service engineering: data-based science & teaching in support … · 2019. 11. 26. · 5....

Service Engineering:Data-Based Science & Teaching

in support of Service Management

Avishai Mandelbaum

Technion, Haifa, Israel

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

Based on joint work with Sergey Zeltyn, . . .

Technion SEE Center / Lab: Paul Feigin, Valery Trofimov, RA’s, . . .

1

Main Messages

1. Simple Useful Models at the Service of Complex Realities.Note: Useful must be Simple; Simple often rooted in Deep analysis.

2. Data-Based Research & Teaching is a Must & Fun.Supported by DataMOCCA = Data MOdels for Call Center Analysis.Initiated with Wharton, developed at Technion, available for adoption.

3. Back to the Basic-Research Paradigm (Physics, Biology, . . .):Measure, Model, Experiment, Validate, Refine, etc.

4. Ancestors & Practitioners often knew/apply the “right answer":simply did/do not have our tools/desire/need to prove it so.Supported by Erlang (1915), Palm (1945),..., thoughtful managers.

5. Scientifically-based design principles and tools (software),that support the balance of service quality, process efficiency andbusiness profitability, from the (often-conflicting) views ofcustomers, servers, managers: Service Engineering .

2

Background Material (Downloadable)

I Technion’s ‘‘Service-Engineering" Course (≥ 1995):http://ie.technion.ac.il/serveng

I Gans (U.S.A.), Koole (Europe), and M. (Israel):“Telephone Call Centers: Tutorial, Review and ResearchProspects." MSOM, 2003.

I Brown, Gans, M., Sakov, Shen, Zeltyn, Zhao:“Statistical Analysis of a Telephone Call Center: AQueueing-Science Perspective." JASA, 2005.

I Trofimov, Feigin, M., Ishay, Nadjharov:"DataMOCCA: Models for Call/Contact Center Analysis."Technion Report, 2004-2006.

I M. “Call Centers: Research Bibliography with Abstracts."Version 7, December 2006.

3

The First Prerequisite: Data & Measurements

Empirical “Axiom": The data one needs is never there for one touse – always problems with historical data (eg. lacking,contaminated, averaged, . . .)

Averages Prevalent.But I need data at the level of the Individual Transaction: For eachservice transaction, its operational history – time-stamps of events.(Towards integrating with marketing / financial history.)

Sources: “Service-floor" (vs. Industry-level, Surveys, . . .)

I Administrative (Court, via “paper analysis")I Face-to-Face (Bank, via bar-code readers)I Telephone (Call Centers, via ACD)I Future: Hospitals (via RFID)

4

Measurements: Face-to-Face Services23 Bar-Code Readers at a Bank Branch

Bank – 2nd Floor Measurements

5

Measurements: Telephone Call-by-Call Data (Log-File)

Telephone Service: Call-by-Call Data

vru+line call_id customer_id priority type date vru_entry vru_exit vru_time q_start q_exit q_time outcome ser_start ser_exit ser_time server

AA0101 44749 27644400 2 PS 990901 11:45:33 11:45:39 6 11:45:39 11:46:58 79 AGENT 11:46:57 11:51:00 243 DORIT

AA0101 44750 12887816 1 PS 990905 14:49:00 14:49:06 6 14:49:06 14:53:00 234 AGENT 14:52:59 14:54:29 90 ROTH AA0101 44967 58660291 2 PS 990905 14:58:42 14:58:48 6 14:58:48 15:02:31 223 AGENT 15:02:31 15:04:10 99 ROTH

