6 ServEng Mini Course Genericie.technion.ac.il/serveng/References/Mini_course_generic/... · 2012....

Serv

iceEngineerin

g(S

cience

,M

anagement)

AviM

andelbaum

Tech

nion

IE&M

Course

Contents

•Introd

uction

to“Services”

and“Service-E

ngin

eering”

•TheTwoPrerequ

isites:Measu

rements,

Models

(Operation

al)

•Empirical

(Data-B

ased)Models

•Fluid

(Determ

inistic)

Models

•Stoch

asticFram

ework:

Dynam

ic-Stoch

asticPERT/C

PM

•TheBuild

ingBlocks

ofaBasic

Service

Station

:

–Arrivals;

Forecastin

g

–Service

Duration

s;Workload

–(Im

)Patien

ce;Abandonment

–Retu

rns(D

urin

g,After;

Positive,

Negative)

•Stoch

aticModels

ofaService

Station

–Markovian

Queues:

Erlan

gB/C

/A,...,/R

,Jackson

–Non-Param

etricQueues:

G/G

/n,...

•Operation

alRegim

esandStaffi

ng:

ED,QD,QED

•Heterogen

eousCustom

ersandServers

(CRM,SBR)

1

Back

gro

und

Materia

l

Downloadable

fromtheReference

smenu

in

http://ie.tech

nion

.ac.il/serveng/R

eferences

Gans(U

.S.A.),

Koole

(Europ

e),andM.(Israel):

“Telep

honeCallC

enters:Tutorial,R

eviewandResearch

Prosp

ects.”

MSOM,2003.

Brow

n,Gans,M.,Sakov,

Shen,Zeltyn

,Zhao:

“Statistica

lAnalysis

ofaTelep

honeCall

Center:

AQueuein

g-

Scien

cePersp

ective.”JA

SA,2005.

Trofi

mov,

Feigin

,M.,Ish

ay,Nadjharov:

”DataM

OCCA:M

odels

forCall/C

ontactCenter

Analysis.

(Model

Descrip

tionandIntrod

uction

toUser

Interface.)”Tech

nion

Report,

2004-2006.

Tech

nion

’s“Serv

ice-E

ngineerin

g”co

urse

lectures:

Measu

re-

ments,

Arrivals,

Service

Tim

es,(Im

)Patien

ce,Fluid

Models,

QED

Q’s.

M.“C

allCenters:

Research

Biblio

gra

phywith

Abstracts.”

Version

7,Decem

ber

2006.

2

Intro

ductio

nto

“Serv

ices”

U.S.EmploymentbySecto

r,1850-2000+

0

0.1

0.2

0.3

0.4

0.5

0.6

18501860187018801890190019101920193019401950

0.7

0.8

19601970198019902000

% Employment

Year

Service

Manufacturing

Agriculture

Wefocu

son:

•Function

:Opera

tions(vs./p

lusIT,HRM,Marketin

g)

•Dim

ension

:Accessib

ility,Capacity

(vs.RM,SCM,...)

•Modellin

gFram

ework:

QueueingTheory

(plusScien

ce)

•Application

s:Call/

Contact

Centers

(Health

care,...)

3

Sco

peofth

eServ

iceIn

dustry

•Wholesale

andretail

trade;

•Govern

ment

services;

•Health

care;

•Restau

rantsandfood

;

•Financial

services;

•Tran

sportation

;

•Com

munication

;

•Education

;

•Hosp

italitybusin

ess:

•Leisu

reservices.

OurApplication

Focu

s:telephoneca

llce

nters,

which

play

anim

portant

rolein

most

ofthese

sectors.

4

Serv

ices:

Subjectiv

eTrends

”Every

thingis

Serv

ice”

Rath

erthan

buyin

gapro

duct,

why

not

buyonly

theserv

ice

itprovides?

For

example,

carleasin

g;or,

why

setupandrun

ahelp-d

esk

fortech

nical

support,

with

itscostly

fast-to-obsolete

hard

ware,

growing-sop

histicated

software,

high

-skilledpeop

leware

andever-exp

andinginfow

are,rath

erthan

letoutso

urcin

gdoit

allfor

you?

“Data;Tech

nologyand

Human

Intera

ction

Far

toolittle

reliance

ondata,th

elanguage

ofnatu

re,in

formulatin

gmodels

forthesy

stemsand

pro

cesse

softh

e

deepest

importa

nce

tohuman

beings,

nam

elythose

in

which

weare

acto

rs.System

swith

fixedrules,

such

asphysical

systems,

arerelatively

simple,

whereas

systemsinvolvin

ghuman

bein

gsexp

ressingtheir

microgoals

...can

exhibitincred

iblecom

-

plexity;

there

isyet

thehopeto

devise

tractable

models

throu

gh

remarkable

colle

ctiveeffects

...

(Robert

Herm

an:”R

eflection

onVehicu

larTra

fficScie

nce

”.)

Fusio

nofDisc

iplin

es:

POM

/IE

,M

ark

etin

g,IT

,HRM

Thehigh

estchallen

gefacin

gbanks

with

respect

toeffi

cientand

effective

innovation

liesin

the”New

Age

Industria

lEngi-

neer”

that

must

combinetech

nological

know

ledge

with

process

design

inord

erto

createthedelivery

systemof

thefuture.

(Frei,

Harker

andHunter:

”Innovatio

nin

RetailBanking”).

5

Serv

ice-E

ngineerin

g

Goal

(Subjective):

Develop

scientifically-based

design

prin

ciples

(rules-o

f-thumb)

andtools

(softw

are)that

support

thebalan

ceofservice

quality

,

process

efficie

ncy

andbusin

esspro

fitability

,from

the(often

conflictin

g)view

sof

custom

ers,servers

andmanagers.

Contrast

with

thetrad

itional

andprevalent

•Service

Managem

ent(U

.S.Busin

essSchools)

•IndustrialE

ngin

eering(Europ

ean/Jap

anese

Engin

eeringSchools)

Addition

alSources

(allwith

websites):

•Frau

nhofer

IAO

(Service

Engin

eering,

1995):...

application

ofengin

eeringscien

ceknow

-how

totheservice

sector...

mod-

els,meth

odsandtools

forsystem

aticdevelop

ment

anddesign

ofservice

prod

ucts

andservice

systems...

•NSF

SEE

(Service

Enterp

riseEngin

eering,

2002):...

Cus-

tomer

Call/C

ontactCenters

...staff

schedulin

g,dynam

icpric-

ing,

facilitiesdesign

,andquality

assuran

ce...

•IB

MSSM

E(Services

Scien

ce,Managem

entandEngin

eering,

2005):...

new

discip

linebrin

gstogeth

ercom

puter

science,

operation

sresearch

,industrial

engin

eering,

busin

essstrategy,

managem

entscien

ces,social

andcogn

itivescien

ces,andlegal

sciences

...

6

Staffing:How

ManyServ

ers?

Fundamentalprob

lemin

serviceoperation

s:Health

care,...

,or

Call

Centers,

asarep

resentativeexam

ple:

•Peop

le:≈70%

operatin

gcosts;≥

3%U.S.workforce.

•Busin

ess-Frontiers

butalso

Sweat-S

hopsof

the21

stCentu

ry.

Reality

•Complex

andbecom

ingmore

so

•Staffi

ngisErlan

g-based

(1913!)

=⇒Solu

tionsurgently

need

ed

•Tech

nology

canaccom

modate

smart

protocols

•Theory

lagssign

ificantly

behindneed

s

=⇒Ad-hoc

meth

odsprevalent:

heuristics-

orsim

ulation

-based

.

Research

Pro

gress

based

on

•Sim

ple

Robust

Models,for

theoretical

insight

into

complex

realities.Their

analysis

requires

andgen

erates:

•Data-B

asedScie

nce

:Model,

Exp

eriment,

Valid

ate,Refin

e.

•M

anagementPrin

ciples,

Tools:

Serv

iceEngineerin

g.

7

TheFirst

Prerequisite

:Data

&M

easu

rements

Robert

Herm

an(“F

ather”

ofTran

sportation

Scien

ce):Far

toolittle

reliance

onData,th

elanguage

ofnatu

re,in

formulatin

g

models

forthesystem

softhedeep

estim

portan

ceto

human

bein

gs,

nam

elythose

inwhich

weare

actors.

Empirica

l“Axiom”:TheData

OneNeed

sis

NeverThere

For

OneToUse

(Always

Prob

lemswith

Historical

Data).

Avera

gesdoNOTtell

thewhole

story

Individual-T

ransactio

nLevelData:Tim

e-Stam

psofE

vents

•Face

-to-Face

:T,C,S,I,O,F(Q

IE,RFID

)

•Telephone:ACD,CTI/C

RM,Surveys

•In

tern

et:

Log-fi

les

•Tra

nsp

orta

tion:measu

ringdevices

onhighw

ays/intersections

OurDatabases:

Opera

tions(vs.

Marketin

g,Surveys,

...)

