Model 5-1: Simple Call Center - American University of Beirutbm05/INDE504/Labs/lab_10.pdf · Model...

Model 5-1: Simple Call Center

• As you gain experience in modeling, and as

your models become bigger, more complex,

and more detailed, you might find that you’d

like to be able to control or model things at a

lower level with much details.

• Call center system provides a central number

that customer call for :

Technical support

Sales Information

Order status

Model 5-1: Simple Call Center• One phone number for customers to call in to:

– The central feeds 26 trunk lines, one needed for each

call (incoming or outgoing, talking or on hold)

– If all 26 lines are in use, arriving calls get a busy

signal and are lost.

• Calls arrive with inter-arrivals ~ EXPO (0.857) min.

– First call arrives at time 0,three incoming call types

– Initial recording to decide ~ UNIF (0.1, 0.6)

min.

– Tech support (76%), sales (16%), order status

(8%)


• If caller chooses Tech-support calls, a second recording requests asking which of the product type he is using :

– For product type 1 (25%), 2 (34%), or 3 (41%)

• Recording/select time ~ UNIF (0.1, 0.5) min

– There are eight technical support employees to answer tech-support calls:

• Two for product type 1, three for type 2, three for type 3

• Separate FIFO queues for each type

• Conversation time ~ TRIA (3, 6, 18) min for all product types.


• Then leaves system, if none of the employees is currently available ,the customer is placed in an electronic queue where he is subjected to annoying rock music until support person is available.

• Sales calls

– Four sales staff, all have the same skills.

• One FIFO queue feeding all sales staff

– Conversation time ~ TRIA (4, 15, 45) min

• Then leaves system, if none of the sales staff is available the customer is placed in an electronic queue where he is subjected to soothing new -age space music because

after all we’re hoping for a sale until support person is available. 4


• Order-status calls

– All the same

– Handled automatically by phone system

• No limit on number in process at a time, except

for trunk-line limit.

– “Conversation” time ~ TRIA (2, 3, 4) min

– After “conversation,” 15% of callers opt to talk to

a person

• Routed to sales staff, conversation lasts an

additional TRIA (2, 3, 4) min• Sales calls have higher priority (non-preemptive) that means if an

order call is in queue waiting and a new arriving sales call enters

the sale call will be given priority and answered first.


• The call Center receives calls from 8am – 6pm

– Must terminate arrival process at 6pm

– Although the system closes to new arriving calls at

6 pm , all calls that enter the system by that time are

answered and served.

6

To


Arrivals, Direct to Service• 1)Create call arrivals

– Entity type Incoming Call

– Max Arrivals = MaxCalls, Variable initialized to

999999 which means that the arrival process will be

terminated after 999999 arriving calls


Arrivals, Direct to Service

8

-We also define the variable CallsPerArrival and initialize it

to a value of 1.

-We want to Record the number of attempted call

Add 1 to Counter Name Attempted Calls using a record

module.



2)Entity data moduleIncoming Call Entity Type already there

For Initial Picture, select Picture.Blue Ball

3)Decide module – Trunk Line Available?Type = 2-way by Condition

Select (logical) Expression for “If”

NR() is number of units of that resource that are busy now

MR() is number of units scheduled for the resource

Expression :

NR(Trunk Line)< MR(Trunk Line)

Steps for Decide Module:

• Define a resource call it trunk line give it capacity 26.

• Fill the entries for the decide module.

10

Decide Module :

– If False – Record rejected call counter, Dispose

– If True:

• Seize a unit of Trunk Line Resource – Release later

11

12



• Use the Delay module to account for initial recording

time.

13


• Decide module – Determine Call Type

– Three-sided coin flip – Type = N-way by Chance

• Note that probabilities are entered as percentages

(0-100, not 0-1)

• Last entry is “else”

• Direct call to one of tech support, sales, or order-status

areas



Tech-Support Calls• Assign module

– Change Entity Type for separating out in results

– Add delay module for Tech Call delay UNIF(0.1,0.5) min

• Decide module for product type

– Different three-sided coin flip

– Direct to appropriate Process module for that product type

• Process modules for tech-support service

– Seize-Delay-Release

– Seize a unit from appropriate multi-unit Resource

– Use Tech Time defined in Expression data module

16


Tech-Support Calls

17


Tech-Support Calls


Sales Calls• Assign module – change Entity Type

• Process module

– Seize-Delay-Release

– Seize a unit of Sales Resource

• Sales calls priority over order-status calls that seek a person?

