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Detailed Modeling and

Terminating Statistical Analysis

Chapter 5

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What We’ll Do ...

• Explore lower-level modeling constructs
• Model 5-1: A generic call-center system

 Nonstationary arrival process  Balking, three-way decisions, sets, variables, expressions, submodels, and costing

• Debugging
• Model 5-2: Animating the call center model

 Plots, global pictures, and storages

• Model 5-3: The model with overall performance

measures

 Run conditions, model size and speed, overall performance measures

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Generic Call Center

(Model 5-1)

• Single telephone number, 26 trunk lines

 If all 26 lines busy, caller gets busy signal and goes away

• Answered call gets recording asking …

 Technical support? (76% of callers choose this)  Sales information? (16%)  Order-status inquiry? (8%)

• Time for caller to choose ~ UNIF (0.1, 0.6)
• All times are in minutes in this model

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Technical Support Calls

• Get second recording asking …

 Product type 1? (25% of tech support callers choose this)  Product type 2? (34%)  Product type 3? (41%)

• Recording and choosing takes UNIF(0.1, 0.5)
• If a qualified tech-support person is available for

chosen product, call routed for immediate service

• If not, call placed in (electronic) queue, subjected

to annoying rock music

• All tech support conversations ~ TRIA (3, 6, 18)
• When call done, customer exits system

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Sales Calls

• Call automatically routed to sales staff
• Sales staff is separate from tech-support staff
• If a sales-staff person is available, call gets

immediate service

• If not, call placed in (electronic) queue, treated to

soothing new-age space music

• All sales conversations ~ TRIA (4, 15, 45)
• When call done, customer exits system

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Order-Status Calls

• Automatically handled by phone system — no people
• No limit on number handled at a time (but still limited

by the 26 trunk lines)

• Time for “conversation” ~ TRIA (2, 3, 4)
• After call, 15% take option to talk to a real person (the

rest exit the system)

 These calls are routed to sales staff  Have same priority as incoming sales calls  Conversation durations ~ TRIA (3, 5, 10)  Then exit the system

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Staffing

• Sales staff: 7 people with staggered schedules

 3 on duty for first 90 minutes (notation: 3@90)  Then 7@90, 6@90, 7@60, 6@120, 7@120, 4@

• