data-based service networksie.technion.ac.il/serveng/references/0_informs_beijing_final.pdf ·...

Data-Based Service Networks:A Research Framework for

Asymptotic Inference, Analysis & Controlof Service Systems

Avi Mandelbaum

Technion, Haifa, Israel

http://ie.technion.ac.il/serveng

INFORMS Beijing, June 2012

1 1

Research Partners� Students:

Aldor∗, Baron∗, Carmeli, Feldman∗, Garnett∗, Gurvich∗, Huang,Khudiakov∗, Maman∗, Marmor∗, Reich, Rosenshmidt∗, Shaikhet∗,Senderovic, Tseytlin∗, Yom-Tov∗, Yuviler, Zaied, Zeltyn∗, Zychlinski,Zohar∗, Zviran∗, . . .

� Theory:Armony, Atar, Gurvich, Jelenkovic, Kaspi, Massey, Momcilovic,Reiman, Shimkin, Stolyar, Wasserkrug, Whitt, Zeltyn, . . .

� Industry:Mizrahi Bank (A. Cohen, U. Yonissi), Rambam Hospital (R. Beyar, S.Israelit, S. Tzafrir), IBM Research (OCR Project), Hapoalim Bank (G.Maklef, T. Shlasky), Pelephone Cellular, . . .

� Technion SEE Center / Laboratory:Feigin; Trofimov, Nadjharov, Gavako, Kutsy; Liberman, Koren,Plonsky, Senderovic; Research Assistants, . . .

� Empirical/Statistical Analysis:Brown, Gans, Zhao; Shen; Ritov, Goldberg; Gurvich, Huang,Liberman; Armony, Marmor, Tseytlin, Yom-Tov; Zeltyn, Nardi,Gorfine, . . .

2 2

Contents

� Service Systems: Call Centers, Hospitals, Websites, · · ·� Prevalent paradigm of modeling and approximations

� Redefining the role of Asymptotics, via Data

� ServNets: QNets, SimNets; FNets, DNets

� Ultimate Goal: Data-based creation and validationof ServNets, automatically in real-time

3 3

Contents





� Why be Optimistic? Pilot at the Technion SEELab

3 4

Contents





� Why be Optimistic? Pilot at the Technion SEELab

� Related themes: Process Mining (BPM), Networks (Social,Biological,· · · ), “Almost-Complex" Systems, Simulation-based. . .,

� Scenic Route: Open Problems, New Directions, UnchartedTerritories

3 5

On Asymptotic Research of Queueing Systems

Queueing asymptotics has grown to become a central researchtheme in Operations Research and Applied Probability, beyond justqueueing theory. Its claim to fame has been the deep insights that itprovides into the dynamics of Queueing Networks (QNets), andrightly so:

� Kingman’s invariance principle in conventional heavy-traffic� Whitt’s sample-path (functional) framework� Reiman’s network analysis via oblique reflection� Bramson-Williams’ framework for state-space collapse� Laws’ resource pooling� Harrison’s paradigm for asymptotic control (Wein; van Mieghem’s Gcμ)� Dai’s fluid-based stability� Halfin-Whitt’s (QED regime) (√-staffing for many-server queues)� P = NP : Atar’s equivalence of Preemptive and Non-Preemptive SBR;

Stolyar, Gurvich� Massey-Whitt’s research of time-varying queues

4 6

On Asymptotic Research of Queueing Systems

Queueing asymptotics has grown to become a central researchtheme in Operations Research and Applied Probability, beyond justqueueing theory. Its claim to fame has been the deep insights that itprovides into the dynamics of Queueing Networks (QNets), andrightly so:

� Kingman’s invariance principle in conventional heavy-traffic� Whitt’s sample-path (functional) framework� Reiman’s network analysis via oblique reflection� Bramson-Williams’ framework for state-space collapse� Laws’ resource pooling� Harrison’s paradigm for asymptotic control (Wein; van Mieghem’s Gcμ)� Dai’s fluid-based stability� Halfin-Whitt’s (QED regime) (√-staffing for many-server queues)� P = NP : Atar’s equivalence of Preemptive and Non-Preemptive SBR;

Stolyar, Gurvich� Massey-Whitt’s research of time-varying queues

4 7

Applying Queueing Asymptotics

Has it helped one approximate or simulate a service systemmore efficiently, estimate its parameters more accurately, teachit to our students more effectively, perhaps even manage thesystem better?

I am of the opinion that the answers to such questions havebeen too often negative, that positive answers must have theoryand applications nurture each other, which is good, and myapproach to make this good happen is by marrying theory with

data .

5 8

Models Approximations

QNets SimNets

Accuracy

Phenomenology

Prevalent Asymptotic Approximations

System (Data)

6 9


QNets SimNets FNet DNet Models

Accuracy

Phenomenology

X

Data–Based Prevalent Asymptotic Approximations Models

System (Data)

X X

7 10



Accuracy

Phenomenology Value

XX


System (Data)

X X

8 11

Value

Call-Center Environment: Service Network

16 12

Call-Center Network: Gallery of Models

Agents(CSRs)

Back-Office

Experts)(Consultants

VIP)Training (

Arrivals(Business Frontier

of the21th Century)

Redial(Retrial)

Busy)Rare(

Goodor

Bad

Positive: Repeat BusinessNegative: New Complaint

Lost Calls

Abandonment

Agents

ServiceCompletion

Service Engineering: Multi-Disciplinary Process View

ForecastingStatistics

New Services Design (R&D)Operations,Marketing

Organization Design:Parallel (Flat)Sequential (Hierarchical)Sociology/Psychology,Operations Research

Human Resource Management

Service Process Design

To Avoid Delay

To Avoid Starvation Skill Based Routing

(SBR) DesignMarketing,Human Resources,Operations Research,MIS

CustomersInterface Design

Computer-TelephonyIntegration - CTIMIS/CS

Marketing

Operations/BusinessProcessArchiveDatabaseDesignData Mining:MIS, Statistics, OperationsResearch,Marketing

InternetChatEmailFax

Lost Calls

Service Completion)75% in Banks (

( Waiting TimeReturn Time)

Logistics

CustomersSegmentation -CRM

Psychology, OperationsResearch,Marketing

Expect 3 minWilling 8 minPerceive 15 min

PsychologicalProcessArchive

Psychology,Statistics

Training, IncentivesJob Enrichment

Marketing,Operations Research

Human Factors Engineering

VRU/IVR

Queue)Invisible (

VIP Queue

(If Required 15 min,then Waited 8 min)(If Required 6 min,then Waited 8 min)

Information DesignFunctionScientific DisciplineMulti-Disciplinary

IndexCall Center Design

(Turnover up to 200% per Year)(Sweat Shops

of the21th Century)

Tele-StressPsychology

18 13

Call-Center Network: Gallery of Models

Agents(CSRs)

Back-Office

Experts)(Consultants

VIP)Training (

Arrivals(Business Frontier

of the21th Century)

Redial(Retrial)

Busy)Rare(

Goodor

Bad

Positive: Repeat BusinessNegative: New Complaint

Lost Calls

Abandonment

Agents

ServiceCompletion

Service Engineering: Multi-Disciplinary Process View

ForecastingStatistics

New Services Design (R&D)Operations,Marketing

Organization Design:Parallel (Flat)Sequential (Hierarchical)Sociology/Psychology,Operations Research

Human Resource Management


To Avoid Delay

To Avoid Starvation Skill Based Routing

(SBR) DesignMarketing,Human Resources,Operations Research,MIS


Computer-TelephonyIntegration - CTIMIS/CS

Marketing


InternetChatEmailFax

Lost Calls

Service Completion)75% in Banks (

( Waiting TimeReturn Time)