– Queue data module, Process Sales Call.Queue

• Type = Lowest Attribute Value

– Attribute Name = Sales Call Priority

– Undefined for sales calls, so has value 0 ... will set to 1 for order-status calls that seek a person, putting sales calls ahead in the queue


Sales Calls

19


Order-Status Calls• Assign module – change Entity Type

• Delay

• Use Decide Module

– No sales person required (15%)– go directly to system-exit logic

– If Sales person required:

• Assign module – set Sales Call PriorityAttribute to 1 so these will have lower priority than real sales calls


Order-Status Calls• Seize module for a unit of Sales resource

– Define Queue Name = Process Sales Call.Queue – shared with sales calls

– Process module does not allow for specifying a shared queue, so can’t use here

– Delay for conversation with sales person TRIA(2,3,4) minutes.

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• Release the unit of Sales resource using release module.

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Order-Status Calls


System Exit• All calls of all types come here when finished

• Release module – release the unit of Trunk Line

resource seized upstream

• Record module – increment Completed Calls counter

• Dispose of call

Final Model 5-1

24

False

De te rm in e Ca l l Ty p e

Else

76

16

e n t i ty ty p eT e c h n i c a l Ca l l

As s i g n

Re c o rd in g De la y

Te c h n ic a l Ca l l

Ty pe

De te rm in e Pro d uc t

Else

25

34

Ca l lT y p e 1 T e c h

Pro c e s s Pro d u c t





En t i ty T y p eAs s i g n Sa l e Ca l l

Ca l lPro c e s s Sa l e

T y p eSta tu s e n ti tyAs s i g n Ord e r

s ta tu s c a l l

d e lay fo r o rd e r

re q u i re d ?

No s a le s pe rs o n Tr ue

False

Ca l l Pri o ri tySe t o rd e r Sta tu s

Sa les p e rs o n

Ca l l s ie z es

s a les p e rs o n

wi th

c o nv e rs a tio n

o rd e r s ta tus

s a les p e rs o n

re lea s e s

o rd e r s ta us c a l l s

L in e

Re lea s e Tru n kCo m p le te d Ca l l s

Re c o rde n t i ty

Di s p o s e o f c a l l

Calls Arrive

Tech Support Calls

Sales Calls

Order Status Calls

Se iz e Tru nk L in e De lay

In i tia l re c o rd in g

c re a te c a l l a rri v a l sAttem p te d Ca l l

Re c o rdTru nk L in e Av a i la b le ?

Tr ue

Ca l ls

Re c o rd Rjec te d

Ca l l sDi s p o s e Re j e c te d

0

0

0

0

0

0

0

0

0

0


Arrival-Cutoff Logic• In our model we indicated that the system closes to new

calls after 6 pm, but all calls that entered the system

before that time are answered and processed.

– This means that we allow calls to enter the system from 8 am to

6 pm ,a total of 600 minutes

– need to shutoff the arrivals after 600 minutes.

making sure just one is created– Time Between Arrivals = 999999 min


Arrival-Cutoff Logic– Assign module to set Variable MaxCalls to

1(shutting off our arrival stream)

– Also after 600 minutes Arena schedules the next

creation as long as the ‘’Max Arrivals’’ is not

reached .So as time 600 is approached,there will

be a last illegal call .

– To cut off this illegal call also set in Assign module CallsPerArrival to 0

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27


Arrival-Cutoff Logic


Run > Setup• Replication Parameters tab (other tabs as usual)

• Base Time Units = Minutes

• Replication Length = Infinite (the default)

• Terminating Condition field:

TNOW >= 600.0 && Total WIP == 0

Arena

clock

Variable

Greater than

or equal to 600

minutes, (6pm)

Logical

“and”

Variable we

maintained

in model

Equality

test for

zero

Base Time Units

It’s 6pm or later and there are no calls in the system.


Run > Setup

29

Terminating

Time frame of interest for each replication

Terminating – specific starting, stopping conditions (this model)stopping

conditions could be of several forms – fixed time, count, condition.

Model 5-1: Simple Call Center• Output performance measures

– As a point of interest will be counting the Number of

calls attempted, rejected(busy signals), and

completed

– By call type – total time in system

– Resource utilization – of personnel, trunk lines..

Viewing Reports of Model 5-1

(one replication)

Number of calls attempted, rejected(busy signals), and completed:

32

• By call type – total time in system

Viewing Reports of Model 5-1

• Resource utilization – of personnel, trunk lines..

Model 5-1: Simple Call Center - American University of Beirutbm05/INDE504/Labs/lab_10.pdf · Model...

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