6 ServEng Mini Course Genericie.technion.ac.il/serveng/References/Mini_course_generic/... · 2012....
Transcript of 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
Time (Resolution 1 sec.)
Relative frequencies, %
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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������������
���
���
���
���
# 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
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 -
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
Case Type 0 Judge1Case Type 01 Judge2Case Type 3 Judge3
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)
.
.
.
..
Case Type 0 Judge1Case Type 01 Judge2Case Type 3 Judge3
Judge4Judge5
Avg
. Mon
ths -
W
Avg. Cases / Month -
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
Case Type 0 Judge1Case Type 01 Judge2Case Type 3 Judge3
Judge4Judge5
Avg
. Mon
ths -
W
Avg. Cases / Month -
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
��
��
���
����
����
��� �� �� �� �� 5� �� �� �� ��
�ambda�t���������on������t�������,������otherw
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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44
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
Time (Resolution 5 sec.)
Relative frequencies, %
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
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��erage�������sec
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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
Time (Resolution 5 sec.)
Relative frequencies, %
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
Probability to abandon
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
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()*+,-./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
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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
Relative frequencies, %
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
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
Probability to abandon
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
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:
Internal arrivals: 643
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
Internal arrivals: 81
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