•Face-to-F

acedata

(bran

chbankin

g)–recitation

s;QUESTA

•Telep

honedata

(smallb

ankin

gcallcenter)

–hom

ework;

JASA

•DataM

OCCA

(largecc’s:

repository,interface)

–class/research

;

Website

Futu

reResearch

:

Health

care,Multim

edia,

Field

-Support;

Operation

+Marketin

g,

8

Measurements: Face-to-Face Services23 Bar-Code Readers at an Israeli Bank

9

Measu

rements:

TelephoneServ

ices

Log-F

ileofCall-b

y-C

allData

vru+line call_id custom

er_id priority type date vru_entry vru_exit vru_tim

e q_start q_exit

q_time outcom

eser_start ser_exit ser_time server

AA

0101 44749 27644400 2

PS 990901 11:45:33 11:45:39 6

11:45:39 11:46:58 79 A

GEN

T11:46:57 11:51:00 243

DO

RIT

AA

0101 44750 12887816 1

PS 990905 14:49:00 14:49:06 6

14:49:06 14:53:00 234 A

GEN

T14:52:59 14:54:29 90

RO

TH A

A0101 44967 58660291

2 PS

990905 14:58:42 14:58:48 6 14:58:48 15:02:31 223

AG

ENT

15:02:31 15:04:10 99 R

OTH

AA

0101 44968 0 0

NW

990905 15:10:17 15:10:26 9 15:10:26 15:13:19 173

HA

NG

00:00:00 00:00:00 0 N

O_SER

VER

AA

0101 44969 63193346 2

PS 990905 15:22:07 15:22:13 6

15:22:13 15:23:21 68 A

GEN

T15:23:20 15:25:25 125

STEREN

AA

0101 44970 0 0

NW

990905 15:31:33 15:31:47 14 00:00:00 00:00:00 0

AG

ENT

15:31:45 15:34:16 151 STEREN

AA

0101 44971 41630443 2

PS 990905 15:37:29 15:37:34 5

15:37:34 15:38:20 46 A

GEN

T15:38:18 15:40:56 158

TOV

A

AA

0101 44972 64185333 2

PS 990905 15:44:32 15:44:37 5

15:44:37 15:47:57 200 A

GEN

T15:47:56 15:49:02 66

TOV

A

AA

0101 44973 3.06E+08 1

PS 990905 15:53:05 15:53:11 6

15:53:11 15:56:39 208 A

GEN

T15:56:38 15:56:47 9

MO

RIAH

AA

0101 44974 74780917 2

NE 990905 15:59:34 15:59:40 6

15:59:40 16:02:33 173 A

GEN

T16:02:33 16:26:04 1411

ELI

AA

0101 44975 55920755 2

PS 990905 16:07:46 16:07:51 5

16:07:51 16:08:01 10 H

AN

G 00:00:00 00:00:00 0

NO

_SERV

ER

AA

0101 44976 0 0

NW

990905 16:11:38 16:11:48 10 16:11:48 16:11:50 2

HA

NG

00:00:00 00:00:00 0 N

O_SER

VER

AA

0101 44977 33689787 2

PS 990905 16:14:27 16:14:33 6

16:14:33 16:14:54 21 H

AN

G 00:00:00 00:00:00 0

NO

_SERV

ER

AA

0101 44978 23817067 2

PS 990905 16:19:11 16:19:17 6

16:19:17 16:19:39 22 A

GEN

T16:19:38 16:21:57 139

TOV

A

AA

0101 44764 0 0

PS 990901 15:03:26 15:03:36 10

00:00:00 00:00:00 0 A

GEN

T15:03:35 15:06:36 181

ZOH

ARI

AA

0101 44765 25219700 2

PS 990901 15:14:46 15:14:51 5

15:14:51 15:15:10 19 A

GEN

T15:15:09 15:17:00 111

SHA

RON

AA

0101 44766 0 0

PS 990901 15:25:48 15:26:00 12

00:00:00 00:00:00 0 A

GEN

T15:25:59 15:28:15 136

AN

AT

A

A0101 44767 58859752

2 PS

990901 15:34:57 15:35:03 6 15:35:03 15:35:14 11

AG

ENT

15:35:13 15:35:15 2 M

ORIA

H

AA

0101 44768 0 0

PS 990901 15:46:30 15:46:39 9

00:00:00 00:00:00 0 A

GEN

T15:46:38 15:51:51 313

AN

AT

AA

0101 44769 78191137 2

PS 990901 15:56:03 15:56:09 6

15:56:09 15:56:28 19 A

GEN

T15:56:28 15:59:02 154

MO

RIAH

AA

0101 44770 0 0

PS 990901 16:14:31 16:14:46 15

00:00:00 00:00:00 0 A

GEN

T16:14:44 16:16:02 78

BEN

SION

AA

0101 44771 0 0

PS 990901 16:38:59 16:39:12 13

00:00:00 00:00:00 0 A

GEN

T16:39:11 16:43:35 264

VICK

Y

AA

0101 44772 0 0

PS 990901 16:51:40 16:51:50 10

00:00:00 00:00:00 0 A

GEN

T16:51:49 16:53:52 123

AN

AT

AA

0101 44773 0 0

PS 990901 17:02:19 17:02:28 9

00:00:00 00:00:00 0 A

GEN

T17:02:28 17:07:42 314

VICK

Y

AA

0101 44774 32387482 1

PS 990901 17:18:18 17:18:24 6

17:18:24 17:19:01 37 A

GEN

T17:19:00 17:19:35 35

VICK

Y

AA

0101 44775 0 0

PS 990901 17:38:53 17:39:05 12

00:00:00 00:00:00 0 A

GEN

T17:39:04 17:40:43 99

TOV

A

AA

0101 44776 0 0

PS 990901 17:52:59 17:53:09 10

00:00:00 00:00:00 0 A

GEN

T17:53:08 17:53:09 1

NO

_SERV

ER

AA

0101 44777 37635950 2

PS 990901 18:15:47 18:15:52 5

18:15:52 18:16:57 65 A

GEN

T18:16:56 18:18:48 112

AN

AT

AA

0101 44778 0 0

NE 990901 18:30:43 18:30:52 9

00:00:00 00:00:00 0 A

GEN

T18:30:51 18:30:54 3

MO

RIAH

AA

0101 44779 0 0

PS 990901 18:51:47 18:52:02 15

00:00:00 00:00:00 0 A

GEN

T18:52:02 18:55:30 208

TOV

A

AA

0101 44780 0 0

PS 990901 19:19:04 19:19:17 13

00:00:00 00:00:00 0 A

GEN

T19:19:15 19:20:20 65

MEIR

AA

0101 44781 0 0

PS 990901 19:39:19 19:39:30 11

00:00:00 00:00:00 0 A

GEN

T19:39:29 19:41:42 133

BEN

SION

A

A0101 44782 0

0 N

W 990901 20:08:13 20:08:25 12

00:00:00 00:00:00 0 A

GEN

T20:08:28 20:08:41 13

NO

_SERV

ER

AA

0101 44783 0 0

PS 990901 20:23:51 20:24:05 14

00:00:00 00:00:00 0 A

GEN

T20:24:04 20:24:33 29

BEN

SION

AA

0101 44784 0 0

NW

990901 20:36:54 20:37:14 20 00:00:00 00:00:00 0

AGEN

T20:37:13 20:38:07 54

BEN

SION

AA

0101 44785 0 0

PS 990901 20:50:07 20:50:16 9

00:00:00 00:00:00 0 A

GEN

T20:50:15 20:51:32 77

BEN

SION

AA

0101 44786 0 0

PS 990901 21:04:41 21:04:51 10

00:00:00 00:00:00 0 A

GEN

T21:04:50 21:05:59 69

TOV

A

AA

0101 44787 0 0

PS 990901 21:25:00 21:25:13 13

00:00:00 00:00:00 0 A

GEN

T21:25:13 21:28:03 170

AV

I

AA

0101 44788 0 0

PS 990901 21:50:40 21:50:54 14

00:00:00 00:00:00 0 A

GEN

T21:50:54 21:51:55 61

AV

I

AA

0101 44789 9103060 2

NE 990901 22:05:40 22:05:46 6

22:05:46 22:09:52 246 A

GEN

T22:09:51 22:13:41 230

AV

I

AA

0101 44790 14558621 2

PS 990901 22:24:11 22:24:17 6

22:24:17 22:26:16 119 A

GEN

T22:26:15 22:27:28 73

VICK

Y

AA

0101 44791 0 0

PS 990901 22:46:27 22:46:37 10

00:00:00 00:00:00 0 A

GEN

T22:46:36 22:47:03 27

AV

I

AA

0101 44792 67158097 2

PS 990901 23:05:07 23:05:13 6

23:05:13 23:05:30 17 A

GEN

T23:05:29 23:06:49 80

VICK

Y

AA

0101 44793 15317126 2

PS 990901 23:28:52 23:28:58 6

23:28:58 23:30:08 70 A

GEN

T23:30:07 23:35:03 296

DA

RMO

N

AA

0101 44794 0 0

PS 990902 00:10:47 00:12:05 78

00:00:00 00:00:00 0 H

AN

G 00:00:00 00:00:00 0

NO

_SERV

ER

AA

0101 44795 0 0

PS 990902 07:16:52 07:17:01 9

00:00:00 00:00:00 0 A

GEN

T07:17:01 07:17:44 43

AN

AT

AA

0101 44796 0 0

PS 990902 07:50:05 07:50:16 11

00:00:00 00:00:00 0 A

GEN

T07:50:16 07:53:03 167

STEREN

10

Measu

rements:

PrevalentAvera

ges(A

CD

Data)

11

DataMOCCA

Daily Report Time SeriesDaily Report of April 20, 2004 – Heavily Loaded Day

EntriesExitsAbnormal Termination

5609

5567

42

VRU

26614

2658 6

28Announce

157820

9382 7

63993

Message

15964

1596

4

Direct

62866

1024

432

1579

1

4974

8

11138

1980

OfferedVolume Handled

Abandon ShortAbandon Cancel Discon

nect

Continued

Week days

0.00

10.00

20.00

30.00

40.00

50.00

Jan-04

Feb-04

Mar-04

Apr-04

May-04

Jun-04

Jul-04

Aug-04

Sep-04

Oct-04

Nov-04

Dec-04

Jan-05

Feb-05

Mar-05

Apr-05

May-05

months

Rate

Abandons rate( Engineering)

Abandons rate( Technical)

Probability of waiting > 30( Engineering)

Probability of waiting > 30( Technical)

Cross Tabulation Histogram

Agent status February 2005

0

50

100

150

200

250

300

350

400

450

500

0:00 2:00 4:00 6:00 8:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00 0:00

Time (Resolution 5 min.)