AA0101 44968 0 0 NW 990905 15:10:17 15:10:26 9 15:10:26 15:13:19 173 HANG 00:00:00 00:00:00 0 NO_SERVER

AA0101 44969 63193346 2 PS 990905 15:22:07 15:22:13 6 15:22:13 15:23:21 68 AGENT 15:23:20 15:25:25 125 STEREN

AA0101 44970 0 0 NW 990905 15:31:33 15:31:47 14 00:00:00 00:00:00 0 AGENT 15:31:45 15:34:16 151 STEREN

AA0101 44971 41630443 2 PS 990905 15:37:29 15:37:34 5 15:37:34 15:38:20 46 AGENT 15:38:18 15:40:56 158 TOVA

AA0101 44972 64185333 2 PS 990905 15:44:32 15:44:37 5 15:44:37 15:47:57 200 AGENT 15:47:56 15:49:02 66 TOVA

AA0101 44973 3.06E+08 1 PS 990905 15:53:05 15:53:11 6 15:53:11 15:56:39 208 AGENT 15:56:38 15:56:47 9 MORIAH

AA0101 44974 74780917 2 NE 990905 15:59:34 15:59:40 6 15:59:40 16:02:33 173 AGENT 16:02:33 16:26:04 1411 ELI

AA0101 44975 55920755 2 PS 990905 16:07:46 16:07:51 5 16:07:51 16:08:01 10 HANG 00:00:00 00:00:00 0 NO_SERVER

AA0101 44976 0 0 NW 990905 16:11:38 16:11:48 10 16:11:48 16:11:50 2 HANG 00:00:00 00:00:00 0 NO_SERVER


AA0101 44978 23817067 2 PS 990905 16:19:11 16:19:17 6 16:19:17 16:19:39 22 AGENT 16:19:38 16:21:57 139 TOVA

AA0101 44764 0 0 PS 990901 15:03:26 15:03:36 10 00:00:00 00:00:00 0 AGENT 15:03:35 15:06:36 181 ZOHARI

AA0101 44765 25219700 2 PS 990901 15:14:46 15:14:51 5 15:14:51 15:15:10 19 AGENT 15:15:09 15:17:00 111 SHARON

AA0101 44766 0 0 PS 990901 15:25:48 15:26:00 12 00:00:00 00:00:00 0 AGENT 15:25:59 15:28:15 136 ANAT AA0101 44767 58859752 2 PS 990901 15:34:57 15:35:03 6 15:35:03 15:35:14 11 AGENT 15:35:13 15:35:15 2 MORIAH

AA0101 44768 0 0 PS 990901 15:46:30 15:46:39 9 00:00:00 00:00:00 0 AGENT 15:46:38 15:51:51 313 ANAT

AA0101 44769 78191137 2 PS 990901 15:56:03 15:56:09 6 15:56:09 15:56:28 19 AGENT 15:56:28 15:59:02 154 MORIAH

AA0101 44770 0 0 PS 990901 16:14:31 16:14:46 15 00:00:00 00:00:00 0 AGENT 16:14:44 16:16:02 78 BENSION

AA0101 44771 0 0 PS 990901 16:38:59 16:39:12 13 00:00:00 00:00:00 0 AGENT 16:39:11 16:43:35 264 VICKY

AA0101 44772 0 0 PS 990901 16:51:40 16:51:50 10 00:00:00 00:00:00 0 AGENT 16:51:49 16:53:52 123 ANAT

AA0101 44773 0 0 PS 990901 17:02:19 17:02:28 9 00:00:00 00:00:00 0 AGENT 17:02:28 17:07:42 314 VICKY

AA0101 44774 32387482 1 PS 990901 17:18:18 17:18:24 6 17:18:24 17:19:01 37 AGENT 17:19:00 17:19:35 35 VICKY

AA0101 44775 0 0 PS 990901 17:38:53 17:39:05 12 00:00:00 00:00:00 0 AGENT 17:39:04 17:40:43 99 TOVA

AA0101 44776 0 0 PS 990901 17:52:59 17:53:09 10 00:00:00 00:00:00 0 AGENT 17:53:08 17:53:09 1 NO_SERVER

AA0101 44777 37635950 2 PS 990901 18:15:47 18:15:52 5 18:15:52 18:16:57 65 AGENT 18:16:56 18:18:48 112 ANAT

AA0101 44778 0 0 NE 990901 18:30:43 18:30:52 9 00:00:00 00:00:00 0 AGENT 18:30:51 18:30:54 3 MORIAH

AA0101 44779 0 0 PS 990901 18:51:47 18:52:02 15 00:00:00 00:00:00 0 AGENT 18:52:02 18:55:30 208 TOVA

AA0101 44780 0 0 PS 990901 19:19:04 19:19:17 13 00:00:00 00:00:00 0 AGENT 19:19:15 19:20:20 65 MEIR

AA0101 44781 0 0 PS 990901 19:39:19 19:39:30 11 00:00:00 00:00:00 0 AGENT 19:39:29 19:41:42 133 BENSION AA0101 44782 0 0 NW 990901 20:08:13 20:08:25 12 00:00:00 00:00:00 0 AGENT 20:08:28 20:08:41 13 NO_SERVER


AA0101 44784 0 0 NW 990901 20:36:54 20:37:14 20 00:00:00 00:00:00 0 AGENT 20:37:13 20:38:07 54 BENSION


AA0101 44786 0 0 PS 990901 21:04:41 21:04:51 10 00:00:00 00:00:00 0 AGENT 21:04:50 21:05:59 69 TOVA

AA0101 44787 0 0 PS 990901 21:25:00 21:25:13 13 00:00:00 00:00:00 0 AGENT 21:25:13 21:28:03 170 AVI

AA0101 44788 0 0 PS 990901 21:50:40 21:50:54 14 00:00:00 00:00:00 0 AGENT 21:50:54 21:51:55 61 AVI

AA0101 44789 9103060 2 NE 990901 22:05:40 22:05:46 6 22:05:46 22:09:52 246 AGENT 22:09:51 22:13:41 230 AVI

AA0101 44790 14558621 2 PS 990901 22:24:11 22:24:17 6 22:24:17 22:26:16 119 AGENT 22:26:15 22:27:28 73 VICKY

AA0101 44791 0 0 PS 990901 22:46:27 22:46:37 10 00:00:00 00:00:00 0 AGENT 22:46:36 22:47:03 27 AVI

AA0101 44792 67158097 2 PS 990901 23:05:07 23:05:13 6 23:05:13 23:05:30 17 AGENT 23:05:29 23:06:49 80 VICKY

AA0101 44793 15317126 2 PS 990901 23:28:52 23:28:58 6 23:28:58 23:30:08 70 AGENT 23:30:07 23:35:03 296 DARMON


AA0101 44795 0 0 PS 990902 07:16:52 07:17:01 9 00:00:00 00:00:00 0 AGENT 07:17:01 07:17:44 43 ANAT

AA0101 44796 0 0 PS 990902 07:50:05 07:50:16 11 00:00:00 00:00:00 0 AGENT 07:50:16 07:53:03 167 STEREN

6

Averages Prevalent

ACD Report: Health Insurance

Time Calls Answered Abandoned% ASA AHT Occ% # of agentsTotal 20,577 19,860 3.5% 30 307 95.1%8:00 332 308 7.2% 27 302 87.1% 59.38:30 653 615 5.8% 58 293 96.1% 104.19:00 866 796 8.1% 63 308 97.1% 140.49:30 1,152 1,138 1.2% 28 303 90.8% 211.110:00 1,330 1,286 3.3% 22 307 98.4% 223.110:30 1,364 1,338 1.9% 33 296 99.0% 222.511:00 1,380 1,280 7.2% 34 306 98.2% 222.011:30 1,272 1,247 2.0% 44 298 94.6% 218.012:00 1,179 1,177 0.2% 1 306 91.6% 218.312:30 1,174 1,160 1.2% 10 302 95.5% 203.813:00 1,018 999 1.9% 9 314 95.4% 182.913:30 1,061 961 9.4% 67 306 100.0% 163.414:00 1,173 1,082 7.8% 78 313 99.5% 188.914:30 1,212 1,179 2.7% 23 304 96.6% 206.115:00 1,137 1,122 1.3% 15 320 96.9% 205.815:30 1,169 1,137 2.7% 17 311 97.1% 202.216:00 1,107 1,059 4.3% 46 315 99.2% 187.116:30 914 892 2.4% 22 307 95.2% 160.017:00 615 615 0.0% 2 328 83.0% 135.017:30 420 420 0.0% 0 328 73.8% 103.518:00 49 49 0.0% 14 180 84.2% 5.8

7

Beyond Averages: Waiting Times in a Call Center

Small Israeli Bank

quantiles of waiting times to those of the exponential (the straight line at the right plot). The �t is reasonableup to about 700 seconds. (The p-value for the Kolmogorov-Smirnov test for Exponentiality is however 0 {not that surprising in view of the sample size of 263,007).

Figure 9: Distribution of waiting time (1999)

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

Waiting time given agent

Exp

qua

ntile

s

0 200 400 600

020

040

060

0

Remark on mixtures of independent exponentials: Interestingly, the means and standard deviations in Table19 are rather close, both annually and across all months. This suggests also an exponential distributionfor each month separately, as was indeed veri�ed, and which is apparently inconsistent with the observerdannual exponentiality. The phenomenon recurs later as well, hence an explanation is in order. We shall besatis�ed with demonstrating that a true mixture W of independent random varibles Wi, all of which havecoeÆcients of variation C(Wi) = 1, can also have C(W ) � 1. To this end, let Wi denote the waiting time inmonth i, and suppose it is exponentially distributed with meanmi. Assume that the months are independentand let pi be the fraction of calls performed in month i (out of the yearly total). If W denotes the mixtureof these exponentials (W =Wi with probability pi, that is W has a hyper-exponential distribution), then

C2(W ) = 1 + 2C2(M);

where M stands for a �ctitious random variable, de�ned to be equal mi with probability pi. One concludesthat if themi's do not vary much relative to their mean (C(M) << 1), which is the case here, then C(W ) � 1,allowing for approximate exponentiality of both the mixture and its constituents.

6.2.1 The various waiting times, and their rami�cations

We �rst distinguished between queueing time and waiting time. The latter does not account for zero-waits,and it is more relevant for managers, especially when considered jointly with the fraction of customers thatdid wait. A more fundamental distinction is between the waiting times of customer that got served and thosethat abandoned. Here is it important to recognize that the latter does not describe customers' patience,which we now explain.

A third distinction is between the time that a customer needs to wait before reaching an agent vs. the timethat a customer is willing to wait before abandoning the system. The former is referred to as virtual waitingtime, since it amounts to the time that a (virtual) customer, equipped with an in�nite patience, would havewaited till being served; the latter will serve as our operational measure of customers' patience. While bothmeasures are obviously of great importance, note however that neither is directly observable, and hence mustbe estimated.

25

Large U.S. BankChart1

Page 1

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 Bankwaitwait

Page 1

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.)


8

The Second Prerequisite: Models

Through Examples Only.

Each example starts with a Complex Reality and ends with a usefulinsight due to a Simple Model.

‘‘Theorem": A useful model must be simple (yet not too simple).

Models in decreasing simplicity-levels:

I Conceptual: Service Networks = Queueing Networks

I Descriptive: Averages, Histograms

I Explanatory: Comparative, Regression

I Analytical/Mathematical: Little’s Law, Fluid Models, QueueingModels, Diffusion Refinements.

“Corollary": To be useful, a simple model sometimes requires deepanalysis.

9

Conceptual Model: Face-to-Face Services

Bank Branch = Queueing Network

23

Teller

Entrance

Tourism

Xerox

Manager

Teller

Entrance

Tourism

Xerox

Manager

Bottleneck!

10

Descriptive Model: Transition Probabilities (Averages)

Bank: A Queuing Network

Transition Frequencies Between Units in The Private and Business Sections:

Private Banking Business

To Unit Bankers Authorized Compens - Tellers Tellers Overdrafts Authorized Full Exit

From Unit Personal - ations Personal Service

Bankers 1% 1% 4% 4% 0% 0% 0% 90%

Private Authorized Personal 12% 5% 4% 6% 0% 0% 0% 73%

Banking Compensations 7% 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%

Services Overdrafts 2% 0% 1% 1% 19% 5% 8% 64%

Authorized Personal 2% 1% 0% 1% 11% 5% 11% 69%

Full Service 1% 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%

Dominant Paths - Business:

Unit Station 1 Station 2 Total Parameter Tourism Teller Dominant Path

Service Time 12.7 4.8 17.5 Waiting Time 8.2 6.9 15.1

Total Time 20.9 11.7 32.6

Service Index 0.61 0.41 0.53

Dominant Paths - Private:

