module 4 slides.ppt
TRANSCRIPT
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Prof. Christian Terwiesch
Response Time
Introduction
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Prof. Christian Terwiesch
Example
-Patients arrive, on average, every five minutes- It takes ten minutes to serve a patient- Patients are willing to wait
What is the implied utiliation of the !ar!er shop"
#ow long will patients have to wait"
Physician office
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Prof. Christian Terwiesch
Example
-Patients arrive, on average, every five minutes- It takes four minutes to serve a patient- Patients are willing to wait
What is the utiliation of the !ar!er shop"
#ow long will patients have to wait"
Physician office
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Prof. Christian Terwiesch
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Prof. Christian Terwiesch
Patient
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Service times
Numberofcases
3ore Realistic .ervice Process
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Prof. Christian Terwiesch
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4aria!ility 5eads to Waiting Time
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The 6urse of 4aria!ility - .ummary
4aria!ility hurts flowWith !uffers% we see waiting times even though there exists excess capacity
4aria!ility is 78 and it does not average itself out
9ew models are needed to understand these effects
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Waiting time models% The
need for excess capacity
Response Time
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Processing
3odeling 4aria!ility in :low
Inflow8emand process is ;randomprocessing times?
Outflow
9o loss, waiting onlyThis re@uires uA'&&B1utflow=Inflow
Flow Rate
3inimumC8emand, 6apacityD = 8emand = 'a
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verage flowtime #
#$eoretica %o& #ime
Ftiliation '&&B
Increasin'
ariabiity
Waiting Time Formula
.ervice time factor
Ftiliation factor
4aria!ility factor
+
=
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22pa CVCV
nutilizatio
nutilizatioTimeActivityqueueinTime
Inflow 1utflow
Inventorywaiting I)
Entry to system 8eparture7egin .ervice
Time in @ueue #) .ervice Time*
:low Time #+#),*
%o& rate
The Waiting Time :ormula
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Example% Walk-in 8oc
9ewt Philly needs to get some medical advise2 #e knows that his 8oc, :rancoise, has a patient arrive every )&minutes >with a standard deviation of )& minutes?2 typical consultation lasts '+ minutes >with a standard
deviation of '+ minutes?2 The 8oc has an open-access policy and does not offer appointments2If 9ewt walks into :rancoisGs practice at '&am, when can he expect to leave the practice again"
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.ummary
Even though the utiliation of a process might !e less than '&&B, it might still re@uire long customer wait time
4aria!ility is the root cause for this effect
s utiliation approaches '&&B, you will see a very steep increase in the wait time
If you want fast service, you will have to hold excess capacity
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3ore on Waiting time models
.taffing to 8emand
Response Time
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nutilizatio
nutilizatio
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timeActivityqueueinTime
Waiting Time Formula for Multiple (m) Serers
Inflow 1utflow
Inventorywaiting I)
Entry to system 8eparture7egin .ervice
Time in @ueue #) .ervice Time*
:low Time #+#),*
Inventoryin service I*
:low rate
Waiting Time :ormula for 3ultiple, Parallel Resources
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6ustomers send emails to a help desk of an online retailer every (minutes, on average, and the standard deviation of the inter-arrival timeis also ( minutes2 The online retailer has three employees answeringemails2 It takes on average * minutes to write a response email2 Thestandard deviation of the service times is ( minutes2
Estimate the average customer wait !efore !eing served2
Example% 1nline retailer
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Waiting Time #) .ervice Time*
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Inventoryin service I*
Ftiliation >9ote% make sure A'?
Time related measures
Inventory related measures >:low rate=1-a?
.ummary of Hueuing nalysis
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6ustomers send emails to a help desk of an online retailer every (minutes, on average, and the standard deviation of the inter-arrival timeis also ( minutes2 The online retailer has three employees answeringemails2 It takes on average * minutes to write a response email2 Thestandard deviation of the service times is ( minutes2
#ow many employees would we have to add to get the average waittime reduced to x minutes"
.taffing 8ecision
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What to 8o With .easonal 8ata
Measure the true !eman! !ata
Slice the !ata "# the hour ($%min& 'min)
ppl# waiting mo!el in each slice
5evel the demand
ssume demand is ;stationary< within a slice
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Target Wait Time >TWT?.ervice 5evel = Pro!a!ilityCWaiting TimeTWTDExample% 7ig 6all 6enter - starting point diagnostic% )&B of calls answered within (& seconds - target% &B of calls answered within (& seconds
&
&2(
&2*
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&2
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& +& '&& '+& (&&
Waiting time *secon!s+
Fraction of
customers who
hae to wait ,secon!s or less "aitin' times for t$ose customers
&$o .o not 'et serve. imme.iatey
%raction of customers &$o 'et serve.
&it$out &aitin' at a
90/ of cas $a. to
&ait 25 secon.s oress
.ervice 5evels in Waiting .ystems
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6apacity Pooling
Response Time
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In.e*en.ent esources
2(m+1!
Pooe. esources
(m+2!
3anagerial Responses to 4aria!ility% Pooling
-,ample
Processing time=* minutesInter-arrival time=+ minutes >at each server?m=', 6va=64p='
T@ =
Processing time=* minutesInter-arrival time=(2+ minutesm=(, 6va=64p='
T@ =
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3anagerial Responses to 4aria!ility% Pooling
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Pooling% .hifting the Efficient :rontier
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Prof. Christian Terwiesch
.ummary
What is a good wait time"
:ire truck or IR."
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Prof. Christian Terwiesch
5imitations of Pooling
ssumes flexi!ility
Increases complexity of work-flow
6an increase the varia!ility of service time
Interrupts the relationship with the customer one-face-to-the-customer
Jroup clinics
Electricity grid smart grid
:lexi!le production plants
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Prof. Christian Terwiesch
The Three Enemies of 1perations
dditional costs due to varia!ility indemand and activity times
Is associated with longer wait timesand or customer loss
Re@uires process to hold excesscapacity >idle time?
4aria!ility
Fse of resources !eyond what isneeded to meet customer
re@uirements 9ot adding value to the product,
!ut adding cost
Reducing the performance of theproduction system
$ different types of waste
WasteWork 4alue-adding
WasteWork 4alue-adding
Waste
Inflexi!ility
dditional costs incurred !ecause of supplydemand mismatches
Waiting customers or Waiting >idle capacity?
6apacity
6ustomerdemand
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Prof. Christian Terwiesch
.cheduling ccess
Response Time
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Prof. Christian Terwiesch
:low units are se@uenced in the waiting area >triage step?
Provides an opportunity for us to move some units forwards and some !ackwards
:irst-6ome-:irst-.erve
- easy to implement- perceived fairness- lowest variance of waiting time
.e@uence !ased on importance- emergency cases- identifying profita!le flow units
3anagerial Responses to 4aria!ility% Priority Rulesin Waiting Time .ystems
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Prof. Christian Terwiesch
Service times
9 minutes
10 minutes
4 minutes
8 minutes
9 min
19 min
23 min
#ota &ait time 9,19,23+51min
4 min
12 min
21 min
#ota &ait time 4,13,21+38 min
.hortest Processing Time Rule- 3inimies average waiting time- Pro!lem of having ;true< processing times
3anagerial Responses to 4aria!ility% Priority Rulesin Waiting Time .ystems
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Prof. Christian Terwiesch
1pen ccess
ppointment systems
ppointments
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Prof. Christian Terwiesch
Redesign the .erviceProcess
Response Time
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Prof. Christian Terwiesch
Reasons for 5ong Response Times>nd Potential Improvement .trategies? Insufficient capacity on a permanent !asis
=K Fnderstand what keeps the capacity low
8emand fluctuation and temporal capacity shortfalls
Fnpredicta!le wait times =K Extra capacity Reduce varia!ility in demand
Predicta!le wait times =K .taff to demand Takt time
5ong wait times !ecause of low priority=K lign priorities with customer value
3any steps in the process poor internal process flow >often driven !y handoffsand rework loops?=K Redesign the service process
http%www2minyanville2com!usinessmarketsarticlesdrive-thrus-emissions-fast-food-mcdonalds+'((&'&id((/'
http://www.minyanville.com/businessmarkets/articles/drive-thrus-emissions-fast-food-mcdonalds/5/12/2010/id/28261http://www.minyanville.com/businessmarkets/articles/drive-thrus-emissions-fast-food-mcdonalds/5/12/2010/id/28261 -
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Prof. Christian Terwiesch
The 6ustomerGs Perspective
Driving Parking Check-in Vitals Waiting PCP Appt. Check outLabs Drive home
20 minutes
#ow much time does a patient spend on a primary care encounter"
Two types of wasted time%uxiliary activities re@uired to get to value add activities >result of process location lay-out?Wait time >result of !ottlenecks insufficient capacity?
#ota vaue a.. time of a unit
#ota time a unit is in t$e *rocess%o& #ime fficiency (or /#! +
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Prof. Christian Terwiesch
Process 3apping .ervice 7lue Prints
.ource% Lves Pigneur
Customer
actions
5ine of interaction
Onstage
actions
5ine of visi!ility
/ac0stage
actions
5ine of internalinteraction
Support
processes
Walk into the
!ranch talk toagent
6ollect !asicinformation
Pre pprovalprocessM set upworkflow accountresponsi!ility
6ustomer
supplies moredata
Re@uest for moredata
6ustomer
supplies moredata
Re@uest for moredata
Pre pprovalprocessM set upworkflow accountresponsi!ility
Run formal creditscoring model
Explain finaldocument
.ign contracts
Process 3apping .ervice 7lue Prints
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Prof. Christian Terwiesch
Process 3apping .ervice 7lue Prints#ow to Redesign a .ervice Process
3ove work off the stageExample% online check-in at an airport
Reduce customer actions rely on support processesExample% checking in at a doctorGs office
Instead of optimiing the capacity of a resource, try to eliminate the step altogetherExample% #ert Jold N 6heck-in offers no valueM go directly to the car
void fragmentation of work due to specialiation narrow Oo! responsi!ilitiesExample% 5oan processing hospital ward
If customers are likely to leave the process !ecause of long wait times, have the wait occurlater in the process re-se@uence the activities
Example% .tar!ucks N Pay early, then wait for the coffee
#ave the waiting occur outside of a line
Example% Restaurants in a shopping malls using !uersExample% ppointment
6ommunicate the wait time with the customer >set expectations?Example% 8isney
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5oss 3odels
Response Time
8ifferent 3odels of 4aria!ility
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Prof. Christian Terwiesch
8ifferent 3odels of 4aria!ility
Waiting pro"lems
Ftiliation has to !e less than '&&B
Impact of varia!ility is on :low Time
1oss pro"lems
8emand can !e !igger than capacity
Impact of varia!ility is on :low Rate
Pure waitingpro!lem, all customersare perfectly patient2
ll customersenter the process,some leave due totheir impatience
6ustomers do notenter the process once!uffer has reached acertain limit
6ustomers are lostonce all servers are!usy
Same if customers are *atient Same if buffer sie+0
Same if buffer sie is etremey ar'e
4aria!ility is always !ad N you pay through lower flow rate andor longer flow time
7uffer or suffer% if you are willing to tolerate waiting, you donGt have to give up on flow rate
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Prof. Christian Terwiesch
nalying 5oss .ystems
#rauma center moves to
.iversion status once a
servers are busy
incomin' *atients
are .irecte. to
ot$er ocations
Resources
) trauma !ays >m+3?
2eman! Process
1ne trauma case comesin every ) hours
>a=) hours?
ais the interarrival time
Exponential interarrival times
Serice Process
Patient stays in trauma !ayfor an average of ( hours
>*=( hours?
*is the service time
6an have any distri!ution
What is Pm& the pro"a"ilit# that all m resources are utili3e!4
m!ulances #elicopters
. > ?
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Prof. Christian Terwiesch
nalying 5oss .ystems% :inding Pm>r?
8efine r + * - a
Example% r= ( hours ) hours r=&2/$
Recall m=)
Fse Erlang 5oss Ta!le
:ind that P) >&2/$?=&2&(++
5ien Pm(r)we can compute
Time per day that system has to deny access:low units lost = 'a Pm >r?
' ( ) * +
&2'& &2&0&0 &2&&*+ &2&&&( &2&&&& &2&&&&
&2(& &2'//$ &2&'/* &2&&'' &2&&&' &2&&&&
&2(+ &2(&&& &2&(** &2&&(& &2&&&' &2&&&&
&2)& &2()&, &2&))+ &2&&)) &2&&&) &2&&&&
&2)) &2(+&& &2&*&& &2&&** &2&&&* &2&&&&
&2*& &2(,+$ &2&+*' &2&&$( &2&&&$ &2&&&'
&2+& &2)))) &2&$/0 &2&'($ &2&&'/ &2&&&(&2/& &2)$+& &2'&'' &2&'0, &2&&)& &2&&&*
&2/$ &2*&&& &2''$/ &2&(++ &2&&*( &2&&&/
&2$& &2*'', &2'(/& &2&(,/ &2&&+& &2&&&$
&2$+ &2*(,/ &2'),+ &2&))+ &2&&/( &2&&&0
&2,& &2**** &2'+&0 &2&),$ &2&&$$ &2&&'(
&20& &2*$)$ &2'$+$ &2&+&' &2&''' &2&&(&
'2&& &2+&&& &2(&&& &2&/(+ &2&'+* &2&&)'
r = p / a
m
Implied utiliation vs pro!a!ility of having all
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Prof. Christian Terwiesch
Implie! utili3ation
Pro"a"ilit#
that all serers
are utili3e!