Number of cases

01.02.2005 02.02.2005 03.02.2005 04.02.2005 05.02.2005 06.02.2005

07.02.2005 08.02.2005 09.02.2005 10.02.2005 11.02.2005 12.02.2005

13.02.2005 14.02.2005 15.02.2005 16.02.2005 17.02.2005 18.02.2005

19.02.2005 20.02.2005 21.02.2005 22.02.2005 23.02.2005 24.02.2005

25.02.2005 26.02.2005 27.02.2005 28.02.2005

Customer service time Private Caller Termination February 2005, Week days

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0

20

40

60

80

100

120

140

160

180

200

220

240

260

280

300

320

340

360

380

400

420

440

460

480

500

520

540

560

580

600

620

Time (Resolution 1 sec.)

Relative frequencies

12

Beyond Averages: Waiting Times in a Call Center

Small Israeli Bank

Time

0 30 60 90 120 150 180 210 240 270 300

29.1 %

20 %

13.4 %

8.8 %

6.9 %5.4 %

3.9 %3.1 %

2.3 % 1.7 %

Mean = 98SD = 105

Large U.S. Bank

0

2

4

6

8

10

12

14

16

18

20

2 5 8 11 14 17 20 23 26 29 32 35

Time

Relative frequencies, %

Medium Israeli Bank

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 320 340 360 380



8

13

TheSeco

nd

Prerequisite

:(O

pera

tional)

Models

Empirica

lM

odels

•Concep

tual

–Service-P

rocessData

=Flow

Netw

ork

–Serv

iceNetw

ork

s=

QueueingNetw

ork

s

•Descrip

tive

–QC-Tools:

Pareto,

Gantt,

Fishb

oneDiagram

s,...

–Histogram

s,Hazard

-Rates,

...

–Data-M

OCCA:Repository

+Interface

•Explan

atory

–Nonparam

etric:Com

parative

Statistics,

Regression

,...

–Param

etric:Log-N

ormal

Services,

(Doubly)

Poisson

Ar-

rivals,Exp

onential

(Im)Patien

ce

Analytica

lM

odels

•Fluid

(Determ

inistic)

Models

•Stoch

asticModels

(Birth

&Death

,G/G

/n,Jackson

,...)

14

Conce

ptu

alM

odel:

Serv

iceNetw

ork

s=

QueueingNetw

ork

s

People,waiting for service: teller, repairm

an, ATM

Telephone-calls,to be answered: busy, m

usic, info.

Forms, to be sent, processed, printed; for a partner

Projects, to be developed, approved, implem

ented

Justice, to be made: pre-trial, hearing, retrial

Ships, for a pilot, berth, unloading crew

Patients, for an ambulance, em

ergency room, operation

Cars, in rush hour, for parking

Checks, w

aiting to be processed, cashed

Queues

Scarce Resources,Synchronization G

aps

Costly, but here to stay

– Face-to-face Nets (C

hat)

(m

in.)

– Tele-to-tele Nets (Telephone)

(sec.)

– Adm

inistrative Nets (Letter-to-Letter)

(days)

– Fax, e.mail

(hours)

– Face-to-ATM

, Tele-to-IVR

– Mixed N

etworks (C

ontact Centers)

15

Conceptual Model:Bank Branch = Queueing Network

23

Teller

Entrance

Tourism

Xerox

Manager

Teller

Entrance

Tourism

Xerox

Manager

Bottleneck!

16

BankBra

nch

:A

QueuingNetw

ork

Transition Frequencies B

etween U

nits in The Private and B

usiness Sections:

Private Banking

Business

To Unit

Bankers

Authorized

Com

pens-T

ellersTellers

Overdrafts

Authorized

FullE

xit

From U

nitPersonal

- ationsPersonal

Service

Bankers

1%1%

4%4%

0%0%

0%90%

PrivateA

uthorizedPersonal

12%5%

4%6%

0%0%

0%73%

Banking

Com

pensations7%

4%18%

6%0%

0%1%

64%

Tellers

6%0%

1%1%

0%0%

0%90%

Tellers

1%0%

0%0%

1%0%

2%94%

ServicesO

verdrafts2%

0%1%

1%19%

5%8%

64%

Authorized

Personal2%

1%0%

1%11%

5%11%

69%

Full Service1%

0%0%

0%8%

1%2%

88%

Entrance

13%0%

3%10%

58%2%

0%14%

0%

Legend:0%

-5%5%

-10%10%

-15%>15%

Dom

inant Paths - Business:

Unit

Station 1Station 2

TotalParam

eterT

ourismT

ellerD

ominant Path

Service Time

12.74.8

17.5W

aiting Time

8.26.9

15.1Total Tim

e20.9

11.732.6

Service Index0.61

0.410.53

Dom

inant Paths - Private:

Unit

Station 1Station 2

TotalParam

eterB

ankerT

ellerD

ominant Path

Service Time

12.13.9

16.0W

aiting Time

6.55.7

12.2Total Tim

e18.6

9.628.2

Service Index0.65

0.400.56

Service Index = % tim

e being served

17

Mappingth

eOfferedLoad(B

ankBra

nch

)

Business

Services

Private

Banking

Banking

Services

Departm

ent

Time

Tourism

TellerTeller

TellerC

omprehensive

8:30 – 9:00

9:00 – 9:30

9:30 – 10:00

10:00 – 10:30

10:30 – 11:00

11:00 – 11:30

11:30 – 12:00

12:00 – 12:30

Break

16:00 – 16:30

16:30 – 17:00

17:00 – 17:30

17:30 – 18:00

Legend:

NotB

usy

Busy

Very B

usy

Note: W

hat can / should be done at 11:00 ?

Conclusion: M

odels are not always necessary but m

easurements are !

18

Conce

ptu

alM

odel:

Call-C

enterNetw

ork

Schematic C

hart –Pelephone C

all-Center 1994

Accounts

General

Technical

Clearing

Typist

Manager

AC

D

€€€ € €

€

112 1

35

2

4

= Tele N

et = Queueing N

etwork

43

19

Conce

ptu

alM

odel:

Call-C

enterNetw

ork

Curre

ntStatu

s-Analysis

Accounts

General

Technical

Center

Center

Center

Peak days in a week

Sun, FriSun

SunPeak days in a m

onth12

8-14, 2-310-20

Avg. applications no. in a day

41362476

1762A

vg. applications no. in an hour - avg

253.6193

167Peak hours in a day

11:00-12:0010:00-11:00

9:00-10:00A

vg. applications no. in peak hours - m

ax422

313230

Avg. w

aiting time (secs.)

10.920.0

55.9A

vg. service time (secs.)

83.5131.3

143.2Service index

0.880.87

0.72A

bandonment percentage

2.75.6

11.2A

vg. waiting tim

e before abandonment (secs.)

9.716.8

43.2A

vg. staffing level9.7

10.35.2

Target w

aiting time

1225

-

20

Conce

ptu

alM

odel:

Hosp

italNetw

ork

Emerg

ency

Departm

ent:

Generic

FlowPhysician

Nurse

Imaging

LabElse

60estim

ated max tim

e

initialexam

ination

decision point for alternative processes

10%probability of events

06vital signs

07

E.C.G

05

decision

awaiting

discharge

40

treatment

41

50 consultation

instructionsprior discharge

discharge /hospitalization

else

triage04

43

54

reception03

observation

46

every 15 minutes

follow up

47

bloodwork13

12

100%

imaging /consultation /

treatment

17

14

decision

20

ultrasound2928

21

Xray27

25,26

CT

3130

22

15

39

37

45

follow up

48every 15 m

inutes49

11

handlingpatient&

family

08

09

38im

aging

36

3534

32,33treatm

ent18

56

hospitalization/discharge

awaiting

evacuation55

52

53

10

treatment

19

16

discharge

51

else

treatment

42

44

reference point

labslabs

consultation

Labs

consultation

imaging

decision

proportion of patients01

process requires bed02

23

24

21

Conceptual Model: Burger King Bottlenecks

Bottleneck Analysis: Short – Run ApproximationsTime – State Dependent Q-Net

3 Minimal:Drive-thruCounterKitchen

Add:#4 Kitchen#5 Help

Drive -thru

22

Analytica

lM

odels:

Little

’sLaw,or

TheFirst

Law

ofCongestio

n

Input(C

ustomers,

units, …)

SystemOutput

•λ=

averagearrival

rate;

•L

=average

numberwith

insystem

;

•W

=average

timewith

insystem

.

Little

’sLaw

L=λW

Finite

-Horizo

nVersio

n

��

��

��

��

��

��

��

��

��

��

��

��

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��

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��

��

��

��

��

��

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��

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��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

# customers

A(T

)=N

arrival

1 2

W7

0tim

e

T

departure

Long-R

un

(Sto

chastic)

Example

M/M

/1:L=

ρ

1−ρ=

λ

μ−λ,

W=

1

μ−λ=

1μ

1

1−ρ.

23

Conceptual Model: The Justice Network, orThe Production of Justice

Queue

Mile Stone

Activity

Appeal

Proceedings

Closure

PrepareAllocateOpen File

Avg. sojourn time in months / years

Processing time in mins / hours / days

Phase Transition

Phase

24

Judges: Operational Performance - Base case

45 100

118

59

33

.

.

.

..

(6.2, 7.4) (13.5, 7.4)

(26.3, 4.5)

(12, 4.9)

(7.2, 4.6) 3

001

3

001

01

0

3

01

3

00

3

01

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20 25 30

Case Type 0 Judge1Case Type 01 Judge2Case Type 3 Judge3

Judge4Judge5

Ave

rage

Num

ber o

f Mon

ths -

W

Average Number of Cases / Month -

25

3 Case-Types: Performance by 5 Judges

45 100

118

59

33

.

.

.

..

(6.2, 7.4) (13.5, 7.4)

(26.3, 4.5)

(12, 4.9)

(7.2, 4.6) 3

001

3

001

01

0

3

01

3

00

3

01

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20 25 30


Judge4Judge5

Ave

rage

Num

ber o

f Mon

ths -

W

Average Number of Cases / Month -

26

5 Judges: Performance by 3 Case-Types

(6.2, 7.4) (13.5, 7.4)

(26.3, 4.5)

(12, 4.9)

(7.2, 4.6)

.