Unit Station 1 Station 2 Total Parameter Banker Teller Dominant Path

Service Time 12.1 3.9 16.0 Waiting Time 6.5 5.7 12.2

Total Time 18.6 9.6 28.2

Service Index 0.65 0.40 0.56

Service Index = % time being served

11

Conceptual Model: Hospital (ED) Network(Marmur, Sinreich)

PhysicianNurseImagingLabElse

60estimated max time

initialexamination

decision point for alternative processes

10%probability of events

06vital signs

07

E.C.G05

decision

awaitingdischarge

40

treatment 41

50

consultation

instructionsprior discharge

discharge /hospitalization

else

triage04

43

54

reception03

observation

46

every 15 minutes

follow up47

bloodwork

1312

100%

imaging /consultation /treatment

17

14

decision

20

ultrasound2928

21

Xray

2725,26

CT

3130

22

15

39

37

45

follow up48

every 15 minutes

49

11

handlingpatient&family

08

09

38imaging

36

3534

32,33 treatment18

56

hospitalization/discharge

awaitingevacuation

55

52

53

10

treatment 19

16

discharge

51

else

treatment42

44

reference point

labs labs

consultation

Labs

consultation

imaging

decision

proportion of patients 01 process requires bed 02

23

24

Figure 2. The Unified Patient Process Chart

12

Descriptive Model: Service Times (Averages) or,Even “Doctors" Can Manage

Afternoon, by Case

Morning, by Hour

Operations Time In a Hospital

Operations Time Histogram: Operations Time - Morning (by Hour) vs. Afternoon (by Case): Ethical?

Even Doctors Can Manage!

0%2%4%6%8%

10%12%14%16%18%20%

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 5 5.5 6 6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 12 12.5 13 13.5 14

Hours

Freq

uenc

y

AVG: 2.08 HoursSTD: 4.12 HoursSample Size: 4347

CV >> 1

0

1

2

3

4

5

6

EEG Orthopedics Surgery Blood Surgery Plastic Surgery Heart/ChestSurgery

Neuro-Surgery Eyes E.I. Surgery

Department

Hou

rs

AM

PM

20

13

Conceptual Model: The “Production of Justice"

The Labor-Court Process in Haifa, Israel

“Production” Of Justice

Queue

Mile Stone

Activity

Appeal

Proceedings

Closure

Prepare AllocateOpen File

Avg. sojourn time ≈ in months / years

Processing time ≈ in mins / hours / days

Phase Transition

Phase

14

Analytical Model: Little’s Law in Court (still Averages)

Operational Performance: Rate λ & Time W

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

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10

0 5 10 15 20 25 30

Judges: Performance Analysis

Case Type 0 Judge1 Case Type 01 Judge2 Case Type 3 Judge3 Judge4 Judge5

Judges: Performance Analysis Judges: Performance by Case-Type

Ave

rage

Num

ber o

f Mon

ths -

W

Average Number of Cases / Month - λ

Judges: Operational Performance – Base Case

15

Expertise “invite" Skills-Base-Routing (SBR)

Operational Performance: Judges’ Heterogeneity (Best / Worse)

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

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0 5 10 15 20 25 30



Ave

rage

Num

ber o

f Mon

ths -

W

Average Number of Cases / Month - λ

Judges: Operational Performance – Base Case Judges: Performance Analysis Judges: Performance by Case-Type

16


Judges’ Profiles (Operational)

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)

.

.

.

..



Avg

. Mon

ths -

W

Avg. Cases / Month - λ

17


Judges: The Best/Worst (Operational) Performer

(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

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0 5 10 15 20 25 30

.

.

.

..

45 100

118

59

33



Avg

. Mon

ths -

W

Avg. Cases / Month - λ

18

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

Customers Interface Design

Computer-Telephony Integration - CTIMIS/CS

Marketing

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

InternetChatEmailFax

Lost Calls

Service Completion)75% in Banks (

( Waiting TimeReturn Time)

Logistics

Customers Segmentation -CRM

Psychology, Operations Research,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

19

The “Phases of Waiting" for Service

Common Experience:I Expected to wait 5 minutes, Required to 10I Felt like 20, Actually waited 10 (hence Willing ≥ 10)

An attempt at “Modeling the Experience":1. Time that a customer expects to wait2. willing to wait ((Im)Patience: τ )3. required to wait (Offered Wait:V )4. actually waits (Wq = min(τ, V ))5. perceives waiting.