Logistics

CustomersSegmentation -CRM

Psychology, OperationsResearch,Marketing

Expect 3 minWilling 8 minPerceive 15 min



Training, IncentivesJob Enrichment

Marketing,Operations Research

Human Factors Engineering

VRU/IVR

Queue)Invisible (

VIP Queue

(If Required 15 min,then Waited 8 min)(If Required 6 min,then Waited 8 min)

Information DesignFunctionScientific DisciplineMulti-Disciplinary

IndexCall Center Design

(Turnover up to 200% per Year)(Sweat Shops

of the21th Century)

Tele-StressPsychology

19 14

Retail

PremierBusiness Platinum Consumer Loans Online BankingEBO TelesalesSubanco Case Quality Priority Service AST CCO Quick&Reilly BPS

1_1 1_57 1_15 2_3 2_63_1 3_5 5_1 6 8 10_1 11 12 13 15 17

10430 189932947 384 9840 157

54 1455 25755551 2372 597 91 195 342 3660 2173639 3251325 487 32 12 619 2352 3668 4844 447

USBank April 2, 2001 16

The Basic Staffing Model: Erlang-A (M/M/N + M)agents

arrivals

abandonment

1

2

n

…

queue

Erlang-A (Palm 1940’s) = Birth & Death Q, with parameters:

� λ – Arrival rate (Poisson)� μ – Service rate (Exponential; E [S] = 1

μ )

� θ – Patience rate (Exponential, E [Patience] = 1θ )

� N – Number of Servers (Agents).69 17

Erlang-A: Practical Relevance?

Experience:� Arrival process not pure Poisson (time-varying, σ2 too large)� Service times not Exponential (typically close to LogNormal)� Patience times not Exponential (various patterns observed).

70 18



� Building Blocks need not be independent (eg. long waitassociated with long service; with w/ M. Reich and Y. Ritov)

� Customers and Servers not homogeneous (classes, skills)� Customers return for service (after busy, abandonment;

dependently; P. Khudiakov, M. Gorfine, P. Feigin)� · · · , and more.

70 19



� Building Blocks need not be independent (eg. long waitassociated with long service; with w/ M. Reich and Y. Ritov)

� Customers and Servers not homogeneous (classes, skills)� Customers return for service (after busy, abandonment;

dependently; P. Khudiakov, M. Gorfine, P. Feigin)� · · · , and more.

Question: Is Erlang-A Relevant?

YES ! Fitting a Simple Model to a Complex Reality, bothTheoretically and Practically

70 20

Erlang-A: Fitting a Simple Model to a Complex Reality

Hourly Performance vs. Erlang-A Predictions (1 year)

% Abandon E[Wait] %{Wait > 0}

0 0.1 0.2 0.3 0.4 0.5 0.60

0.1

0.2

0.3

0.4

0.5

Probability to abandon (Erlang−A)

Pro

babi

lity

to a

band

on (d

ata)

0 50 100 150 200 2500

50

100

150

200

250

Waiting time (Erlang−A), sec

Wai

ting

time

(dat

a), s

ec

0 0.2 0.4 0.6 0.8 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Probability of wait (Erlang−A)

Pro

babi

lity

of w

ait (

data

)

� Empirically-Based & Theoretically-Supported Estimation of(Im)Patience: θ = P{Ab}/E[Wq])

� Small Israeli Bank (more examples in progress)� Hourly performance vs. Erlang-A predictions, 1 year: aggregated

groups of 40 similar hours71 21

Universal Approximations: Erlang-A (M/M/N + M)agents

arrivals

abandonment

1

2

n

…

queuew/ I. Gurvich & J. Huang

82 22


arrivals

abandonment

1

2

n

…


� QNet: Birth & Death Queue, with B - D rates

F (q) = λ− μ · (q ∧ n)− θ · (q − n)+, q = 0, 1, . . .

82 23

F q n q n +F (q) = λ− μ · (q ∧ n)− θ · (q − n)+,


arrivals

abandonment

1

2

n

…



F (q) = λ− μ · (q ∧ n)− θ · (q − n)+, q = 0, 1, . . .

� FNet: Dynamical (Deterministic) System – ODEdxt = F (xt)dt , t ≥ 0

82 24

dxtxx F xtxx dt ,= F (xt)d


arrivals

abandonment

1

2

n

…



F (q) = λ− μ · (q ∧ n)− θ · (q − n)+, q = 0, 1, . . .

� FNet: Dynamical (Deterministic) System – ODEdxt = F (xt)dt , t ≥ 0

� DNet: Universal (Stochastic) Approximation – SDE

dYt = F (Yt)dt +√

2λ dBt , t ≥ 0

eg. μ = θ, or n = ∞: x = λ− μ · x , Y = OU process

Accuracy increases as λ ↑ ∞ (no additional assumptions)83 25

,dBt ,

Universal Approximation: Why 2λ?

� Semi-martingale representation of the B&D process:Fluid + Martingale

� Predictable quadratic variation:∫ t

0[λ+ μ(Qs ∧ n) + θ(Qs − n)+]ds

� In steady-state, arrival rate ≡ departure rate:

λ = E[μ(Qs ∧ n) + θ(Qs − n)+]

� Expectation of the predictable quadratic variation:

E

∫ t

0[λ+ μ(Qs ∧ n) + θ(Qs − n)+]ds = 2λt

� dMartingalet ≈√

2λ · dBrowniant

94 27

Why 22λ?

Value of Universal Approximation

� Tractable - closed-form stable expressions� Accurate - more than heavy traffic limits� Robust - all many-server regimes, and beyond, with hardly any

assumptions� Value

� Performance Analysis� Optimization (Staffing)� Inference (w/ G. Pang)� Simulation (w. J. Blanchet)

� Limitation: Steady-State (but working on it)

Why does it work so well?

Coupling “Busy" + “Idle" Excursions of B&D and the correspondingDiffusion (durations order 1√

λ)

83 26

Inference SimLab

Control

Design

Predictions



Accuracy

Phenomenology Value

XX

X


System (Data)

X X

10 28

System = Coin Tossing, Model = Binomial ; de Moivre 1738

Approx. / Models: SLLN (FNets), CLT (DNets) ; Laplace 1810

Value: Exceeds Value of originating stylized model

Normal, Brownian Motion ; Bachalier 1900

Poisson ; Poisson 1838



Accuracy

Phenomenology Value

XX


System (Data)

X X

9 29

Normal,

Poisson

Coin Tossing, Binomial

SLLN CLT

Asymptotic Landscape: 9 Operational Regimes, and then someErlang-A, w/ I. Gurvich & J. Huang

Erlang-A Conventional scaling Many-Server scaling NDS scalingμ & θ fixed Sub Critical Over QD QED ED Sub Critical OverOffered load 1

1+δ1− β√

n1

1−γ1

1+δ1− β√

n1

1−γ1

1+δ 1− βn

11−γper server

Arrival rate λ μ1+δ

μ− β√nμ μ

1−γnμ1+δ

nμ− βμ√

n nμ1−γ

nμ1+δ

nμ− βμ nμ1−γ

# servers 1 n nTime-scale n 1 n

Impatience rate θ/n θ θ/n

Staffing level λμ(1 + δ) λ

μ(1 + β√

n) λ

μ(1− γ) λ

μ(1 + δ) λ

μ+ β

√λμ

λμ(1− γ) λ

μ(1 + δ) λ

μ+ β λ

μ(1− γ)

Utilization 11+δ

1−√

θμ

h(β)√n

1 11+δ

1−√

θμ

h(β)√n

1 11+δ

1−√

θμ

h(β)n

1

E(Q) 1δ(1+δ)

√ng(β) nμγ

θ(1−γ)1δ�n

√ng(β)α nμγ

θ(1−γ)o(1) ng(β) n2μγ

θ(1−γ)

P(Ab) 1n

1δ

θμ

θ√nμ

g(β) γ 1n

(1+δ)δ

θμ�n

θ√nμ

g(β)α γ o( 1n2 )