.

.

..

3

001

3

001

01

0

3

01

3

00

3

01

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20 25 30


Judge4Judge5

Avg

. Mon

ths -

W

Avg. Cases / Month -

27

Judges: Performance Analysis

3

001

3

001

01

0

3

01

3

00

3

01

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20 25 30

(6.2, 7.4) (13.5, 7.4)

(26.3, 4.5)

(12, 4.9)

(7.2, 4.6)

.

.

.

..


Judge4Judge5

Avg

. Mon

ths -

W


28

Judges: Best/Worst Performance

(6.2, 7.4) (13.5, 7.4)

(26.3, 4.5)

(12, 4.9)

(7.2, 4.6) 3

001

3

001

01

0

3

01

3

00

3

01

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20 25 30

.

.

.

..

45 100

118

59

33


Judge4Judge5

Avg

. Mon

ths -

W


29

Conce

ptu

alFluid

Model

Custom

ers/units

aremodeled

byfluid

(contin

uous)

flow.

Labor-d

ayQueueingatNiagara

Falls

•Approp

riatewhen

predicta

ble

varia

bility

prevalent;

•Usefu

lfirst-o

rdermodels/ap

proxim

ations,often

suffice

;

•Rigorou

slyjustifi

able

viaFunction

alStron

gLaw

sof

Large

Numbers.

30

Empirical Fluid Model: Queue-Length at aCatastrophic/Heavy/Regular Day

Bank Queue

Catastrophic Heavy Load Regular

8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13Time of Day

0

10

20

30

40

50

60

Queu

e31

Empirica

lM

odels:

Fluid,Flow

Derived

directly

fromevent-b

ased(call-by-call)

measu

rements.

For

example,

anisolated

service-station:

•A(t)

=cu

mulativ

e#

arrivalsfrom

time0to

timet;

•D(t)

=cu

mulativ

e#

departu

resfrom

systemdurin

g[0,t];

•L(t)

=A(T

)−D(t)

=#

custom

ersin

systemat

t.

Arriv

als

and

Departu

resfro

maBankBra

nch

Face

-to-Face

Serv

ice

0 50

100

150

200

250

300

350

400

89

1011

1213

time

customers

cumulative arrivals

cumulative departures

number in

system

waiting

time

When

isitpossib

leto

calculate

waitin

gtim

ein

thisway?

32

Math

ematica

lFluid

Models

Differentia

lEquatio

ns:

•λ(t)

–arriv

alra

teat

timet∈

[0,T].

•c(t)

–maxim

alpotentia

lpro

cessin

gra

te.

•δ(t)

–effectiv

eprocessin

g(departu

re)rate.

•Q(t)

–to

talam

ount

inthesystem

.

Then

Q(t)

isasolu

tionof

Q(t)

=λ(t)−

δ(t);Q(0)

=q0 ,

t∈[0,T

].

InaCallCenterSettin

g(n

oabandonment)

N(t)

statistically-identical

servers,each

with

servicerate

μ.

c(t)

=μN

(t):maxim

alpotential

processin

grate.

δ(t)=μ·

min(N

(t),Q(t)):

processin

grate.

Q(t)

=λ(t)−

μ·min(N

(t),Q(t)),

Q(0)

=q0 ,

t∈[0,T

].

How

toactu

ally

solve?Math

ematics

(theory,

numerical),

orsim

ply:

Start

with

t0=0,

Q(t

0 )=q0 .

Then,for

tn=tn−

1+Δt:

Q(t

n )=

Q(t

n−1 )+λ(t

n−1 )·Δ

t−μmin(N

(tn−

1 ),Q(t

n−1 ))·Δ

t.

33

Tim

e-V

ary

ingQueueswith

Abandonmentand

Retria

ls

Based

onthree

paper

with

Massey,

Reim

an,Rider

andStolyar.

CallCenter:

aM

ultise

rverQueuewith

Abandonmentand

Retria

ls

Q1 (t)

βt ψt ( Q

1 (t) − nt ) +

βt (1−ψt ) ( Q

1 (t) − nt ) +

λt

2

Q2 (t)

21

8

. . .

nt 1...μt Q

2 (t)2

μt (Q1 (t) nt )

1

34

Prim

itives:

Tim

e-V

ary

ing

Predicta

bility

λt

exogenousarrival

rate;

e.g.,continu

ously

changin

g,sudden

peak.

μ1t

servicerate;

e.g.,change

innatu

reof

work

orfatigu

e.

nt

number

ofservers;

e.g.,in

response

topred

ictably

varyingworkload

.

Q1 (t)

number

ofcustom

ersin

callcenter

(queue+

service).

βt

abandonment

ratewhile

waitin

g;

e.g.,in

response

toIV

Rdiscou

ragement

atpred

ictableoverload

ing.

ψt

prob

ability

ofnoretrial.

μ2t

retrialrate;

ifcon

stant,1/μ

2–average

timeto

retry.

Q2 (t)

number

ofcustom

ersthat

will

retry.

Inourexam

ples,

wevary

λtonly,

other

prim

itivesare

constant.

35

Fluid

Model

Replacing

randomprocesses

bytheirrates

yields

Q(0

)(t)=

(Q(0

)1

(t),Q

(0)

2(t))

Solution

tononlineardifferentialbalance

equations

ddtQ

(0)

1(t)

=λt −

μ1t(Q

(0)

1(t)∧

nt )

+μ2tQ

(0)

2(t)−

βt(Q

(0)

1(t)−

nt )

+

ddtQ

(0)

2(t)

=β1 (1−

ψt )(Q

(0)

1(t)−

nt )

+

−μ2tQ

(0)

2(t)

Justification:FunctionalStrong

LawofLarge

Num

bers,w

ithλt →

ηλt ,

nt →

ηnt .

Asη↑∞

,1ηQ

η(t)→Q

(0)(t)

,uniform

lyon

compacts,a.s.

givenconvergence

att=

036

SuddenRush

Hour

n=

50

servers�μ=

1

λt

=110

for9≤

t≤11,

λt=

10

otherwise

��

��

��

��

��

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ise�.�n��5�,�mu��.�,�m

u��.�,�beta��.�,��retrial��.�5

time

��ode

��ode

��sim

��sim

variance�envelopes

37

Sto

chastic

Fra

mework

:DSPERT/CPM

DS

=Dynamic

Sto

chastic

(Fork-Join

,Split-M

atch)

PERT

=Program

Evalu

ationandReview

Tech

niqu

e

CPM

=Critical

Path

Meth

od

Operation

sResearch

inProject

Managem

ent:Stan

dard

Successfu

l.

New-Y

ork

Arre

st-to-A

rraignmentSyste

m

(Larso

netal.,

1993)

Lodged atPrecinct(12 hrs.)

Arrive at

Precinct(1 hr.)

Arrive at

Central

Booking

(5 hrs.)O

ff.

Arrives at

Com

plaintR

oom(6 hrs.)

Transmitted

to Albany

(10 hrs.)

Com

plaintSw

orn(14 hrs.)

Rap Sheet

Received

(15 hrs.)

Arrives at

Courthouse(39 hrs.)

Paperwork

Com

pleted(18 hrs.)

Arrestee

Arraigned

(48 hrs.)

Arrestee

Arrest

(0 hrs.)

fingerprints

CRM

–task

times

aredeterm

inistic/averages

(standard

).

S-P

ERT

(Stoch

asticPERT)–task

times

random

variables.

DS-P

ERT/CPM

–multi-p

roject

(dynam

ic)environ

ment,

with

tasksprocessed

atdedicated

servicestation

s.

•Capacity

analysis:

Can

wedoit?

(LP)

•Resp

onse-tim

eanalysis:

How

longwill

ittake?

(S-Nets)

•W

hatif:

Can

wedobetter?

(Sensitivity,

Param

etric)

•Optim

ality

:What

isthebest

onecan

do?

38

Sto

chastic

Modelofa

Basic

Serv

iceStatio

n

Build

ingblock

s:

•Arrivals

•Service

duration

s(tim

es)

•Custom

ers’(im

)patien

ce.

•Custom

ers’retu

rns(durin

gservice

process,

afterservice)

First

studythese

build

ingblocks

one-by-on

e:

•Empirical

analysis,

which

motivates

•Theoretical

model(s).

Then

integratebuild

ingblocks,

viaprotocols,

into(B

asic)Models:

•Erlan

g-B/C

(Arrivals,

Services)

•Erlan

g-A(+

Abandonment),

Erlan

g-R(+

Retu

rns).

Themodels

support,

forexam

ple,

•Staffi

ngWorkforce,

forwhich

Basic

Models

arealread

yusefu

l;

andbeyon

d:

•Routin

gCustom

ers

•Schedulin

gServers

•Match

ingCustom

ers-Need

swith

Servers-S

kills(SBR).

39

Arrivals to Service

Arrivals to a Call Center (1999): Time Scale

Strategic Tactical

Yearly Monthly

Operational Stochastic

DailyHourly

40

Arrivals Process, in 1976

(E. S. Buffa, M. J. Cosgrove, and B. J. Luce, “An Integrated Work Shift Scheduling System”)

Yearly Monthly

Daily Hourly

41

Q-S

cience

:Predicta

ble

Varia

bility

May

1959!

Dec

1995!

(Help D

esk Institute)

Arrival

Rate

Time

24 hrsTime

24 hrs

% A

rrivals

(Lee A

.M., A

pplied Q-Th)

42

Arriv

als

toServ

ice:

Poisso

nPro

cesse

s

WeekdayArriv

alRates(Isra

eli

CC,M

OCCA)

Arrivals to call center July 2005

0

100

200

300

400

500

600

700

8000:002:00

4:006:00

8:0010:00

12:0014:00

16:0018:00

20:0022:00

Time (Resolution 30 min.)