Experienced customers ⇒ Expected = Required“Rational" customers ⇒ Perceived = Actual.

Then left with (τ, V ).

20

Call Center Data: Hazard Rates (Un-Censored)

Israel

U.S.

(Im)Patience Time τ

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 V

36

0 10 20 30 40 50 600

2

4

6

8

10

12

14

16

time, sec

haza

rd r

ate

actuarial estimatespline smoother

21

A Patience Index

Quantifying (Im)Patience: “Willing to wait 15 min" = Patient?

Theoretical Patience-Index ∆=

Willing to waitExpected to wait

=E[τ ]

E[V ],

“assuming" Experienced; further “assuming" that τ and V areExponential, the M-L estimate of Index is the easily-measurable:

Empirical Patience-Index ∆=

% Served% Abandoning

Index Validation: Theoretical vs. Empirical

0

1

2

3

4

5

6

7

8

9

10

2 3 4 5 6 7 8 9

Empirical Index

Theo

retic

al In

dex

22

Predicting Performance

Model Primitives:

I Arrivals to service (random process)I (Im)Patience while waiting τ (r.v.)I Service times (r.v.)I # Servers / Agents (parameter / r.v.)

Model Output: Offered-Wait V (r.v.)

Operational Performance Measure calculable in terms of (τ, V ).

I eg. Average Wait = E[min{τ, V}]I eg. % Abandonment = P{τ < V}

Application: Staffing – How Many Agents? (When? Who?)

23

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

agents

arrivals

abandonment

λ

µ

1

2

n

…

queue

θ

Erlang-A Parameters:

I λ – Arrival rate (Poisson)I µ – Service rate (Exponential)I θ – Impatience rate (Exponential)I n – Number of Service-Agents.

24

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 (

data

)

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

)

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

I Small Israeli Bank (more examples in progress)

25

Testing the Erlang-A Primitives

I Arrivals: Poisson?I Service-durations: Exponential?I (Im)Patience: Exponential?

Validation: Support? Refute?

26

Arrivals to Service: only Poisson-Relatives

Arrival Rate to Three Call Centers

Dec. 1995 (U.S. 700 Helpdesks) May 1959 (England)

Q-Science

May 1959!

Dec 1995!

(Help Desk Institute)

Arrival Rate

Time 24 hrs

Time 24 hrs

% Arrivals

(Lee A.M., Applied Q-Th)

28

Q-Science

May 1959!

Dec 1995!

(Help Desk Institute)

Arrival Rate

Time 24 hrs

Time 24 hrs

% Arrivals

(Lee A.M., Applied Q-Th)

28

November 1999 (Israel)

Arrival Process, in 1999

Yearly Monthly

Daily Hourly

Observation:Peak Loads at 10:00 & 15:00

27

Service Durations: LogNormal Prevalent

Israeli Bank Survival-FunctionsLog-Histogram by Service-Class

0

100

200

300

400

500

600

700

800

900

0.8 1 1.2 1.4 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6 3.8

Log(service time)

Freq

uenc

y

frequency normal curve

Average = 2.24St.dev. = 0.42

31

Service TimeSurvival curve, by Types

Time

Surv

ival

Means (In Seconds)

NW (New) = 111

PS (Regular) = 181

NE (Stocks) = 269

IN (Internet) = 381

34

I New Customers: 2 min (NW);I Regulars: 3 min (PS);

I Stock: 4.5 min (NE);I Tech-Support: 6.5 min (IN).

Observation: VIP require longer service times.

28

(Im)Patience while Waiting (Palm 1943-53)

Irritation ∝ Hazard Rate of (Im)Patience DistributionRegular over VIP Customers – Israeli Bank

14

16

I Peaks of abandonment at times of AnnouncementsI Call-by-Call Data (DataMOCCA) required (& Un-Censoring).