θnμ

g(β) γ

P(Wq > 0) 11+δ

≈ 1 �n α ∈ (0,1) ≈ 1 ≈ 0 ≈ 1

P(Wq > T ) 11+δ

e− δ

1+δμT 1 +O( 1√

n) 1 +O( 1

n) ≈ 0 f(T ) ≈ 0 Φ(β+

√θμT )

Φ(β)1 +O( 1

n)

CongestionEWq

ES1δ

√ng(β) nμγ/θ 1

n(1+δ)

δ�n

α√ng(β) μγ

θo( 1

n) g(β) nμγ/θ

� Conventional: Ward & Glynn (03, G/G/1 + G)� Many-Server:

� QED: Halfin-Whitt (81), Garnett-M-Reiman (02)� ED: Whitt (04)� NDS: Atar (12)

81 30

Conventional Many--Server- NDSQEDQEDQDQD EDED

Offered load

# servers

Staffing

Asymptotic Landscape: 9 Operational Regimes, and then someErlang-A, w/ I. Gurvich & J. Huang

Erlang-A Conventional scaling Many-Server scaling NDS scalingμ & θ fixed Sub Critical Over QD QED ED Sub Critical OverOffered load 1

1+δ1− β√

n1

1−γ1

1+δ1− β√

n1

1−γ1

1+δ 1− βn

11−γper server

Arrival rate λ μ1+δ

μ− β√nμ μ

1−γnμ1+δ

nμ− βμ√

n nμ1−γ

nμ1+δ

nμ− βμ nμ1−γ

# servers 1 n nTime-scale n 1 n

Impatience rate θ/n θ θ/n

Staffing level λμ(1 + δ) λ

μ(1 + β√

n) λ

μ(1− γ) λ

μ(1 + δ) λ

μ+ β

√λμ

λμ(1− γ) λ

μ(1 + δ) λ

μ+ β λ

μ(1− γ)

Utilization 11+δ

1−√

θμ

h(β)√n

1 11+δ

1−√

θμ

h(β)√n

1 11+δ

1−√

θμ

h(β)n

1

E(Q) 1δ(1+δ)

√ng(β) nμγ

θ(1−γ)1δ�n

√ng(β)α nμγ

θ(1−γ)o(1) ng(β) n2μγ

θ(1−γ)

P(Ab) 1n

1δ

θμ

θ√nμ

g(β) γ 1n

(1+δ)δ

θμ�n

θ√nμ

g(β)α γ o( 1n2 )

θnμ

g(β) γ

P(Wq > 0) 11+δ

≈ 1 �n α ∈ (0,1) ≈ 1 ≈ 0 ≈ 1

P(Wq > T ) 11+δ

e− δ

1+δμT 1 +O( 1√

n) 1 +O( 1

n) ≈ 0 f(T ) ≈ 0 Φ(β+

√θμT )

Φ(β)1 +O( 1

n)

CongestionEWq

ES1δ

√ng(β) nμγ/θ 1

n(1+δ)

δ�n

α√ng(β) μγ

θo( 1

n) g(β) nμγ/θ

� Conventional: Ward & Glynn (03, G/G/1 + G)� Many-Server:

� QED: Halfin-Whitt (81), Garnett-M-Reiman (02)� ED: Whitt (04)� NDS: Atar (12)

� “Missing": ED+QED; Hazard-rate scaling (M/M/N+G); Time-Varying,Non-Parametric; Moderate- and Large-Deviation; Networks; Control

81 31

“Missing":

Protocols: Staffing (N) vs. Offered-Load (R = λ× E(S))IL Telecom; June-September, 2004; w/ Nardi, Plonski, Zeltyn

2205 half-hour intervals (13 summer weeks, week-days)67 32

QNets FNets DNets

Models

Value

Data–Based Asymptotic Framework

System (Data)

SimNets

11 33

Scope of the Service Industry

Guangzhou Railway Station, Southern China

13 34

Operation Focus: The “Production of Justice"The Labor-Court Process in Haifa, Israel

Queue

Mile Stone

Activity

Appeal

Proceedings

Closure

PrepareAllocateOpen File

Avg. sojourn time in months / years

Processing time in mins / hours / days

Phase Transition

Phase

• Operational Performance surrogate for

Financial, Psychological, Clinical,. . .14 36

Call Centers, Then Hospitals, Now Internet

Call Centers - U.S. Stat.

� $200 – $300 billion annual expenditures� 100,000 – 200,000 call centers� “Window" into the company, for better or worse� Over 3 million agents = 2% – 4% workforce

15 37

Call Centers, Then Hospitals, Now Internet

Call Centers - U.S. Stat.

� $200 – $300 billion annual expenditures� 100,000 – 200,000 call centers� “Window" into the company, for better or worse� Over 3 million agents = 2% – 4% workforce

Healthcare - similar and unique challenges:

� Cost-figures far more staggering� Risks much higher� ED (initial focus) = hospital-window� Over 3 million nurses

Internet - . . .

15 39

ER / ED Environment: Service Network

Acute (Internal, Trauma) Walking

Multi-Trauma

21 40

Emergency-Department Network: Gallery of Models

ImagingLaboratory

Experts

Interns

Returns (Old or New Problem)

“Lost” Patients

LWBS

Nurses

Statistics,HumanResourceManagement(HRM)

New Services Design (R&D)Operations,Marketing,MIS

Organization Design:Parallel (Flat) = ERvs. a true ED Sociology, Psychology,Operations Research


Quality

Efficiency


Medicine

(High turnoversMedical-Staff shortage)


StretcherWalking

Service Completion(sent to other department)

( Waiting TimeActive Dashboard )

PatientsSegmentation

Medicine,Psychology, Marketing


Human FactorsEngineering(HFE)

InternalQueue

OrthopedicQueue

Arrivals

FunctionScientific DisciplineMulti-Disciplinary

Index

ED-StressPsychology

OperationsResearch, Medicine

Emergency-Department Network: Gallery of Models

Returns

TriageReception

Skill Based Routing (SBR) DesignOperations Research,HRM, MIS, Medicine

IncentivesGame Theory,Economics

Job EnrichmentTrainingHRM

HospitalPhysiciansSurgical

Queue

Acute,Walking

Blocked(Ambulance Diversion)

Forecasting

Information DesignMIS, HFE,Operations Research


Home

� Forecasting, Abandonment = LWBS, SBR ≈ Flow Control24 41

Prerequisite I: Data

Averages Prevalent (and could be useful / interesting).But I need data at the level of the Individual Transaction:For each service transaction (during a phone-service in a call center,or a patient’s visit in a hospital, or browsing in a website, or . . .), itsoperational history = time-stamps of events (events-log files).

25 43

Beyond Averages: The Human Factor

Histogram of Service-Time in an Israeli Call Center, 1999

January-OctoberJanuary-October

0

2

4

6

8

0 100 200 300 400 500 600 700 800 900

AVG: 185STD: 238

?6.83%

November-DecemberNovember-December

0

2

4

6

8

0 100 200 300 400 500 600 700 800 900

AVG: 201STD: 263

5.59%

Log-Normal

� 6.8% Short-Services:

26 44

Human

Beyond Averages: The Human Factor

Histogram of Service-Time in an Israeli Call Center, 1999

January-OctoberJanuary-October

0

2

4

6

8

0 100 200 300 400 500 600 700 800 900

AVG: 185STD: 238

?6.83%

November-DecemberNovember-December

0

2

4

6

8

0 100 200 300 400 500 600 700 800 900

AVG: 201STD: 263

5.59%

Log-Normal

� 6.8% Short-Services: Agents’ “Abandon" (improve bonus, rest),(mis)lead by incentives

� Distributions must be measured (in seconds = natural scale)� LogNormal service times common in call centers

26 45

Durations: Phone Calls (2 Surprises)

Israeli Call Center, Nov–Dec, 1999

Log(Service Times)

0 2 4 6 8

0.0

0.1

0.2

0.3

0.4

Log(Service Time)

Pro

porti

on

LogNormal QQPlot

Log-normal

Ser

vice

tim

e

0 1000 2000 30000

1000

2000

3000

� Practically Important: (mean, std)(log) characterization� Theoretically Intriguing: Why LogNormal ? Naturally multiplicative

but, in fact, also Infinitely-Divisible (Generalized Gamma-Convolutions)

54 46

Infinitely--Divisible-

Pause for a Commercial:

47

Pause for a Commercial: The Technion SEE Center

28 48

SEETechnion

Technion SEE = Service Enterprise Engineering

SEELab: Data-repositories for research and teaching

� For example:� Bank Anonymous: 1 years, 350K calls by 15 agents - in 2000.

