improvement: Tools andTechniquesMcGraw-Hill IrwinISBN: 0072857129 Marvin S Seppanen, Productive SystemsSameer Kumar, University of St. Thomas, Minneapolis

EditionDr. Soemon Takakuwa (Japanese Translator)January 2005. McGraw Hill Publisher.ISBN 4-339-08246-5Moon Il Kyeong (Korean Translator)Kyobo Book Centre Publisher. January 2005ISBN 8970855122 Applied Simulation ModelingISBN: 0534381596Copyright year: 2003 Andrew Seila - University of GeorgiaVlatko Ceric - University of Zagreb

Pandu Tadikamalla - University of Pittsburgh Introduction to Modeling and Simulation ofSystems with ArenaVisual BooksCopyright 2003 PortugueseISBN 85-7502-046-3

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