Observation: VIP are more patient (Needy)

29

A “Service-Time" Puzzle at a Small Israeli BankInter-related Primitives

Average Service Time over the Day – Israeli Bank

�

�

�

�

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

42613)

Time of Day

Mea

n S

ervi

ce T

ime

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

3011

Prevalent: Longest services at peak-loads (10:00, 15:00). Why?Explanations:

I Common: Service protocol different (longer) during peak times.I Operational: The needy abandon less during peak times;

hence the VIP remain on line, with their long service times.30

Erlang-A: Simple, but Not Too Simple

Experience:I Arrival process not pure Poisson (time-varying, σ2 too large)I Service times not exponential (typically close to lognormal)I Patience times not exponential (various patterns observed).I Customers and Servers not homogeneous (classes, skills)

Questions naturally arise:

1. Why does Erlang-A practically work? justify robustness.2. When does it fail? chart boundaries.3. Generalize: time-variation, SBR, networks, uncertainty , . . .

Answers via Asymptotic Analysis, as load- and staffing-levels ↑ ,which captures model-essentials:

I Efficiency-Driven (ED) regime: Fluid models (deterministic).I Quality- and Efficiency-Driven (QED) regime: Diffusion

refinements (eg. revealing that the patience-density at the originis “all" that is needed).

31

DataMOCCA = Data MOdels for Call Center Analysis

I Technion: P. Feigin, V. Trofimov, Statistics / SEE Laboratory.I Wharton: L. Brown, N. Gans, H. Shen (UNC).I industry:

I U.S. Bank: 2.5 years, 220M calls, 40M by 1000 agents.I Israeli Cellular: 2.5 years, 110M calls, 25M calls by 750 agents;

ongoing.

Project Goal: Designing and Implementing a (universal)data-base/data-repository and interface for storing, retrieving,analyzing and displaying Call-by-Call-based Data / Information.

System Components:I Clean Databases: operational-data of individual calls / agents.I Graphical Online Interface: easily generates graphs and tables,

at varying resolutions (seconds, minutes, hours, days, months).

Free for academic adoption: Mini version available on a DVD;working version 7GB tables, or 20GB raw zipped, for each callcenter – ask for my mini-HD.

32

Arrivals to Service: Predictable vs. RandomArrival Rates on Tuesdays in a September – U.S. Bank

0

500

1000

1500

2000

2500

3000

3500

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

Time (Resolution 30 min.)

Arrival rate

04.09.2001 11.09.2001 18.09.2001 25.09.2001

I Tuesday, September 4th: Heavy, following Labor Day.I Tuesdays, September 18 & 25: Normal.I Tuesday, September 11th, 2001.

33

A “Waiting-Times" Puzzle at a Medium Israeli Bankwaitwait

Page 1

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, %

Peaks Every 60 Seconds. Why?I Human: Voice-announcement every 60 seconds.I System: Priority-upgrade (unrevealed) every 60 seconds.

Served Customers Abandoning Customerswaithandled

Page 1

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



waitab

Page 1

0.0

0.1

0.2

0.3

0.4

0.5

0.6

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



34

Priorities, Economies-of-Scale, SBR

Regular vs. VIP Customers: Cellular – March 23, 2004

Average Wait Staffing Level

0

5

10

15

20

25

30

35

40

45

50

7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00

Time

Average waiting time, sec

Private Private Platinum

0

10

20

30

40

50

60

7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00

Time

Number of agents


I Design: VIP-dedicated agents, Regular-dedicated Agents.I VIP’s are not served better than Regular’s

I Solutions: Add VIP agents (costly), or Re-Design.

35

Priorities and Routing Protocols I

Regular vs. VIP Customers: Cellular – October 2004

Delay Probability Average Wait

0

10

20

30

40

50

60

70

80

90

100

7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00


Delay Probability, %


0

5

10

15

20

25

30

35

40

7:00 9:00 11:00 13:00 15:00 17:00 19:00 21:00 23:00


Average Wait, sec


More VIPs delayed than Regulars, yet their average wait is shorter.

What changed since last March?

36

Priorities and Routing Protocols II

Waiting-Time Histograms: Cellular – October 2004

Regular Customers VIP (Platinum) Customersprivate_hist

Page 1

0.0

0.5

1.0

1.5

2.0

2.5

3.0

2 14 26 38 50 62 74 86 98



platinum_hist

Page 1

0.0

2.0

4.0

6.0

8.0

10.0

12.0

14.0

16.0

18.0

2 14 26 38 50 62 74 86



After 25 seconds of wait, VIP customers are routed with highpriority to Regular agents. Hence, almost no long waiting times forVIP’s.