Number of cases

03.07.2005 Private04.07.2005 Private

05.07.2005 Private06.07.2005 Private

07.07.2005 Private10.07.2005 Private

11.07.2005 Private12.07.2005 Private

13.07.2005 Private14.07.2005 Private

17.07.2005 Private18.07.2005 Private

19.07.2005 Private20.07.2005 Private

21.07.2005 Private24.07.2005 Private

25.07.2005 Private26.07.2005 Private

27.07.2005 Private28.07.2005 Private

31.07.2005 Private

•Arrivals

overshort

(butnot

tooshort)

intervals(15,

30min)

areclose

tohom

ogeneou

sPoisso

n,with

over-d

ispersio

n.

•Arrivals

overtheday

are(over-d

ispersed

)non-h

omogeneous

Poisson

.

Practice:

modelas

Poisson

with

piecew

ise-constant

arrivalrates.

Poisso

nPhenomena:

•PASTA

=Poisson

Arrivals

See

Tim

eAverages;

•Biased

samplin

g:Why

istheservice

timeweencou

nter

upon

arrivallon

gerthan

a“typ

ical”service

time?

43

Arriv

als

toServ

ice:Foreca

sting

How

topredict

Poisson

arrivalrates?

Tim

eSerie

smodels.

Days

aredivid

edinto

timeintervals

overwhich

arrivalrates

are

assumed

consta

nt.

Standard

Reso

lutio

ns:

15min,30

min,1hour.

Njk

=number

ofarrivals

onday

jdurin

ginterval

k.

Assu

meK

timeintervals

andJdays

overall.

•One-d

ay-aheadpred

iction:

N1· ,...,N

j−1,·

know

n.Pred

ictN

j1 ,...,NjK.

•Severa

ldays(w

eeks)

aheadpred

iction.

•W

ithin-d

aypred

iction.

Foreca

stAccu

racy

(U.S.Bank,W

einberg

)

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Serv

iceTim

es(D

ura

tions)

http

://iew3.tech

nion

.ac.il/serveng/L

ectures/S

erviceFull.p

df

Why

Sign

ificant?

+1secon

dof

1000agents

costs$500K

yearly.

Why

Interesting?

Must

accurately

Model,Estim

ate,Predict,

Analyze

:

•Resolu

tion:Sec’s

(phone)?

min’s(em

ail)?hr’s

(hosp

ital)

•Param

eter,Distrib

ution

(Static)

orProcess

(Dynam

ic)?

•Does

itinclu

deafter-call

work?

•Does

itinclu

deinterru

ption

s?

–Whisp

ertim

e,hold

time,phones

durin

gface-to-face,...

•Does

isaccou

ntfor

return

services?

How

affected

bycovariates?

•Exp

erience

andSkill

ofagents

(Learn

ingCurve)

•Typ

eof

Custom

er:Service

Typ

e,VIP

Statu

s

•Tim

e-of-Day:

Congestion

-Level

•Human

Factor:

Incentives,

pendingworkload

,fatigu

e

45

Serv

iceTim

es:

TrendsandStability

Average

Custom

erService

Tim

e,Weekd

ays(M

OCCA)

150

175

200

225

250

275

300

325Mar-01Jun-01

Sep-01Dec-01

Mar-02Jun-02

Sep-02Dec-02

Mar-03Jun-03

Sep-03

months

Means

RetailPremier

BusinessPlatinum

USBankService-T

imeHistogram

sfor

Telesales

(MOCCA)

0.0

0.5

1.0

1.5

2.0

2.5

0100

200300

400500

600700

800900

1000



May-01May-02

May-03

46

Serv

iceTim

es:

Static

Models,

or

Avera

gesDoNotTellth

eW

hole

Story

Distrib

utio

ns:

Param

etric(Exp

onential,

Logn

ormal),

Sem

i-Param

etric(Phase-T

ype),

Non-Param

etric(Empirical).

Lognorm

alServ

iceTim

esin

an

Israeli

Bank

Histogram

Histogram

inLogarith

micScale

�

��

��

��

��

��

��

��

��

��

��More

Ser�ice�time

Fre�uenc�

fre�uenc�lognorm

al�cur�e

��erage��sec

St�de��sec

�

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

��

Log�ser�ice�time�

Fre�uenc�

fre�uenc�norm

al�cur�e

��erage��

St�de��

ATypica

lCall

Center?

January-O

ctober

Novem

ber-D

ecember

��

��

S��

��

��

��

S��

��

��?

Jan – Oct:

Log-N

ormal

��

��

S��

��

Nov – D

ec:

47

Serv

iceTim

es:

5Sec’s

Reso

lutio

n

USBank.

Service-T

imeHistogram

sfor

Telesales

(MOCCA)

0.0

0.5

1.0

1.5

2.0

2.5

0100

200300

400500

600700

800900

1000



May-01May-02

May-03

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

0100

200300

400500

600700

800900

1000

Time (Resolution 5 sec.)Relative frequencies, %

Apr-03May-03

Jun-03

48

Loca

lM

unicip

alitie

s

Departm

ent Station

No.

Total C

ustomers

Avg. A

rrival R

ate A

vg. Service T

ime

STD

Maxim

al Service T

ime

Utilization

Avg.

Waiting

Time

(1/H

r) (M

ins) (M

ins) (M

ins)

(Mins)

Water

N/A

187

1.8 0.2

8.871.0

8.15 54.68

13.3%

4.76 Tellers

N/A

1328

12.6 0.5

8.820.4

8.55 49.37

30.8%

7.73 C

ashier N

/A

757 7.2

0.4 6.64

0.4 6.94

29.95 79.7%

3.89

Manager

N/A

190

1.8 0.2

7.991.0

8.44 38.97

24.1%

9.16 D

iscounts N

/A

317 3.0

0.3 4.59

0.4 4.54

36.72 23.1%

3.65

1 57

N/A

7.80

1.70 7.61

31.28 6.5%

N

/A W

ater 2

130 N

/A

9.341.20

8.37 54.68

19.3%

N/A

3 336

N/A

9.04

0.80 8.93

49.05 48.2%

N

/A 4

208 N

/A

9.931.00

8.82 49.12

33.0%

N/A

5 417

N/A

8.97

0.70 8.55

49.37 59.4%

N

/A 6

144 N

/A

9.531.20

8.75 41.70

21.8%

N/A

7 156

N/A

8.03

1.10 7.96

35.27 19.8%

N

/A

Tellers

8 67

N/A

3.74

0.70 3.58

21.03 4.0%

N

/A C

ashier 9

757 N

/A

6.640.40

6.94 29.95

79.7%

N/A

Manager

10 190

N/A

1.99

1.00 8.44

38.97 24.1%

N

/A D

iscounts 11

317 N

/A

4.590.40

4.54 36.72

23.1%

N/A

*Service time ranges given w

ith 90% confidence.

Service Tim

e Histogram

– Overall:

Range

Frequency 0-5

51.3 5-10

21.1 10-15

12.6 15-20

6.7 20-25

3.8 25-30

2.3 30-35

1.1 35-40

0.6 40-45

0.3 45-

0.2 0%

10%

20%

30%

40%

50%

60%

0-55-10

10-1515-20

20-2525-30

30-3535-40

40-4545-

Minutes

Frequency

AVG: 7.69 M

insSTD

: 7.86 Mins

MAX: 54.68 M

ins

49

Serv

iceTim

es:

Exponentia

l(P

honeCalls)

C

all-Duration Frequency - N

orth:

C

all-Duration Frequency – C

entral:

Q. H

ow to recognize “E

xponential” when you "see" one?

A

. Geom

etric Approxim

ation.

0%

10%

20%

30%

40%

50%

0-11-2

2-33-4

4-55-6

6-77-8

8-99-10

10-

Minutes

Frequency

Practice

Average C

all Duration:

1.95 Mins.

Theory

0%

10%

20%

30%

40%

50%

0-11-2

2-33-4

4-55-6

6-77-8

8-99-10

10-

Minutes

Frequency

Practice

Average C

all Duration:

2.01 Mins.

Theory

50

Serv

iceTim

es:

Phase-T

ypeM

odel

5.0 (Secs.)

22.0 24.8

62.2

Yes

N

o

Billing

Billing

114.0

Late C

onnections

? Where does hum

an-service start / end (recall 144)?

“A

verage” picture.

Custom

erIdentified?

Custom

er’s Query

Custom

er Identification

Information Service

Date of C

onnection A

ccording to Periodical U

pdates D

ate of Purchase of C

able

To Marketing

(Sales)

Beginning

End

51

Serv

iceTim

es:

Exponentia

l,Phase-T

ype

Static

Model:

Exponentia

lDura

tion

Face

-to-Face

Serv

icesin

aGovern

mentOffice

Service Times H

istogram:

0%

10%

20%

30%

40%

0-11-2

2-33-4

4-55-6

6-77-8

8-99-10

10-1111+

Minutes

Frequency

AVG: �.6 M

insSTD

: �.6 Mins

�: ��6� ��45� �er ��y�

Dynamic

Model:

Phase-T

ypeDura

tion

General

Hyp

erexponential

Coxian

jk

m

P

j

jkq

j

12k

q

qq... .

1

2k

...1

k

1-p1-p

k-1

p1

k-11

52

Service Times: Returns

Bank Classification of “Continued – Calls”

0

200

400

600

800

1000

1200

Techn

ical P

roblem

sMisc

.

Conne

cting

Or D

iscon

necti

ng

Calls L

isting

Conne

cting

Secret

ary

Long

Dist

ance

Call

s

Option

s

Free Tim

e Prog

ram

Instru

ction

s Man

ual

Monthl

y Inv

oice

Means

of Pay

ment

Addres

s Cha

nge

Forms

�� Ty�e

� �

��s

Total: 2,400 calls -

20% of all calls.

53

Serv

iceTim

es:

TheHumanFacto

r,or

WhyLongest

Durin

gPeakLoads?

