What’s with Scheduling? (Queues, Delays & Throughput)

G. Mustafa ©

11|21|2016

PART I : Erik’s Deli – Customer Flow

Erik’s Deli – The Lunch Scene

Erik’s Lunch Scene Erik’s lunch menu consists of cold cuts

and hot food. Customers, upon entrance

choose between cold or hot food, and

form queues, one for the cold, the other

for hot. In addition, each customer is

attributed with patience (low to high).

Those with low patience will leave the

queue, after a pre-assigned time and is

lost business. Customers wait in

respective queues to be served by

servers, attributed by service time –

some are slower. After customers are

served, they proceed to form a queue at

the cash register. The cashiers charge

them – these are also characterized by

their service time. Customers leave

Erik’s Deli with their food.

Erik plans to include a dinning area to

entice customers to stay longer and

hopefully order more food.

Co

ld F

oo

d H

ot Fo

od

Menu

Cashier

Customers Enter

Customers Exit

Customers Leaving

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Erik’s Deli Open for Lunch

Customers come in (exponentially distributed mean arrival time 1)

They randomly choose between cold and hot food (with 50% probability)

Customers are assigned serve time (exp. 5 mean)

They are handed menus (Assigned attributes)

Hostess routes them to cold or hot counters

Hot food queue

Cold cut queue

Hot Food servers

Cold Food servers

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Erik’s Deli Customer Flow Diagram

Customers Enter

Assigned Number

Handed Menu

Cold or Hot Cold Queue Hot Queue

Cold Counter Hot Counter

Cold Cus.

Served

Hot Cus.

Served

Checkout

Queue

Checkout

Cashier

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Erik’s Deli Customer Flow Model

Customers come in (exponentially distributed mean arrival time 1)

They randomly choose between cold and hot food (with 50% probability)

Customers are assigned serve time (exp. 5 mean)

They are handed menus (Assigned attributes)

Hostess routes them to cold or hot counters

Cold food queue

Hot food queue

Cold food queue length

Hot food queue length

Cold food serve counter

Hot Food counter

Cold food served

Cold food average wait

Hot Food served

Hot Food average wait

Served Customers

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Erik’s Deli Customer Flow Simulation

Cold Food Queue Hot Food Queue

Hot Food Wait Cold Food Wait

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Traffic on N85 @ Almedan Expressway (6-9am)

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Average wait @ Almedan

Queue @ Almedan

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PART II : Cluster Tool Scheduling

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Input

Output

Process

Module A

Process

Module B

Wafer

Handling

Robot

Tool Architecture A wafer processing tool comprises

of two process modules. A single

wafer handling robot serves process

modules. Incoming wafers are

sorted and put in FOUPS of given

capacity. Once inside FOUPS, wafers

are transferred to process models A

or B. After the wafers are

processed, they are moved by the

Tool Architecture & Wafer Sequence

FOUP

A

FOUP

B

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Tool Architecture & Wafer Sequence

Wafer Process Sequence A wafer processing tool consists of two

process modules. Wafers, as they arrive,

are assigned a process A or B, and form

two queues, one for A, the other for B.

In addition, each wafer is attributed

with pre-process qualification metric

(process time etc). The wafers wait in

their respective queues (FOUPS) to be

served by process modules, that are

endowed with some process time with some

variability. After the wafers have been

processed, they proceed to form a queue

at the tool output. Wafers depart the

tool.

It has been determined that wafer handing

presents a major bottleneck. There are

plans to improve robot designs and motion

profiles. Tool architecture also needs

improvement (multiple process modules,

process time reduction, etc.) The

baseline architecture, as described,

needs to be evaluated for throughput to

prioritize design options.

Incoming wafers

FOUP A

Robot

Process

A Process

B

Outgoing wafers

Inspection

Queue

FOUP B

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Create discrete wafers

can be timed, random

or event based Assign attributes to wafers

They can be characteristics

Process time type, quality

Rout wafers

Based on attributes

Provide Process Modules

Define process characteristics

(constraints, timeouts, queue length)

System Model

process, wafer handling

Retire wafers

System Output

Bottlenecks

Efficiency

Utilization

Uptime

Downtime

Failure Rate

Statistics

Statistics Statistics

Statistics Statistics

System Optimization

Cluster Tool Discrete Event Model

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Cluster Tool Model

Incoming wafers FOUP

A

FOUP

B

Process

A

Process

B

Robot

Wafers come in at regular

Intervals, based on an

event Or randomly

Wafers are sorted based

on Attributes,

characteristics, process

Wafers are moved based

on motion profile or

robot characteristics

Wafers are processed

according to attributes.

Modules are assigned

process times, process

steps, etc.

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Cluster Tool Performance

Incoming wafers

Wafers in

FOUP B

Robot

Process B

Process A Wafers in

FOUP A

Utilization

Handling

Time

Utilization

Utilization Process

Time

Process

Time

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Wafer Sorter (2 POD)

A1 A2

B1 B2 R

A1 A2

B1 B2

R

Fast Robotics Slow Robotics

Wafer Sorting

Two type of wafers are to be sorted (A, B) and transported from input FOUPS

(A1, B2) to output FOUPS (A2, B2). Wafer handling is carried out by a wafer

handling robot that can move one wafer at a time from input to output. Sorting

is done according to FIFO. G. Mustafa©| 2016

PART II : Tool Design Optimization

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Throughput Improvement

Wafer Process Sequence A wafer processing tool consists of two

process modules. Wafers, as they arrive,

are assigned a process A or B, and form

two queues, one for A, the other for B.

In addition, each wafer is attributed

with pre-process qualification metric (low

to high). Those with low will leave the

queue. This amounts to productivity loss.

The wafers wait in their respective queues

to be served by process modules, that are

with some process time with some

variability – some are slower. After the

wafers have been processed, they proceed

to form a queue at the tool output for

inspection – these are also characterized

by their inspection time. Wafers depart

the tool.

There are plans to include a storage area

to improve wafer flow bottleneck; wafer

handling robots and process modules. The

baseline architecture, as described, needs

to be evaluated for throughput to

prioritize design options.

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PART III : Tool Architectures

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Sorters, Buffers and Clusters

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Cluster Tool Architectures

Robotics

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Cluster Tool Architectures

G. Mustafa©| 2016