37

Network Balancing via Inter-Queues at a U.S. Bank

73

Distributed Call Center (U.S. Bank)

NY 1

RI 3

PA 2

MA 4

179+5

619+3

11+1

74+7

8+1

19+1

20

508+2

101+2

2

External arrivals:2092 2063(98.6%Served)+29(1.4%Aban)

Not Interqueued:1209(57.8%)

• Served: 1184(97.9/56.6)

• Aban: 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 d t 3

External arrivals: 16941687(99.6%

Served)+7( 0.4% Aban)

Not Interqueued: 1665(98.3)

• Served: 1659 (99.6/97.9)

• Aban: 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)

• Aban: 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)

• Aban: 6 (0.4/0.3) Interqueued:258+9

(15.1) • Served here: 110

(41.2/6.2) • Served at 1:58

(21 7/3 3)

Internal arrivals: 224

• Served at 1: 67 (29.9)

• Served at 2: 41 (18.3)

• Served at 3: 87 (38.8)

• Served at 4:


• Served at 1: 157 (24.4)

• Served at 2: 195 (30.3)

• Served at 3: 282 (43.9)

• Served at 4: 4 (0.6)

• Aban at 1: 3


• Served at 1: 17(21)

• Served at 3: 42(51.9)

• Served at 4: 15(18 5)

Internal arrivals: 613• Served at 1:

41(6.7) • Served at 2:

513(83.7) • Served at 3:

55(9.0) • Aban at 1:

2(0.3)

10 AM – 11 AM (03/19/01): Interflow Chart Among the 4 Call C t f Fl t B k

38

Balancing Protocols and Performance Level

U.S. Bank: Histograms of Waiting Times

Retail BusinessChart1

Page 1

0

2

4

6

8

10

12

14

16

18

20

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

Time


Sheet3 Chart 1

Page 1

0

2

4

6

8

10

12

2 8 14 20 26 32 38 44 50 56 62 68 74 80 86 92

Time


Peak for Retail service at 10 seconds – Why?After 10 seconds of wait, Retail customers sent into the inter-queue.

Business customers – peak at 5 seconds, for the same reason.Second peak – unclear, maybe priority-upgrade.

39

Data-Based Service-Research(with DataMOCCA, even before tenure)

I Contrast with EmpOM: Industry / Company / Survey Data(Social Sciences)

I Converge to: Measure, Model, Validate, Experiment, Refine(Physics, Biology, . . .).

I Prerequisites:I OR, OM, IE, (Mktg.) - for DesignI CS, IS, Stat. - for Implementation.

I Outcomes: Relevance, Credibility; Interest, Fun;Call Centers as a Pilot (eg. for Healthcare). Moreover,

I Teaching: Class, Homework (Experimental Data Analysis); Cases.I Research: Validate Existing (Queueing) Theory/Laws and Suggest

New Models/Research.I Practice: OM Tools (Scenario Analysis), Mktg. (Trends,

Benchmarking).

40

Live Demonstration of DataMOCCA5-7 minutes, to emphasize “online" capabilities.

U.S. Bank

I Daily Reports: October 2003, weekdays; typically takes 10-20sec till a first output, but this is because of PowerPoint/Windows.Then do few additional Daily Reports, say Monday, Tuesday,...(starting with STATCCA, as opposed to by minimizing thepowerpoint screnn) - this will be now happening very fast.

I Time-Series: Number of agents, for ALL classes, all months,weekdays. (Including total). Shows scale, trends. Then doService Durations, indicating that 1 second of 1000 agents couldcost $500M per year. Could also do Unhandled (lower middleentry in list), for only Retail and Premium - Premium is worse,and deteriorating,

I Daily Summaries:I Tuesdays in September 2001; September 11th; shown during

lecture under the heading “Predictable or Random";I 30 sec scale - stoch. variability, 1 hour scale - the “right" scale;I % to mean, to show very similar shape over 3 Tuesdays. Suggests

the model λ(t) = λ0(t) · Z , for 0 ≤ t ≤ T .41

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