Brown, Gans, Sakov, Shen, Zeltyn, Zhao (JASA), paved the wayfor:

� U.S. Bank: 2.5 years, 220M calls, 40M by 1000 agents.� Israeli Cellular: 2.5 years, 110M calls, 25M calls by 750 agents.� Israeli Bank: from January 2010, daily-deposit at a SEESafe.� Israeli Hospital: 4 years, 1000 beds; 8 ED’s- Sinreich’s data.

29 49

Technion SEE = Service Enterprise Engineering

SEELab: Data-repositories for research and teaching

� For example:� Bank Anonymous: 1 years, 350K calls by 15 agents - in 2000.

Brown, Gans, Sakov, Shen, Zeltyn, Zhao (JASA), paved the wayfor:

� U.S. Bank: 2.5 years, 220M calls, 40M by 1000 agents.� Israeli Cellular: 2.5 years, 110M calls, 25M calls by 750 agents.� Israeli Bank: from January 2010, daily-deposit at a SEESafe.� Israeli Hospital: 4 years, 1000 beds; 8 ED’s- Sinreich’s data.

SEEStat: Environment for graphical EDA in real-time

� Universal Design, Internet Access, Real-Time Response.

SEEServer: Free for academic useRegister; access U.S. Bank, Israeli Bank, Rambam Hospital.

29 50

eg. RFID-Based Data: Mass Casualty Event (MCE)Drill: Chemical MCE, Rambam Hospital, May 2010

Focus on severely wounded casualties (≈ 40 in drill)Note: 20 observers support real-time control (helps validation)

30 51

Data Cleaning: MCE with RFID SupportData-base Company report comment

Asset id order Entry date Exit date Entry date Exit date 4 1 1:14:07 PM 1:14:00 PM 6 1 12:02:02 PM 12:33:10 PM 12:02:00 PM 12:33:00 PM 8 1 11:37:15 AM 12:40:17 PM 11:37:00 AM exit is missing

10 1 12:23:32 PM 12:38:23 PM 12:23:00 PM 12 1 12:12:47 PM 12:35:33 PM 12:35:00 PM entry is missing 15 1 1:07:15 PM 1:07:00 PM 16 1 11:18:19 AM 11:31:04 AM 11:18:00 AM 11:31:00 AM 17 1 1:03:31 PM 1:03:00 PM 18 1 1:07:54 PM 1:07:00 PM 19 1 12:01:58 PM 12:01:00 PM 20 1 11:37:21 AM 12:57:02 PM 11:37:00 AM 12:57:00 PM 21 1 12:01:16 PM 12:37:16 PM 12:01:00 PM

22 1 12:04:31 PM 12:20:40 PMfirst customer is missing

22 2 12:27:37 PM 12:27:00 PM 25 1 12:27:35 PM 1:07:28 PM 12:27:00 PM 1:07:00 PM 27 1 12:06:53 PM 12:06:00 PM

28 1 11:21:34 AM 11:41:06 AM 11:41:00 AM 11:53:00 AMexit time instead of entry time

29 1 12:21:06 PM 12:54:29 PM 12:21:00 PM 12:54:00 PM 31 1 11:40:54 AM 12:30:16 PM 11:40:00 AM 12:30:00 PM 31 2 12:37:57 PM 12:54:51 PM 12:37:00 PM 12:54:00 PM 32 1 11:27:11 AM 12:15:17 PM 11:27:00 AM 12:15:00 PM 33 1 12:05:50 PM 12:13:12 PM 12:05:00 PM 12:15:00 PM wrong exit time 35 1 11:31:48 AM 11:40:50 AM 11:31:00 AM 11:40:00 AM 36 1 12:06:23 PM 12:29:30 PM 12:06:00 PM 12:29:00 PM 37 1 11:31:50 AM 11:48:18 AM 11:31:00 AM 11:48:00 AM 37 2 12:59:21 PM 12:59:00 PM

- Imagine “Cleaning" 60,000+ customers per day (call centers) !

- “Psychology" of Data Trust and Transfer (e.g. 2 years till transfer)31 52

The Basic Service-Network Model: Erlang-R

w/ G. Yom-Tov Needy (st-servers)

rate-

Content (Delay) rate -

1-p

p

1

2

Arrivals Poiss( t) Patient discharge

Erlang-R (IE: Repairman Problem 50’s; CS: Central-Server 60’s) =2-station “Jackson" Network = (M/M/S, M/M/∞) :

� λt – Time-Varying Arrival rate� St – Number of Servers (Nurses / Physicians).� μ – Service rate (E [Service] = 1

μ)

� p – ReEntrant (Feedback) fraction� δ – Content-to-Needy rate (E [Content] = 1

δ)

63 53

Erlang-R: Fitting a Simple Model to a Complex Reality

Chemical MCE Drill (Israel, May 2010)

Arrivals & Departures (RFID) Erlang-R (Fluid, Diffusion)

0

10

20

30

40

50

60

11:02 11:16 11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26

Tota

l Nu

mb

er

of

Pat

ien

ts

Time

Cumulative Arrivals

Cumulative Departures

15

20

25

30

erof

MCE

Patien

tsinED

Actual Q(t)

Fluid Q(t)

Lower Envelope Q(t) (Theoretical)

Upper Envelope Q(t) (Theoretical)

Fluid Q1

0

5

10

11:02 11:16 11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26

Num

beTime

� Recurrent/Repeated services in MCE Events: eg. Injection every 15 minutes

65 56

Erlang-R: Fitting a Simple Model to a Complex Reality

Chemical MCE Drill (Israel, May 2010)

Arrivals & Departures (RFID) Erlang-R (Fluid, Diffusion)

0

10

20

30

40

50

60

11:02 11:16 11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26

Tota

l Nu

mb

er

of

Pat

ien

ts

Time

Cumulative Arrivals

Cumulative Departures

15

20

25

30

erof

MCE

Patien

tsinED

Actual Q(t)

Fluid Q(t)

Lower Envelope Q(t) (Theoretical)

Upper Envelope Q(t) (Theoretical)

Fluid Q1

0

5

10

11:02 11:16 11:31 11:45 12:00 12:14 12:28 12:43 12:57 13:12 13:26

Num

beTime

� Recurrent/Repeated services in MCE Events: eg. Injection every 15 minutes� Fluid (Sample-path) Modeling, via Functional Strong Laws of Large Numbers� Stochastic Modeling, via Functional Central Limit Theorems

� ED in MCE: Confidence-interval, usefully narrow for Control� ED in normal (time-varying) conditions: Personnel Staffing65 57

The Asymptotic Framework: Erlang-R in the ED

System = Emergency Department (eg. Rambam Hospital)� SimNet = Customized ED-Simulator (Marmor & Sinreich)� QNet = Erlang-R (time-varying 2-station Jackson; w/ Yom-Tov)� FNet = 2-dim dynamical system (Massey & Whitt)� DNet = 2-dim Markovian Service Net (w/ Massey and Reiman)

66 58

The Asymptotic Framework: Erlang-R in the ED

System = Emergency Department (eg. Rambam Hospital)� SimNet = Customized ED-Simulator (Marmor & Sinreich)� QNet = Erlang-R (time-varying 2-station Jackson; w/ Yom-Tov)� FNet = 2-dim dynamical system (Massey & Whitt)� DNet = 2-dim Markovian Service Net (w/ Massey and Reiman)

Asymptotic Framework� Start with Data� Fit a simple QNet (time-varying Erlang-R)

to a complex reality (ED Physicians)� Develop FNet (Offered-Load of Physicians) and DNet� Use QNet + FNet + DNet for Design (√-Staffing), Analysis (of

Feedback), . . .� Virtual reality: SimNet of ED with √-staffing of Physicians)� Validation: stable performance, confidence intervals, . . .