m+1
m+2
m+5 m+10
m+20
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Implied utiliation vs pro!a!ility of having allserversutilied% Pooling Revisited
-rlang 1oss Ta"le m' ( ) * + / $ , 0 '&
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Prof. Christian Terwiesch
&2'& &2&0&0 &2&&*+ &2&&&( &2&&&& &2&&&& &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&
&2(& &2'//$ &2&'/* &2&&'' &2&&&' &2&&&& &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&
&2(+ &2(&&& &2&(** &2&&(& &2&&&' &2&&&& &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&
&2)& &2()&, &2&))+ &2&&)) &2&&&) &2&&&& &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&
&2)) &2(+&& &2&*&& &2&&** &2&&&* &2&&&& &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&
&2*& &2(,+$ &2&+*' &2&&$( &2&&&$ &2&&&' &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&
&2+& &2)))) &2&$/0 &2&'($ &2&&'/ &2&&&( &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&
&2/& &2)$+& &2'&'' &2&'0, &2&&)& &2&&&* &2&&&& &2&&&& &2&&&& &2&&&& &2&&&&
&2/$ &2*&&& &2''$/ &2&(++ &2&&*( &2&&&/ &2&&&' &2&&&& &2&&&& &2&&&& &2&&&&
&2$& &2*'', &2'(/& &2&(,/ &2&&+& &2&&&$ &2&&&' &2&&&& &2&&&& &2&&&& &2&&&&
&2$+ &2*(,/ &2'),+ &2&))+ &2&&/( &2&&&0 &2&&&' &2&&&& &2&&&& &2&&&& &2&&&&
&2,& &2**** &2'+&0 &2&),$ &2&&$$ &2&&'( &2&&&( &2&&&& &2&&&& &2&&&& &2&&&&
&20& &2*$)$ &2'$+$ &2&+&' &2&''' &2&&(& &2&&&) &2&&&& &2&&&& &2&&&& &2&&&&
'2&& &2+&&& &2(&&& &2&/(+ &2&'+* &2&&)' &2&&&+ &2&&&' &2&&&& &2&&&& &2&&&&
'2'& &2+(), &2(()$ &2&$+, &2&(&* &2&&*+ &2&&&, &2&&&' &2&&&& &2&&&& &2&&&&
'2(& &2+*++ &2(*// &2&,0, &2&(/( &2&&/) &2&&'( &2&&&( &2&&&& &2&&&& &2&&&&
'2(+ &2+++/ &2(+$$ &2&0$& &2&(0* &2&&$) &2&&'+ &2&&&) &2&&&& &2&&&& &2&&&&
'2)& &2+/+( &2(/,$ &2'&*) &2&)(, &2&&,+ &2&&', &2&&&) &2&&&' &2&&&& &2&&&&
'2)) &2+$'* &2($+0 &2'&0( &2&)+' &2&&0) &2&&(' &2&&&* &2&&&' &2&&&& &2&&&&
'2*& &2+,)) &2(,00 &2''0( &2&*&& &2&''' &2&&(/ &2&&&+ &2&&&' &2&&&& &2&&&&
'2+& &2/&&& &2)'&) &2')*) &2&*,& &2&'*( &2&&)+ &2&&&, &2&&&' &2&&&& &2&&&&
'2/& &2/'+* &2)(00 &2'*0/ &2&+/+ &2&'$$ &2&&*$ &2&&'' &2&&&( &2&&&& &2&&&&
'2/$ &2/(+& &2)*(+ &2'+0, &2&/(* &2&(&* &2&&+/ &2&&') &2&&&) &2&&&' &2&&&&
'2$& &2/(0/ &2)*,/ &2'/+& &2&/++ &2&(', &2&&/' &2&&'+ &2&&&) &2&&&' &2&&&&
'2$+ &2/)/* &2)+$$ &2'$(/ &2&$&( &2&(*& &2&&/0 &2&&'$ &2&&&* &2&&&' &2&&&&
r + *-a '2,& &2/*(0 &2)//+ &2',&) &2&$+& &2&(/) &2&&$, &2&&(& &2&&&+ &2&&&' &2&&&&'20& &2/++( &2),)/ &2'0++ &2&,+& &2&)') &2&&0, &2&&($ &2&&&/ &2&&&' &2&&&&
(2&& &2///$ &2*&&& &2('&+ &2&0+( &2&)/$ &2&'(' &2&&)* &2&&&0 &2&&&( &2&&&&
(2'& &2/$$* &2*'+/ &2((+* &2'&+, &2&*(+ &2&'*$ &2&&** &2&&'' &2&&&) &2&&&'
(2(& &2/,$+ &2*)&/ &2(*&& &2''// &2&*,, &2&'$/ &2&&++ &2&&'+ &2&&&* &2&&&'
(2(+ &2/0() &2*)$, &2(*$( &2'((' &2&+(' &2&'0( &2&&/' &2&&'$ &2&&&* &2&&&'
(2)& &2/0$& &2***0 &2(+*) &2'($/ &2&++* &2&(&, &2&&/, &2&&'0 &2&&&+ &2&&&'
(2)) &2$&&& &2**0+ &2(+0' &2')') &2&+$$ &2&((& &2&&$) &2&&(' &2&&&+ &2&&&'