Mean

-Service-T

ime(R

egular)

vs.Tim

e-of-Day

(95%CI)

(n=42613)

�Tim

e of Day

Mean Service Time

1015

20

100 120 140 160 180 200 220 240

78

910

1112

1314

1516

1718

1920

2122

2324

Arrivals

toQueueor

Service

-Regu

larCalls

(Inhom

ogeneou

sPoisson

)

0

20

40

60

80

100

120

C a l l s / H r ( R e g )

78

91

01

11

21

31

41

51

61

71

81

92

02

12

22

32

4

VR

U E

xit T

ime

54

Custo

mers’

(Im)P

atie

nce

Mark

etin

gCampaign

ataCall

Center

Average

wait

376sec,

24%calls

answ

ered

Abandonment

Importa

ntandIn

terestin

g

•Oneoftw

ocustom

er-subjective

perform

ance

measu

res(2 n

d=Redials)

•Poor

servicelevel

(future

losses)

•Lost

busin

ess(present

losses)

•1-800

costs(present

gains;out-of-p

ocketvs.

alternative)

•Self-selection

:the“fittest

survive”

andwait

less(m

uch

less)

•Accu

rateRobust

models

(vs.distorted

instab

ility-pron

e)

•Beyon

dOperation

s/OR:Psych

ology,Marketin

g,Statistics

•Beyon

dTelep

hony:

VRU/IV

R(O

pt-O

ut-R

ates),Internet(over

60%),Hosp

italsED

(LWBS).55

Understa

nding(Im

)Patie

nce

•Observ

ing(Im

)Patiecn

e–Heterogen

eity:

Under

asin

gleroof,

thefraction

abandoningvaries

from6%

to40%

,dependingon

thetyp

eof

service/custom

er.

•Describ

ing(Im

)Patien

ceDynam

ically:

Irritationprop

ortional

toHazard

Rate

(Palm

’sLaw

).

•M

anaging(Im

)Patien

ce:

–VIP

vs.Regu

lars:whoismore

“Patient”?

–What

areweactu

allymeasu

ring?

–(Im

)Patien

ceIndex:

“How

longExp

ectto

wait”

relativeto

“How

longWillin

gto

wait”.

•Estim

atin

g(Im

)Patien

ce:Censored

Sam

plin

g.

•M

odelin

g(Im

)Patien

ce:

–The“W

ait”Cycle:

Exp

ecting,

Willin

g,Requ

ired,Actu

al,Perceived

,etc.

Thecase

oftheExp

erienced

&Ration

alcustom

er.

–(N

ash)Equilib

rium

Models.

56

Palm

’sLaw

ofIrrita

tion(1943-53):

∝Haza

rd-R

ate

of(Im

)Patie

nce

Distrib

utio

n

Small

Israeli

Bank(1

999):

Regularover

Prio

rity(V

IP)Custom

ers

Haza

rd-R

ate

function

ofτ≥

0(ab

solutely

continuous):

h(t)

=g(t)

1−G(t)

,

g=

Density

function

ofτ,

G=

Distrib

ution

function

ofτ.

Intu

ition:P{τ≤

t+Δ|τ

>t}≈

h(t)·

Δ.

57

P{Ab}

∝E[W

q]

Claim

:(Im

)Patien

cethat

isexp

(θ)im

plies

P{Ab}

=θ·

E[W

q ].

Small

Israeli

Bank:1999Data

Hourly

Data

Aggregated

050

100150

200250

300350

4000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Averag

e waitin

g tim

e, sec

Probability to abandon

050

100150

200250

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Averag

e waitin

g tim

e, sec


Thegrap

hsare

based

on4158

hourintervals.

Regression⇒

averagepatien

ce(1/θ)≈

250

0.56 ≈446

sec.

But(im

)patien

ceat

thisbankisnotexp

onential

!?

Moreover,

58

QueueingScie

nce

:Human

Behavior

Delayed A

bandons (IVR

) Balking (N

ew C

ustomers)

Learning (Internet C

ustomers)

59

�� !"!#�$� �%&#� ��'�

()*+,-./012341.567*�2 ,-8

020

4060

80100

1200

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

average waiting tim

e, sec

probability to abandon

erlang determ

inisticlognorm

al det m

ixture

D−M

ix

Er

D

LN

020

4060

80100

1200

0.05

0.1

0.15

0.2

0.25

0.3

0.35

average waiting tim

e, sec

probability to abandon

erlang determ

inisticlognorm

al det m

ixture

D−M

ix

ErD

LN

9:2 41;7./<�=#.>,-;78?410@;7A�BC41;7*%<�8DE

FGHI5JKL?MNL?OPQRSTU SV MWSXYZI�[RQRSXU/\3MNLVL�]^ Y�MW_X`a

FGb0 Icd�OP_^ U efSgMhMfiRL�]j�k QlL^ Umnopjh ^V LV a

FGqrI5s�iDe#U3iDOPQ^ _tu3v�iDMh^ wDL?O^ eDL^ U xV M^ U x^ OPx�x3L?wyS^ MWSgi#U�Lz \^ _+MNi{[a

FGH|}~�;��I�Z�@��Z��QRS�]yMW\3OWL�iD��Mfi�Y�i#UV M^ U�MV I'�� [^ U x5��

60

APatie

nce

Index

How

toquantify

(im)p

atie

nce

?

Theoretica

lPatien

ceIndex

=Willin

gto

Wait

Exp

ectedto

Wait .

How

tomeasu

re?Calcu

late?Assu

meExperie

nce

dcustom

ers.

Then,asim

ple

(butnot

toosim

ple)

model

suggests

theeasy-to-

measu

re:Empirica

lPatien

ceIndex

Δ=%

Served

%Abandoned

.

Patie

nce

index–Empirica

lvs.

Theoretica

l

0 1 2 3 4 5 6 7 8 9 10

23

45

67

89

Empirical Index

Theoretical Index

61

Queues=

Integra

tingth

eBuild

ingBlock

s

0 2 4 6 8 10 12 14

��

�i��

��r��

��

0 2 4 6 8 10 12 14

��

�i��

��r��

��

0 2 4 6 8 10 12 14

��

�i��

��r��

��

62

Delays=

Integra

tingth

eBuild

ingBlock

s

Exp

onential

Delays:

Small

Call

Center

ofan

IsraeliBank(1999)

Time

030

6090

120150

180210

240270

300

29.1 %

20 %

13.4 %

8.8 %

6.9 %5.4 %

3.9 %3.1 %

2.3 %1.7 %

Mean = 98

SD

= 105

Waiting tim

e

Exp quantiles

0200

400600

0 200 400 600

Delays:

Medium-Size

Call

Center

ofan

IsraeliBank(2006)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

2242

6282

102122

142162

182202

222242

262282

302322

342362

382

Waiting time, sec


63

Basic

(Mark

ovian)QueueingM

odels

ofa

Basic

Serv

iceStatio

n

Poisso

narrivals,E

xponentia

lservice

times,E

xponentia

l(im

)patien

ce.

Math

ematica

lFra

mework

:Markov

Jump-Processes

(Birth

&Death

).

M/M

/n

(Erla

ng-C

)Queue

agents

arrivals

12…

queue

n

M/M

/n+M

(Palm

/Erla

ng-A

)Queue

agents

arrivals

abandonment

12n …

queue

Additio

nalM

ark

ovian

Models:

Balkin

g,Trunks;

Retrials.

Applica

tions:

Perform

ance

Analysis,

Design

(EOS),Staffi

ng.

64

”TheFitte

stSurv

ive”and

Wait

Less

-M

uch

Less!

Erla

ng-A

vs.

Erla

ng-C

48calls

per

min,1min

averageservice

time,

2min

averagepatien

ce

prob

ability

ofwait

averagewait

vs.number

ofagents

vs.number

ofagents

3540

4550

5560

6570

0

0.2

0.4

0.6

0.8 1

number of agents

probability of wait

Erlang−

AE

rlang−C

3540

4550

5560

6570

0 10 20 30 40 50

number of agents

average waiting time, sec

Erlang−

AE

rlang−C

If50

agents:

M/M

/nM/M

/n+M

M/M

/n,λ↓

3.1%

Fraction

abandoning

–3.1%

-

Average

waitin

gtim

e20.8

sec3.7

sec8.8

sec

Waitin

gtim

e’s90-th

percentile

58.1sec

12.5sec

28.2sec

Average

queuelen

gth17

37

Agents’

utilization

96%93%

93%

65

Modellin

g(Im

)Patie

nce

:Tim

eW

illingvs.

Tim

eRequire

dto

Wait

agents

arrivals

abandonment

(lost calls)

12n …

queue

•(Im

)Patie

nce

Tim

eτ∼

G:

Tim

eacustom

erwillin

gto

wait

forservice.

•Offered

Wait

V:

Tim

eacustom

errequire

dto

wait

forservice;

inoth

erword

s,waitin

g-timeof

aninfin

itely-patient

custom

er.

•Ifτ≤

V,custom

erAbandons;

otherw

ise,custom

erServ

ed;

•Actu

alwait

W=min(τ,V

).

66

Call Center Data: Hazard Rates (Un-Censored)

Israel

U.S.

(Im)Patience Time

0 50 100 150 2000

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5x 10

−3

time, sec

haza

rd r

ate

0 10 20 30 40 50 600

0.05

0.1

0.15

0.2

0.25

0.3

0.35

time, sec

haza

rd r

ate

Required/Offered Wait

0 10 20 30 40 50 600

2

4

6

8

10

12

14

16

time, sec

haza

rd r

ate

actuarial estimatespline smoother

30

67

Predictin

gPerfo

rmance

ModelPrim

itives(eg.

Erlan

g-A):

•Arrivals

toservice

(eg.Poisson

)

•(Im

)Patien

cewhile

waitin

gτ(eg.

Exp)

•Service

times

(eg.Exp)

•Number

ofAgents.

ModelOutp

ut:

Offered-W

aitV

Operation

alPerform

ance

Measu

recalcu

lablein

termsof

(τ,V).

•eg.

Average

Wait

=E[m

in{τ,V}

]

•eg.