66 59

ServNets: Data-Based Online Automatic Creationw/ V. Trofimov, E. Nadjharov, I. Gavako = Technion SEELab

� Towards creating ServNets = QNets, SimNets, FNets, DNets

� SimNets of Service Systems = Virtual Realities, for ExploratoryData Analysis (EDA), Performance Analysis, Optimization, . . .

� SimNets also of QNEts, FNets, DNets, for “Valuation"(Validation, Accuracy)

32 60

ServNets: Data-Based Online Automatic Creationw/ V. Trofimov, E. Nadjharov, I. Gavako = Technion SEELab

� Towards creating ServNets = QNets, SimNets, FNets, DNets

� SimNets of Service Systems = Virtual Realities, for ExploratoryData Analysis (EDA), Performance Analysis, Optimization, . . .

� SimNets also of QNEts, FNets, DNets, for “Valuation"(Validation, Accuracy)

� Ultimately: Empirical Research Lab, necessitated by thecomplexity of service systems and human-behavior:

� Daily routine in Physics, Chemistry, Biology; Psychology� But also in Transportation (Science), and recently (Behavioral)

Economics

� Why not in Service Science / Engineering / Management ?

32 61

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MessageTelesales

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NonBusiness LineSubanco

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NonBusiness Line NonCC ServiceCCO

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TrunkPremier

TrunkBusiness

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TrunkOnline Banking

TrunkEBO

TrunkTelesales

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Trunk

Trunk

Trunk

Trunk

Trunk

InternalTotal

OutgoingTotal

NormalTermination

NormalTermination

UndeterminedTermination

AbandonedShort

Abandoned

OtherUnhandled

Transfer

Transfer

1 Day in a Call Center - Customers

USBank April 2, 2001

62

33975

4221

2006

2886

2741

361

354697

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43

1049

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319

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2281

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Business LineTelesales

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AnnouncementOnline Banking

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MessageTelesales

NonBusiness LineBusiness

NonBusiness LineSubanco

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NonBusiness Line NonCC ServiceCCO

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Overnight ClosedConsumer Loans

Overnight ClosedEBO

TrunkRetail

TrunkPremier

TrunkBusiness

TrunkConsumer Loans

TrunkOnline Banking

TrunkEBO

TrunkTelesales

TrunkPriority Service

Trunk

Trunk

Trunk

Trunk

Trunk

InternalTotal

OutgoingTotal

NormalTermination

NormalTermination

UndeterminedTermination

AbandonedShort

Abandoned

OtherUnhandled

Transfer

Transfer

1 Day in a Call Center - Customers


63

ILDUBank January 24, 2010 from 06:00 to 23:59:59

Call-Backs Outgoing

Inbound

Available

IdleBreak

64

ILDUBank January 24, 2010 from 06:00 to 23:59:59

Call-Backs Outgoing

Inbound

Available

IdleBreak

65

ED

Pediatric

Neurology Nephrology Derrmatology

Internal

IntensiveCare

Cardiology

Rheumatology

UrologyOtorhinolaryngology Orthopedics

Surgery

Maternity

Gynecology

Psychiatry Ophthalmology

R

L

D

Out

R

R

R

R

R R

R

RR RR

R

R

R

R

R

L

LL

L

L

L

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L

L

D

D

D

D

D DD

D

DD

D

D

Out

Out

Out

Out Out

Out

OutOut Out OutOut

Out

Out

1 Day in a Hospital - Patients

Rambam August, 2004

Released (Home)

Left with Medical File

Deceased

Transfer

66

Hospital

115

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2

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serveng

lectures

references

predictionmay1809.pdf

homeworks

hw1_amusement_park_mgt.pdf

recitations

hazard_phase_type.pdf

course2011winter

icpr_service_engineering.pdfon_cc_data_frommsom.pdf pivot_table.pdf

thesis_polyna.pdf

proposal_polina.pdf

moss.pdf

files

nurse_proj_psu_tech.pdf

national_cranberry_1.pdf

hw9par_sol_2012w.pdf

syllabus8.pdfexams

statanalysis.pdf

agent-heterogeneity-brown-book-final.pdf

1_1_qed_lecture_introduction_2011w.pdf

course2004

retail.pdf hall_6.pdf

jasa_callcenter.pdf dantzig.pdf

bacceli.pdf

avishai-class-april-2003.ppt

hw7_2011w_par_sol_part2.pdf

ibmrambam technion srii presentation final.ppt

dimensioning.pdf

palmannoyance.pdf

yair_sergurywaitingtimeanalysis.pdf

nejmsb1002320.pdf

qed_qs_scientific_generic_caschina.pdf

web_summary13_2011s.pdf

4callcenters_coverpage.pdf

documentation.pdf rec9part2.pdf

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qed_qs_scientific_wharton_stat_seminar.pdf

l2_measurements_class_2009s.pdf

ccreview.pdfvdesign_ecompanion.pdf

wharton_lecture_avi_printout.pdflarson_atoa.pdf

proposal_michael.pdf

stanford_seminar_avi_printout.pdf

solver_guide.pdf

fitz.pdf

rec10_part2.pdf rec5.pdf

paxson.pdf

connect_to_see_terminal.pdf

project_ug_simulationinterface.pdf revenue_manage.pdf

hw7_2009s_forecast.xls

syllabus2.pdf

infocom04.pdf

hall_transportation.pdf

whitt_handout_chapter1.pdf

fromprojecttoprocess.pdf

nytimes.2007-06-23.pdf ds_pert_lec1.pdf syllabus6.pdf hw9_2011w.pdf hw7_2011w.pdf

mmng_constraint_supp_or.pdf

awam-april_2011.pdfwhitt_scaling_slides.pdfmmng_seminar.pdf

syllabus4.pdf

syllabus12_2012w.pdf

syllabus5.pdf

mm1_strong_apprximations.pdf seestat_tutorial.ppt

kaplan_porter_2011-9_how-to-solve-the-cost-crisis-in-health-care_hbr.pdf

rec9_part2.pdf

callcenterdata

bocaraton.ps

gccreport 20-04-07 uk version.pdf hall_manpower_planning.pdf

bi18.pdf

syllabus12.pdf fluidview_2010w_short_version.pdf hw7_2009s_par_sol_part2.pdf

moed_b_2007w_solution.pdf

newell.pdf

rec11.pdf

moedb_2009w.pdf

rec3.pdf

hw10_par_sol_2011s.pdf

thirdlevel support ijtm1_cs.pdf

hw4_full.pdf

moedb_2010s_sol.pdf

chandra.pdf

gurvich_seminar.pdf

ed_sinreich_marmor.ppt regimes_supplement.pdf

web_summary10_2011s.pdf hw6par_sol_2009s.xls

exam_2005s_sol.pdf

servicefull.pdf

witor09_empirical_adventures_sep2009.pdf

web_summary12_2011s.pdf

heb_summary_yulia.pdf

hw9par_sol_2011s.pdf

seminar_yulia_9_2.pdf

bpr_2003.pdf staffing_italian_us_2011w.xlsdesignofqueues.pdf thepsychologyofwaitinglines.pdf