(2*& &2$&+0 &2*+,/ &2(/,* &2'),$ &2&/(* &2&(** &2&&,) &2&&(+ &2&&&$ &2&&&(
(2+& &2$'*) &2*$'$ &2(,(( &2'*00 &2&/0$ &2&(,( &2&'&& &2&&)' &2&&&0 &2&&&(
(2/& &2$((( &2*,*( &2(0+/ &2'/'( &2&$$) &2&)(* &2&''0 &2&&)0 &2&&'' &2&&&)
(2/$ &2$($) &2*0() &2)&** &2'/,$ &2&,(+ &2&)+* &2&')) &2&&** &2&&') &2&&&)
(2$& &2$(0$ &2*0/) &2)&,$ &2'$(+ &2&,+( &2&)/0 &2&'*& &2&&*$ &2&&'* &2&&&*
(2$+ &2$))) &2+&(' &2)'+( &2'$,' &2&,0( &2&)0) &2&'+( &2&&+( &2&&'/ &2&&&*
(2,& &2$)/, &2+&$, &2)('+ &2',)$ &2&0)) &2&*'$ &2&'/* &2&&+$ &2&&', &2&&&+
(20& &2$*)/ &2+',, &2))*& &2'0*0 &2'&'/ &2&*/, &2&'0& &2&&/, &2&&(( &2&&&/
)2&& &2$+&& &2+(0* &2)*/( &2(&/' &2''&' &2&+(( &2&('0 &2&&,' &2&&($ &2&&&,
)2'& &2$+/' &2+)0/ &2)+,& &2('$( &2'',$ &2&+$, &2&(*0 &2&&0/ &2&&)) &2&&'&
)2(& &2$/'0 &2+*0* &2)/0+ &2((,' &2'($* &2&/)/ &2&(,) &2&''( &2&&*& &2&&')
)2(+ &2$/*$ &2++*' &2)$+' &2())/ &2')', &2&/// &2&)&& &2&'(& &2&&*) &2&&'*
)2)& &2$/$* &2++,$ &2),&$ &2()0& &2')/( &2&/0$ &2&)', &2&')& &2&&*$ &2&&'/
)2)) &2$/0( &2+/', &2),*) &2(*(/ &2')0( &2&$', &2&))' &2&')/ &2&&+& &2&&'$
)2*& &2$$($ &2+/$, &2)0'+ &2(*0$ &2'*+( &2&$/& &2&)+/ &2&'*0 &2&&+/ &2&&'0
)2+& &2$$$, &2+$/+ &2*&(' &2(/&) &2'+*' &2&,(+ &2&)0/ &2&'$& &2&&// &2&&()
)2/& &2$,(/ &2+,*, &2*'(* &2($&$ &2'/)' &2&,0' &2&*), &2&'0) &2&&$$ &2&&(,
)2/$ &2$,+$ &2+0&( &2*'0' &2($$+ &2'/0' &2&0)$ &2&*/, &2&('& &2&&,+ &2&&)'
)2$& &2$,$( &2+0(0 &2*((* &2(,&0 &2'$(' &2&0/& &2&*,) &2&(', &2&&,0 &2&&))
)2$+ &2$,0+ &2+0/, &2*($) &2(,/& &2'$// &2&00* &2&+&/ &2&()( &2&&0/ &2&&)/
)2,& &2$0'$ &2/&&$ &2*)(' &2(0'& &2','' &2'&(0 &2&+(0 &2&(*+ &2&'&( &2&&)0
)20& &2$0+0 &2/&,( &2**'+ &2)&&0 &2'0&' &2''&& &2&+$$ &2&($* &2&''$ &2&&*/*2&& &2,&&& &2/'+* &2*+&$ &2)'&$ &2'00' &2''$( &2&/($ &2&)&* &2&')) &2&&+)
Probability{all mservers busy}=
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Erlang 5oss Ta!le
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Prof. Christian Terwiesch
Review
Response Time
(M#6law com)
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Prof. Christian Terwiesch
(M#6law.com)
3y-law2com is a recent start-up trying to cater to customers in search of legal services online2 Fnlike traditionallaw firms, 3y-law2com allows for extensive interaction !etween lawyers and their customers via telephone andthe Internet2 This process is used in the upfront part of the customer interaction, largely consisting ofanswering some !asic customer @uestions prior to entering a formal relationship2 In order to allow customers tointeract with the firmGs lawyers, customers are encouraged to send e-mails to my-lawyerQ3y-law2com2 :rom
there, the incoming e-mails are distri!uted to the lawyer who is currently ;on call2< Jiven the !road skills of thelawyers, each lawyer can respond to each incoming re@uest2