%Abandonment

=P{

τ<

V}

Application

s:

•Perfo

rmance

Analysis

•Desig

n,Phenomena(Poolin

g,Econ

omies

ofScale)

•Staffing–How

ManyAgents

(FTE’s=Full-T

ime-E

quivalent’s)

•Note:

Control

requires

model-refin

ements

-later,

inSBR.

68

Erla

ng-A

:A

Sim

ple

Modelatth

eServ

iceofComplexRealitie

s

•Small

Israelibank(10

agents);

•Data-B

asedEstim

ationof

Patien

c(P{

Ab}

/E[W

q ]);

•Grap

h:Actu

alPerform

ance

vs.Erlan

g-APred

ictions(aggre-

gationof

40sim

ilarhours).

P{Ab}

E[W

q ]P{W

q>

0}

00.1

0.20.3

0.40.5

0.60

0.1

0.2

0.3

0.4

0.5

Probability to abandon (E

rlang−A)

Probability to abandon (data)

050

100150

200250

0 50

100

150

200

250

Waiting tim

e (Erlang−A

), sec

Waiting time (data), sec

00.2

0.40.6

0.81

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

Probability of w

ait (Erlang−A

)

Probability of wait (data)

•Questio

n:Why

Erlan

g-Aworks?

indeed

,all

itsunderlyin

g

assumption

sfail

(Arrivals,

Services,

Impatien

ce)

•Toward

saTheoretica

lAnsw

er:

Robustn

essandLim

i-

tations,via

Asym

ptotic

(QED)Analysis.

•Pra

cticalSignifica

nce

:Asym

ptotic

results

applicab

lein

small

systems(eg.

health

care).

69

QueueingScie

nce

:In

Support

ofErla

ng-A

Israeli

Bank:Yearly

Data

Hourly

Data

Aggregated

050

100150

200250

300350

4000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

Averag

e waitin

g tim

e, sec


050

100150

200250

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

0.5

0.55

Averag

e waitin

g tim

e, sec


Data:P{

Ab}

∝E[W

q ].

Theory

:P{

Ab}

=θ·E

[Wq ],

if(Im

)Patien

ce=

Exp(θ).

Proof:

Let

λ=Arrival

Rate.

Then,by

Conservation

&Little:

λ·P{

Ab}

=θ·

E[L

q ]=

θ·λ·E[W

q ],q.e.d

.

Recip

e:Use

Erlan

g-A,with

θ=

P{

Ab}

/E[W

q ](slop

eabove).

But(Im

)Patien

ceisnotExp

onentially

distrib

uted

!?

QueueingScie

nce

:via

Data

&Theory,

Linearity

Robust.

Serv

iceEngineerin

g:via

Theory

&Simulation

s,often-en

ough,

•Reality≈

M/G

/n+

G≈

Erlan

g-A,in

which

θ=g(0);

•P{

Ab}

≈g(0)·

E[W

q ],hence

recipeprevails,

oftenenough.

70

4CallC

enters:

Perso

nalToolfor

Work

force

Management

Calcu

lationsbased

ontheM.Sc.thesis

ofOfer

Garn

ett.

Isexten

sivelyused

inService

Engin

eering.

Install

at

http://ie.technion.ac.il/serveng/4CallCenters/Downloads.htm

4CallC

enters:

Outp

utExample

71

4CallC

enters:

Congestio

nCurv

es

Vary

inputparam

etersof

Erlan

g-Aanddisp

layoutput

(perform

ance

measu

res)in

atab

leor

graphically.

Example:1/μ

=2minu

tes,1/θ

=3minu

tes;

λvaries

from40

to230

callsper

hour,in

stepsof

10;

nvaries

from2to

12.

Pro

bability

toabandon

Avera

gewait

.0%

10.0%

20.0%

30.0%

40.0%

50.0%

60.0%

70.0%

80.0%

4090

140190

Calls per Interval

%Abandon

23

45

67

89

1011

12EO

S curve

0 20 40 60 80

100

120

140

4090

140190

Calls per Interval

Average Time in Queue (secs)

23

45

67

89

1011

12EO

S curve

Red

curve:

offered

loadper

serverfixed

.

EOS(Econ

omies-O

f-Scale)

observed

.

Why

thetwograp

hsare

similar?72

4CallC

enters:

Advance

dStaffingQuerie

s

Set

multip

leperform

ance

goals.

Example:1/μ

=4minu

tes,1/θ

=5minu

tes;

λvaries

from100

to1200,

instep

sof

50.

Perfo

rmancetarg

ets:

P{Ab}≤

3%;

P{Wq<

20sec;

Sr}≥

0.8.

4CallC

enters

outp

ut

73

Advance

dStaffingQuerie

sII

Recom

mended

staffinglevel

Target

perform

ance

measu

res

0 10 20 30 40 50 60 70 80 90100300

500700

9001100

Calls per Interval

Number of Agents

.0%

.5%

1.0%

1.5%

2.0%

2.5%

3.0%

3.5%

100300

500700

9001100

Calls per Interval

%Abandon

78%

80%

82%

84%

86%

88%

90%

92%

%Served within 20 sec

%Abandon

%Abandon Target

%Served w

ithin 20 sec%

Served within 20 sec Target

EOS:10

agentsneed

edfor

100calls

per

hourbutonly83

for1200

callsper

hour.

74

Call

Centers:

Hiera

rchicalOpera

tionalView

Forecasting Custom

ers: Statistics, Time-Series

Agents : H

RM

(Hire, Train; Incentives, C

areers)

Staffing: Queueing Theory

Service Level, Costs

#FTE’s (Seats)

per unit of time

Shifts: IP, Com

binatorial Optim

ization; LP

Union constraints, C

osts

Shift structure

Rostering: H

euristics, AI (C

omplex) Individual constraints

Agents A

ssignments

Skills-based Routing: Stochastic C

ontrol

75

Opera

tionalRegim

esin

Many-S

erv

erQueues

TheQuality

-Efficie

ncy

Tra

deoff

¯in

services(call

centers).

Offered

Load:R

=λ×

E[S]

Erlan

gs,nam

ely

minu

tesof

work

(=service)

that

arriveper

minu

te.

Efficie

ncy

-Driv

en

(ED):

n≈

R−

γR

,γ>

0.

Understa

ffingwith

respect

totheoffered

load.

Quality

-Driv

en

(QD):

n≈

R+δR

,δ>

0.

Oversta

ffingwith

respect

totheoffered

load.

Quality

and

Efficie

ncy

-Driv

en

(QED):

n≈

R+β √

R,

−∞<

β<

∞.

TheSquare-R

ootStaffingRule:

•Introd

uced

byErla

ng,alread

yin

1924!

•Rigorized

byHalfin-W

hitt,

only

in1981

(Erlan

g-C);

•Above

version:with

Garn

ett,Reim

an,Zeltyn

(Erlan

g-A/G

).

76

Opera

tionalRegim

es:

Rules-o

f-Thumb

Assu

methat

offeredloadR

isnot

small

(λ→∞).

ED

regim

e:n

≈R−

γR

,0.1≤

γ≤0.25

.

•Essentially

allcustom

ersdelayed

prior

toservice;

•%Abandoned≈

γ(10-25%

);

•Average

wait≈

30secon

ds-2minu

tes.

QD

regim

e:n

≈R+δR

,0.1≤

δ≤0.25

.

Essentially

nodelays.

QED

regim

e:

n≈

R+β √

R,

−1≤

β≤

1.

•%Delayed

betw

een25%

and

75%;

•%Abandoned

is1-5%

;

•Average

wait

isone-ord

erless

than

averageservice-tim

e

(secondsvs.

minu

tes).

77

TheQED

Regim

ein

Erla

ng-A

:DelayPro

bability

−3−2

−10

12

30

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9 1

service grade

delay probability

Erlang−C

μ/θ=10μ/θ=4μ/θ=1μ/θ=0.25μ/θ=0.1

Note.Erla

ng-C

isthelim

itofE

rlang-A

,as

patien

ceincreases

indefinitely.

78

Dim

ensio

ningErla

ng-A

:Optim

alQoS

Cost

=c·n+d·λE[W

q ].

(Abandonment

costcan

beaccom

modated

viaP{A

b}=θE

[Wq ].)

Optim

alsta

ffinglevel:

n ∗≈

R+β∗(r;s) √

R,

r=d/c,

s=

√μ/θ

,

•r<

θ/μim

plies

that

“close-the-gate”

isoptim

al.

•r≤

20⇒

β∗<

2;r≤

500⇒

β∗<

3!

•Remarkable

accuracy

androb

ustn

ess,via

numerical

tests.

79

Non-P

ara

metric

QueueingM

odels:

ABasic

Serv

iceStatio

n

Assu

mption

s:

•Non-Poisson

(Renew

al)Arrivals;

•Non-Exp

onential

i.i.d.Service

Tim

es;

•Non-Exp

onential

i.i.d.(Im

)Patien

ce.

Analysis:

•Intractab

leModels,

hence

resortto

Approxim

ations;

•Single-

andModerately-F

ewServers

inHeavy-T

raffic;

(Many-S

erverModels

with

General

Service

Tim

esis

stilla

Theory

intheMakin

g);

•Stead

y-State

Analysis;

•Two-M

oment

Theory:

Mean

sandCoeffi

cients-of-Variation

s;

•Priorities;

•Optim

alSchedulin

gof

Custom

erClasses:

Thecμ

-Rule,

and

Relatives.