erlangabc.pdf

studentsevaluations.pdf hw8_2011s.pdf

hw9_2012w.pdf

edie.pdf

syllabus9.pdf

ds_pert_lec2.pdf

zohar_seminar.ppt

hist-normal.pdf

vandergraft.pdf

rec13.pdf

desighn_ivr.pdf

cohen_aircraft_failures.pdf

sbr.pdf

nano.pdf

hw2_2011w.pdfseminar_presentation_boaz_estimating

er load.ppt

project_ug_meirav.pdf see_report_output_june_2011.pdf

see_report_2010.pdf

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serveng

lectures

hall_flows_hospitals_chapter1text.pdf

references

4callcenterscourse2004 homeworks

icpr_service_engineering.pdf keycorp.pdf

files

revenue_manage.pdfhw1_amusement_park_mgt.pdf

recitations

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garnett.pdf abandon02.pdf erlang_a.pdf ccbib.pdf

us7_cc_avi.pdf

jasa_callcenter.pdfsbr.pdf

hazard_phase_type.pdf

mazeget_noa_yul.pptexams technion-call-center-report-sept-2004.pdfbrandt.pdf statanalysis.pdfmjp_into_erlang_a.pdf loch.pdf sbr_stolyar.pdf

callcenterdata

larson_atoa.pdf sivanthesisfinal.pdf columbia05.pdf crmis.pptfluid_systems.rar

januarytxt.zip

sbr_wharton_ccforum_short_may03.pdf predictingwaitingtime.pdf avishaicourse_munichor.ppt vdesign_pub.pdf hierarchical_modelling_chen_mandelbaum_part1.pdf

solver_guide.pdf

datamocca_february_2008_cc_forum_lecture.ppt seminar_presentation_galit.pptntro_to_serveng_teaching_note.pdf

pivot_table.pdf

project_ug_simulationinterface.pdf

course2010winter

ed_simulation_modeling_supp.pdf avim_cv.pdfdantzig.pdf yariv_phd.pdf

rec10_part2.pdf

fr6.pdfnejmsb1002320.pdf

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Entry Entry Entry Entry EntryEntry Entry

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Retail Premier Business PlatinumConsumer Loans EBOTelesales Subanco Summit

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In:

ILDUBank January 24, 2010 Agent #043 Shift: 16:00 - 23:45

Inbound Call-Backs

Outgoing

Available Idle

Private Call

Break

73

Private Prepaid

PrivatePrivate VIP Private Customer RetentionBusiness Business VIP Business Customer Retention

Language 2 Prepaid Language 2 Prepaid Low PriorityLanguage 2 PrivateLanguage 3 Internet Surfing Internet

Overseas

1 24 5 810 11 12 1315161718 20 21 24 25

2104

2208 26264592 445 3411432049 1484 8734785 4658 411 444480 43 847 181 974

1253823 843343 1390109630 4454 1240792 3793 49 735

1433 193

Zoom In: Skills - Based Routing (SBR) Network Structure (Protocol)

Israeli Telecom February 10, 2008

N -Design

L -Design

Agent Pool

Customer Class

Connected Component 74

1 24 5 810 11 12 1315161718 20 21 24 25

2104

2208 26264592 445 3411432049 1484 8734785 4658 411 444480 43 847 181 974

1253823 843343 1390109630 4454 1240792 3793 49 735

1433 193

Goal: Data-Based Real-Time Simulation (SimNet)

Private Prepaid Language 3 Language 2 Private Language 2 Prepaid Language 2 Prepaid Low Priority Internet Surfing Internet

Private VIP Private Business Business VIP Business Customer Retention Private Customer Retention Overseas

What is lacking?

1. Dynamics

2. Durations

3. Protocols

Israeli Telecom February 10, 2008

75

Dynamics

Durations

Protocols

Goal:

8 AM - 9 AM


76

8 AM - 9 AM77

9 AM - 10 AM78

10 AM - 11 AM79

11 AM - 12 PM80

Dynamics: Time-Varying Arrival-Rates2 Daily Peaks

CC: Dec. 1995, (USA, 700 Helpdesks) CC: May 1959 (England)

Dec 1995!

(Help Desk Institute)

Time24 hrs

% Arrivals

May 1959!

ArrivalRate

Time24 hrs

CC: Nov. 1999 (Israel) ED: Jan.–July 2007 (Israel)Daily

0.00

2.50

5.00

7.50

10.00

12.50

15.00

17.50

20.00

22.50

25.00

27.50

30.00

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

Ave

rage

num

ber

of c

ases

Time (Resolution 60 min.)

HomeHospital Patients Arrivals to Emergency Department Total for January2007 February2007 March2007 April2007 May2007 June2007 July2007,Sundays

53 81

1995, 1959

1999 ED: 2007

Durations: Answering MachineIsraeli Bank: IVR/VRU Only, May 2008

IVR_onlyMay 2008, Week days

0.000.100.200.300.400.500.600.700.800.901.001.101.201.301.40

00:00 00:30 01:00 01:30 02:00 02:30 03:00 03:30 04:00 04:30

Time(mm:ss) (Resolution 1 sec.)

Rel

ativ

e fr

eque

ncie

s %

mean=99st.dev.=101

Mixture: 7 LogNormals

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

1.00

1.10

1.20

1.30

00:00 00:30 01:00 01:30 02:00 02:30 03:00 03:30 04:00 04:30

Rel

ativ

e fr

eque

ncie

s %

Time(mm:ss) (Resolution 1 sec.)

Fitting Mixtures of Distributions for VRU only timeMay 2008, Week days

Time(mm:ss) (Resolution 1 sec.)Empirical Total Lognormal Lognormal Lognormal

55 82

Mixture:

Durations: Waiting Times in a Call Center⇒ Protocols

Exponential in Heavy-Traffic (min.)Small Israeli Bank

0.00

2.50

5.00

7.50

10.00

12.50

15.00

17.50

20.00

22.50

25.00

27.50

30.00

0.00 100.00 200.00 300.00 400.00 500.00 600.00

Rel

ativ

e fre

quen

cies

%

Time(seconds)( resolution 30)

AnonymousBank Handled Wait Time, TOTAL Total for January1999 February1999 March1999 April1999 May1999 June1999 July1999 August1999 September1999 October1999

November1999 December1999,Weekdays

Empirical Exponential (scale=106.67)

Mean = 106 SD = 109

Routing via Thresholds (sec.)Large U.S. Bank

0.00

2.50

5.00

7.50

10.00

12.50

15.00

17.50

20.00

2.00 7.00 12.00 17.00 22.00 27.00 32.00 37.00

Rel

ativ

e fre

quen

cies

%


USBank Wait time(waiting), Retail May 2002, Weekdays

Scheduling Priorities (sec.) [compare Hospital LOS (hours)]Medium Israeli Bank

0.000

0.050

0.100

0.150

0.200

0.250

0.300

0.350

0.400

0.450

0.500

0.550

0.600

0.650

20.00 70.00 120.00 170.00 220.00 270.00 320.00 370.00

Rel

ativ

e fre

quen

cies

%


ILBank Wait time (all) August 2007, Weekdays

56 83

LogNormal & Beyond: Length-of-Stay in a Hospital

Israeli Hospital, in Days: LN

0 2 4 6 8 10 13 16 19 22 25 28 31 34 37 40 43 46 49

57 84

Hospital

Days:

LogNormal & Beyond: Length-of-Stay in a Hospital

Israeli Hospital, in Days: LN

0 2 4 6 8 10 13 16 19 22 25 28 31 34 37 40 43 46 49

Israeli Hospital, in Hours: Mixture

0 .2.4 .6 .8 11.21.51.82.12.42.7 33.23.53.84.14.44.7 55.25.55.86.16.46.7 7 7.37.67.98.28.58.89.19.49.710

Explanation: Patients releasedaround 3pm (1pm in Singapore)

Why Bother ?� Hourly Scale: Staffing,. . .� Daily: Flow / Bed Control,. . .