E-mails arrive from 232 to / P232 at a rate of '& e-mails per hour >coefficient of variationfor the arrivals is '?2 t each moment in time, there is exactly one lawyer ;on call,with a standard deviation of '& minutes?2 P: has astaff of + computer technicians2 .ervice times average around *& minutes >with a standard deviation of *&minutes?2
6'2 If im walks into P:, how long must he wait in line !efore he can see a technician" >1nly include thewaiting time, not any service time?
6(2 #ow many customers will, on average, !e waiting for their computer to !e fixed"
Real Compute
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Prof. Christian Terwiesch
Real6ompute offers real-time computing services2 The company owns * supercomputers that can !e accessedthrough the internet2 Their customers send Oo!s that arrive on average every * minutes >inter-arrival times areexponentially distri!uted and, thus, the standard deviation of the inter-arrival times is * minutes?2
Each Oo! takes on average '& minutes of one of the supercomputers >during this time, the computer cannotperform any other work?2 6ustomers pay S(& for the execution of each Oo!2 Jiven the time-sensitive nature of
the calculations, if no supercomputer is availa!le, the Oo! is redirected to a supercomputer of a partner companycalled 1n6omp, which charges S*& per Oo! to Real 6ompute >1n6omp always has supercomputer capacityavaila!le?2
R6'2 What is the pro!a!ility with which an incoming Oo! can !e executed !y one of the supercomputers owned!y Real6ompute"
R6(2 #ow much does Real6ompute pay on average to 1n6omp >in Ss per hour?"
Contractor
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Prof. Christian Terwiesch
Contractor
contractor !uilding houses and doing renovation work has currently six proOects planned for the season2 7eloware the items, and the estimated times to complete them%
9ew construction at .pringfield - /& days7athroom remodeling at #erne - '& days
Training time for solar roof installation - ( daysFpdate we!-site - / daysRenovation of deck at #averford - days9ew kitchen at Rosemont - (& days.uppose the contractor starts immediately with the first proOect, no other proOects get added to this list, and thecontractor se@uences them so as to minimie the average time the proOect waits !efore it gets started2 What willthe contractor !e doing in )& days from the start date of the first proOect"
Call Center
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6onsider a call center that has a constant staffing level2 7ecause of increased demand in the morning,the call center has a very high utiliation in the morning and a very low utiliation in the afternoon2 Whichof the following will decrease the average waiting time in the call center">a? dd more servers>!? 8ecrease the service time coefficient of variation
>c? 8ecrease the average service time>d? 5evel the demand !etween the morning hours and the afternoon hours>e? ll of the a!ove