80

Interdependence of the Building Blocks

�

�

�

�

Figure 12: Mean Service Time (Regular) vs. Time-of-day (95% CI) (n =

42613)

�i�e o� �ay

�ea

n �

ervi

ce �

i�e

10 15 20

100

120

140

160

180

200

220

240

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

81

Arrival Rates: Longest Services at Peak Loads

�

�

�

�

Arrivals: Inhomogeneous Poisson

Figure 1: Arrivals (to queue or service) – “Regular” Calls

0

20

40

60

80

100

120

Calls/Hr (Reg)

7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

VRU Exit Time

82

Service Times: Short and Long

Service Time

Overall Regular service

New customers

Internet Stock

Mean 188

181 111 381 269

SD 240 207 154 485 320

Med 114 117 64 196 169

83

Service Times: Stochastically Ordered

Service TimeSurvival curve, by Types

Time

Surv

ival

Means (In Seconds)

NW (New) = 111

PS (Regular) = 181

NE (Stocks) = 269

IN (Internet) = 381

84

(Im)Patience: Regulars vs. VIP

8586

Custo

merRelatio

nsh

ipsM

anagement

Natio

nsB

ank’s

Desig

nofth

eServ

iceEnco

unter

ExamplesofSpecifi

catio

ns:

Assig

nable

Gra

deOfServ

ice

90% of calls

85% of calls

70% of calls

VRU

Target

within 8 business days

within 2 business days

during callProblem

Resolution

basic productproduct experts

universalR

ep. Training

< 9%< 5%

< 1%A

bandonment rate

mail

call / mail

call / faxTrans. Confirm

ation

FCFS

FCFS

request rep / callbackR

ep. Personalization

2 min. average

4 min. average

no limit

Average Talk Tim

e

50% in 20 seconds

80% in 20 seconds

100% in 2 rings

Speed of Answ

er

RG3

RG2

RG1

Natio

nsB

ankCRM

:Relatio

nsh

ipGro

ups:

•RG1:

high

-valuecustom

ers;

•RG2:

margin

allyprofitab

lecustom

ers(w

ithpotential);

•RG3:

unprofi

tablecustom

er.

CRM

=Custom

erRevenueManagem

ent

87

Distrib

utedCallCenter(U

.S.Bank)

NY

1R

I 3

PA2MA4

179+5619+3

11+174+7

8+1

19+120

508+2

101+2

2

External arrivals:20922063(98.6%

Served)+29(1.4%

Aban)

Not

Interqueued:1209(57.8%)

Served: 1184(97.9/56.6) A

ban: 25(2.1/1.2) Interqueued :883(42.2)

Served here:174(19.7/8.3)Served at 2: 438(49.6/20.9) S

dt3

External arrivals: 16941687(99.6%

Served)+7( 0.4%

Aban)

Not Interqueued:

1665(98.3)Served: 1659 (99.6/97.9) A

ban: 6 (0.4/04)Interqueued:28+1 (1.7)

Served here: 17(58.6/1) Served at 1: 3 (10.3/0.2)

External arrivals: 122 112(91.8

Served)+10(8.2 Aban)

Not Interqueued: 93

(76.2)Served: 85 (91.4/69.7) A

ban: 8 (8.6/6.6) Interqueued:27+2

(23.8)Served here: 14(48.3/11.5) Served

at 1:6

External arrivals: 1770 1755(99.2

Served)+15(0.8 Aban)

Not Interqueued:

1503(84.9)Served: 1497 (99.6/84.6) A

ban: 6 (0.4/0.3) Interqueued:258+9

(15.1)Served here: 110 (41.2/6.2) Served at 1:58 (21

7/33)

Internal arrivals: 224

Served at 1: 67 (29.9) Served at 2: 41 (18.3) Served at 3: 87 (38.8) Served at 4:


Served at 1: 157 (24.4) Served at 2: 195 (30.3) Served at 3: 282 (43.9) Served at 4: 4 (0.6) A

banat1:3


Served at 1: 17(21) Served at 3: 42(51.9) Served at 4: 15(18

5)

Internal arrivals: 613Served at 1: 41(6.7) Served at 2: 513(83.7) Served at 3: 55(9.0) A

ban at 1: 2(0.3)

10 AM

– 11 AM

(03/19/01): Interflow C

hart Am

ong the 4 Call

Ct

fFltB

k

88

Skills-B

ase

Routin

g:

Opera

tionalComplexitie

s

Multi-queue parallel-server system

= schematic depiction of a telephone call-center

:

1

2

3

4

1 12

2

3 3

4

4

12

34

56

7

8

S

1

S2

S

3

Here the

's designate arrival rates, the 's service rates, the

's abandonment rates, and the S's are the

number of servers in each server-pool.

Skills-Based D

esign:

-Queue: "custom

er-type" requiring a specific type of service;

-Server-Pool: "skills" defining the service-types it can perform;

-Arrow

: leading into a server-pool define its skills / constituency.

For example, a server w

ith skill 2 (S2) can serve customers of type 3 (C

3)at rate

6 customers/hour.

Custom

ers of type 3 arrive randomly at rate

3 customers/hour, equipped w

ith

an impatience rate of

3 .

89

SomeCanonica

lDesig

ns-Anim

atio

n

I N X

W (V

) M

12

12

12

12 1 3 2

I– dedicated (specialized) agents

N: for exam

ple,

- C1 = V

IP, then S2 are serving C1 to im

prove service level.

- C2 = V

IP, then S2 serve C1 to im

prove efficiency.

- S2 = Bilingual.

X: for exam

ple, S1 has C1 as Prim

ary and C2 as Secondary Types.

V: Pure

Scheduling;U

pside-down V

: Pure Routing.

90

MajorD

esign / Engineering Decisions

1. Classifying custom

ers into types (Marketing):

Tech. support vs. Billing, V

IP vs. Mem

bers vs. New

2. Determ

ining server skills, incentives, numbers (H

RM

, OM

,OR

)

Universal vs. Specialist, Experienced / N

ovice, Uni- / M

ulti-lingual;

Staffing: how m

any servers?

3. Prerequisite Infrastructure - MIS / IT / D

ata-Bases (C

S, Statistics)

CTI, ER

P, Data-M

ining

MajorC

ontrol Decisions

4. Matching custom

ers and agents (OR

)

- Custom

er Routing: W

henever an agent turns idle and there

are queued customers, w

hich customer (if any) should be routed

to this agent.

- Agent Scheduling: W

henever a customer arrives and there

are idle agents, which agent (if any) should serve this custom

er.

5. Load B

alancing

- Routing of custom

ers to distributed call centers (eg. nation-wide)

91

SBR:W

here

are

We?

Still

ach

alle

nge,both

theoretically

andpractically.

•“E

xact”analysis

ofMarkovian

models

(butmostly

“queue-

less”),by

Koole

etal.

•TheED-regim

eisrelatively-w

ellcovered,in

conventionalh

eavy-

traffica-la

Stolyar’s

(control)andtheflu

id-m

odels

ofHarrison

etal

(staffing+

control,accom

modatin

galso

non-param

etric

models

with

“time-varyin

gran

dom

ness”).

•Control

intheQED-regim

eis“th

eoretically-covered”by

Atar

etal.

(exponential

service-times).

•Staffi

ng+

Control

intheQED-regim

ecovers

special

cases:

Gurvich

,Arm

ony;Dai,

Tezcan

;Gurvich

,Whitt;

...

Still

plenty

todo.

92

Interestin

gandSignifica

ntAdditio

nalTopics

•Stoch

asticService

Netw

ork

s:

–ClassicalM

arkovian:Jackson

andGord

on-New

ell,Kelly/B

CMP

Netw

orks;

–Non-Param

etricNetw

orkApproxim

ations(Q

NA,SBR).

•Service

Quality

(Psych

ology,Marketin

g);

•Addition

alSign

ificant

Service

Sectors:

Health

care,Hosp

ital-

ity,Retail,

Profession

alServices

(Consultin

g),...;

e-health

,

e-retail,e-·,

...;

•Convergen

ceof

Services

andManu

facturin

g:

After-S

aleor

Field

Support

(life-timecustom

er-value);

•Service

Supply-C

hain

s;

•New

-Service

Develop

ment

(orService-E

ngin

eeringinGerm

any);

•Design

andManagem

entof

theCustom

er-System

Interface:

Multi-M

edia

Channels;

Appointm

ents;Pricin

g;...

•Revenu

eManagem

ent(Finite

Horizon

,Call

Centers,

...)

93

CallCenters

=Q’s

w/Im

patie

ntCusto

mers

15Years

Histo

ry,or“A

Modellin

gGalle

ry”

1.Kella,

Meilijson

:Practice⇒

Abandonment

important

2.Shim

kin,Zohar:

Nodata⇒

Ration

alpatien

cein

Equilib

rium

3.Carm

on,Zakay:

Cost

ofwaitin

g⇒Psych

ologicalmodels

4.Garn

ett,Reim

an;Zeltyn

:Palm

/Erlan

g-Ato

replace

Erlan

g-

C/B

asthestan

dard

Stead

y-statemodel

5.Massey,

Reim

an,Rider,

Stolyar:

Pred

ictablevariab

ility⇒Fluid

models,

Diffusion

refinem

ents

6.Ritov;

Sakov,

Zeltyn

:Finally

Data⇒

Empirical

models

7.Brow

n,Gans,Haip

eng,

Zhao:

Statistics⇒

Queuein

gScien

ce

8.Atar,

Reim

an,Shaikh

et:Skills-b

asedrou

ting⇒

Controlm

od-

els

9.Nakib

ly,Meilijson

,Pollatch

ek:Pred

ictionof

waitin

g⇒Onlin

eModels

andReal-T

imeSimulation

10.Garn

ett:Practice⇒

4CallC

enters.com

11.Zeltyn

:Queuein

gScien

ce⇒Empirically-B

asedTheory

12.Borst,

Reim

an;Zeltyn

:Dim

ension

ingM/M

/N+G

13.Mom

cilovic:Non-Param

etric(G

/GI/N

+GI)QED

Q’s

14.Jen

nings;

Feld

man,Massey,

Whitt:

Tim

e-stableperform

ance

(ISA)

94

6 ServEng Mini Course Genericie.technion.ac.il/serveng/References/Mini_course_generic/... · 2012....

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Transcript of 6 ServEng Mini Course Genericie.technion.ac.il/serveng/References/Mini_course_generic/... · 2012....