57 85

Hours:

Durations: (Im)Patience while Waiting (Psychology)Palm: (1943–53): Irritation ∝ Hazard Rate

Regular over VIP Customers – Israeli Bank

� Challenges: Un-Censoring, Dependence, Smoothing- requires Call-by-Call Data

58 86

Durations: (Im)Patience while Waiting (Psychology)Palm: (1943–53): Irritation ∝ Hazard Rate

Regular over VIP Customers – Israeli Bank

� Challenges: Un-Censoring, Dependence, Smoothing- requires Call-by-Call Data

� VIP Customers are more Patient (Needy)� Peaks of abandonment at times of Announcements

58 87

Protocols + PsychologyPatient Customers, Announcements, Priority Upgrades

0.000

0.001

0.002

0.003

0.004

0.005

0.006

0.007

0.008

0.009

0 60 120 180 240 300 360 420 480 540 600 660 720 780 840 900

Ha

zard

Fu

nct

ion

Time (seconds)

USBank December 2002, Week days, Quick&Reilly

time willing to wait (hazard rate)

time willing to wait (Pspline)

virtual wait (hazard rate)

virtual wait (Pspline)

59 88

Little’s Law: Call Center & Emergency Department

Time-Gap: # in System lags behind Piecewise-Little (L = λ × W )

USBank Customers in queue(average), Telesales10.10.2001

0.0020.0040.0060.0080.00

100.00120.00140.00160.00180.00200.00

07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00


Num

ber o

f cas

es

Customers in queue(average) Little's law

HomeHospital Average patients in EDFebruary 2004, Wednesdays

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

00:00 02:00 04:00 06:00 08:00 10:00 12:00 14:00 16:00 18:00 20:00 22:00


Ave

rage

num

ber o

f cas

es

Average patients in ED Lambda*E(S) smoothed

⇒ Time-Varying Little’s Law� Berstemas & Mourtzinou;� Fralix, Riano, Serfozo; . . .

60 89

ED

Telesales

Congestion Laws: Parsimonious Models3 Queue-Lengths at 30 sec. resolution (ILBank, 10/6/2007)

ILBank Customers in queue (average)10.06.2007

0.00

25.00

50.00

75.00

100.00

125.00

150.00

175.00

200.00

225.00

06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00

Time (Resolution 30 sec.)

Num

ber o

f cas

es

Medium priority Low priority Unidentified

Queue “Shape"ILBank Customers in queue (average)

10.06.2007

0.0000

0.0005

0.0010

0.0015

0.0020

0.0025

06:00 07:00 08:00 09:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00

Time (Resolution 30 sec.)

Perc

enta

ge

Medium priority Low priority Unidentified

� Area normalized to 100%� State-Space Collapse

61 90

30

Protocols: Staffing (N) vs. Offered-Load (R = λ× E(S))IL Telecom; June-September, 2004; w/ Nardi, Plonski, Zeltyn

2205 half-hour intervals (13 summer weeks, week-days)67 91

The Basic Staffing Model: Erlang-A (M/M/N + M)agents

arrivals

abandonment

1

2

n

…

queue

Erlang-A (Palm 1940’s) = Birth & Death Q, with parameters:

� λ – Arrival rate (Poisson)� μ – Service rate (Exponential; E [S] = 1

μ )

� θ – Patience rate (Exponential, E [Patience] = 1θ )

� N – Number of Servers (Agents).69 92

QED Theory (Erlang ’13; Halfin & Whitt ’81; w/Garnett & Reiman ’02)

Consider a sequence of steady-state M/M/N + M queues, N = 1, 2, 3, . . .Then the following points of view are equivalent, as N ↑ ∞:

• QED %{Cust Wait > 0} ≈ α, 0 < α < 1;

or %{Serv Idle > 0} ≈ 1 − α

• Customers {Abandon} ≈ γ√N, 0 < γ;

• Agents OCC ≈ 1 − β+γ√N

−∞ < β < ∞ ;

• Managers N ≈ R + β√

R , R = λ× E(S) not small;

Here R = Offered Loadeg. R = 25 call/min. × 4 min./call = 100

72 93

Erlang-A: QED Approximations (Examples)

Assume Offered Load R not small (λ → ∞).

Let β = β

√μ

θ, h(·) = φ(·)

1 − Φ(·) = hazard rate of N (0, 1).

� Delay Probability:

P{Wq > 0} ≈[

1 +

√θ

μ· h(β)

h(−β)

]−1

.

� Probability to Abandon:

P{Ab|Wq > 0} ≈ 1√N

·√

θ

μ·[h(β)− β

].

� P{Ab} ∝ E[Wq] , both order 1√N

:

P{Ab}E[Wq]

= θ (≈ g(0) > 0).

73 94

QED Theory vs. Data: P(Wq > 0)

IL Telecom; June-September, 2004

� 2205 half-hour intervals (13 summer weeks, week-days)� Erlang-A approximations for the appropriate μ/θ ≈ 3

74 95

Process Limits (Queueing, Waiting)• QN = {QN(t), t ≥ 0} : stochastic process obtained by

centering and rescaling:

QN =QN −N√

N

• QN(∞) : stationary distribution of QN

• Q = {Q(t), t ≥ 0} : process defined by: QN(t)d→ Q(t).

��

�

�

� �

QN(t) QN(∞)

Q(t) Q(∞)

t → ∞

t → ∞

N → ∞ N → ∞

Approximating (Virtual) Waiting Time

VN =√N VN ⇒ V =

[1

μQ

]+(Puhalskii, 1994)

stochastic process

Waiting Time

75 96

QED Q’s in Practice, beyond Call Centers

Traditional Queueing Theory predicts that Service-Quality andServers’ Efficiency must be traded off against each other.

For example, M/M/1 (single-server queue): 91% server’s utilizationgoes with

Congestion Index =E [Wait ]

E [Service]= 10.

68 97

QED Q’s in Practice, beyond Call Centers

Traditional Queueing Theory predicts that Service-Quality andServers’ Efficiency must be traded off against each other.

For example, M/M/1 (single-server queue): 91% server’s utilizationgoes with

Congestion Index =E [Wait ]

E [Service]= 10.

Yet, heavily-loaded queueing systems with Congestion Index = 0.1(Waiting-time one order of magnitude less than Service-time)are prevalent:

� Call Centers: Wait “seconds" for minutes service;� Transportation: Search “minutes" for hours parking;� Hospitals: Wait “hours" in ED for days hospitalization in IW’s.

⇒ QED Systems68 98

QED Intuition: Why P{Wq > 0} ∈ (0, 1) ?

1. Why subtle: Consider a large service system (e.g. call center).� Fix λ and let N ↑ ∞: P{Wq > 0} ↓ 0, P(I > 0) ↑ 1.

76 99


1. Why subtle: Consider a large service system (e.g. call center).� Fix λ and let N ↑ ∞: P{Wq > 0} ↓ 0, P(I > 0) ↑ 1.� Fix N and let λ ↑ ∞: P{Wq > 0} ↑ 1, P(I > 0) ↓ 0.

76 100


1. Why subtle: Consider a large service system (e.g. call center).� Fix λ and let N ↑ ∞: P{Wq > 0} ↓ 0, P(I > 0) ↑ 1.� Fix N and let λ ↑ ∞: P{Wq > 0} ↑ 1, P(I > 0) ↓ 0.� ⇒ Must have both λ and N increase simultaneously:� ⇒ (CLT) Square-root staffing: N ≈ R + β

√R(

λ ≈ Nμ− β√

Nμ)

76 101


1. Why subtle: Consider a large service system (e.g. call center).� Fix λ and let N ↑ ∞: P{Wq > 0} ↓ 0, P(I > 0) ↑ 1.� Fix N and let λ ↑ ∞: P{Wq > 0} ↑ 1, P(I > 0) ↓ 0.� ⇒ Must have both λ and N increase simultaneously:� ⇒ (CLT) Square-root staffing: N ≈ R + β

√R(

λ ≈ Nμ− β√

Nμ)

2. QED Excursions

76 102

Server Networks (w/ A. Senderovic)

ILDUBank January 24, 2010 Agent #043 Shift: 16:00 - 23:45

Inbound Call-Backs

Outgoing

Available Idle

Private Call

Break

84 107

Individual Agents: Service-Duration, Variabilityw/ Gans, Liu, Shen & Ye

Agent 14115

Service-Time Evolution: 6 month Log(Service-Time)

� Learning: Noticeable decreasing-trend in service-duration� LogNormal Service-Duration, individually and collectively

85 108

Individual Agents: Learning, Forgetting, Switching

Daily-Average Log(Service-Time), over 6 monthsAgents 14115, 14128, 14136

Day Index

Mea

n Lo

g(S

ervi

ce T

ime)

0 20 40 60 80 100 120 1404.2

4.4

4.6

4.8

5.0

5.2

5.4

Day Index

Mea

n Lo

g(S

ervi

ce T

ime)

a 102−day break

0 20 40 60 80 1004.

44.

64.

85.

05.

25.

45.

6Day Index

Mea

n Lo

g(S

ervi

ce T

ime)

switch to Online Banking after 18−day break

0 50 100 150

4.5

5.0

5.5

6.0

86 109

Individual Agents: Learning, Forgetting, Switching

Daily-Average Log(Service-Time), over 6 monthsAgents 14115, 14128, 14136

Day Index

Mea

n Lo

g(S

ervi

ce T

ime)

0 20 40 60 80 100 120 1404.2

4.4

4.6

4.8

5.0

5.2

5.4

Day Index

Mea

n Lo

g(S

ervi

ce T

ime)

a 102−day break

0 20 40 60 80 1004.

44.

64.

85.

05.

25.

45.

6Day Index

Mea

n Lo

g(S

ervi

ce T

ime)

switch to Online Banking after 18−day break

0 50 100 150

4.5

5.0

5.5

6.0

Weakly Learning-Curves for 12 Homogeneous(?) Agents

5 10 15 20

34

56

Tenure (in 5−day week)

Ser

vice

rate

per

hou

r

86 110

Tele-Service Process (Beyond present SEE Data)

RetailService(IsraeliBank)

StatisticsORIEPsychol.MIS

START

Hello14 / 20

I.D.24 / 23Request

15 / 8

Stock17 / 21

Question14 / 20

Password creation62 / 42

Processing49 / 24

Confirmation29 / 9

Answer32 / 19

END202/190

Dead time18 / 17

Paperwork22 / 12

End of call5 / 3

Credit34 / 32

Others21 / 21

Checking21 / 9

1

0.65

0.050.27

0.950.03

0.62

0.29

0.17

0.28

0.17

0.11

0.05

0.05 0.17

0.23 0.08

0.38

0.15

0.15

0.93

0.14

0.03

0.5

0.03 0.26

0. 4

0.23

0.590.09

0.05

0.67

0.11

0.17

0.67

0.330.7

0.25

0.66

0.43

0.57

0.130.2

0.93

0.04

0. 6

Password creation62 / 42

0.67

0.33

STDAVG

87 111

The Technion SEE Center / LaboratoryData-Based Service Science / Engineering

89 112

Technion Research Impact: An Example

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call centers Search Advanced Scholar Search

Scholar Preferences

Scholar Articles and patents anytime include citations Results 1 - 10 of about 2,510,000. (0.06 sec)

N Gans, G Koole, A Mandelbaum - Manufacturing and service operations …, 2003 - Citeseer � The Wharton School, University of Pennsylvania,Philadelphia, PA 19104, USA [email protected] ... † Vrije Universiteit, De Boelelaan 1081a, 1081 HV Amsterdam, The Netherlands [email protected] ... ‡ Industrial Engineering and ... Cited by 455 - Related articles - View as HTML - All 32 versions

[PDF] Telephone call centers: Tutorial, review, and research prospects psu.edu [PDF]

O Garnet, A Mandelbaum, M … - Manufacturing & Service …, 2002 - iew3.technion.ac.il ABSTRACT. The most common model to support workforce management of telephone call centers is the M/M/N/B model, in particular its special cases M/M/N (Erlang C, which models out busy-signals) and M/M/N/N (Erlang B, disallowing waiting). All of these models lack a ... Cited by 245 - Related articles - View as HTML - All 18 versions

[PDF] Designing a call center with impatient customers technion.ac.il [PDF]

L Brown, N Gans, A Mandelbaum, A Sakov, H … - Journal of the American …, 2005 - ASA A call center is a service network in which agents provide telephone-based services. Customers who seek these services are delayed in tele-queues. This article summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history ... Cited by 205 - Related articles - All 41 versions

Statistical Analysis of a Telephone Call Center psu.edu [PDF]

S Borst, A Mandelbaum, MI Reiman - Operations research, 2004 - JSTOR CWI, P. O. Box 94079, 1090 GB Amsterdam, The Netherlands, and Bell Labs, Lucent Technologies, Murray Hill, New Jersey 07974-0636, [email protected] Avi Mandelbaum Faculty of Industrial Engineering and Management, Technion, Haifa 32000, Israel, avim@tx. ... Cited by 156 - Related articles - BL Direct - All 19 versions

Dimensioning large call centers bell-labs.com [PDF]

G Koole, A Mandelbaum - Annals of Operations Research, 2002 - Springer ... the modern call center is a complex socio-technical system. It thus enjoys central features that

Queueing models of call centers: An introduction psu.edu [PDF]

2,510,000.

call centers

N Gans, [ ]

O Garnet, [ ]

L Brown,

91 113

Data-Based Creation ServNets: some Technicalities

� ServNets = QNets, SimNets, FNets, DNets� Graph Layout: Adapted from but significantly extends Graphviz

(AT&T, 90’s); eg. edge-width, which must be restricted topoly-lines, since there are “no parallel Bezier (Cubic) curves(Bn(p) = EpF [B(n, p)], 0 ≤ p ≤ 1)

� Algorithm: Dot Layout (but with cycles), based on Sugiyama,Tagawa, Toda (’81): “Visual Understanding of HierarchicalSystem Structures"

33 114

Data-Based Creation ServNets: some Technicalities

� ServNets = QNets, SimNets, FNets, DNets� Graph Layout: Adapted from but significantly extends Graphviz

(AT&T, 90’s); eg. edge-width, which must be restricted topoly-lines, since there are “no parallel Bezier (Cubic) curves(Bn(p) = EpF [B(n, p)], 0 ≤ p ≤ 1)

� Algorithm: Dot Layout (but with cycles), based on Sugiyama,Tagawa, Toda (’81): “Visual Understanding of HierarchicalSystem Structures"

� Draws data directly from SEELab data-bases:� Relational DBs (Large! eg. USBank Full Binary = 37GB, Summary

Tables = 7GB)� Structure: Sequence of events/states, which (due to size)

partitioned (yet integrated) into days (eg. call centers) or months(eg. hospitals)

� Differs from industry DBs (in call centers, hospitals, websites)

33 115

Skills-Based Routing in Call CentersEDA and OR, with I. Gurvich and P. Liberman

Mktg. ⇒

OR ⇒

HRM ⇒

MIS ⇒

20 119

Operational Regimes in a Call Center: Q vs. E

Large Israeli Bank

P{Wq > 0} vs. (R, N) R-Slice: P{Wq > 0} vs. N

3 Operational Regimes:� QD: ≤ 25%� QED: 25%− 75%� ED: ≥ 75%

80 120

data-based service networksie.technion.ac.il/serveng/references/0_informs_beijing_final.pdf ·...

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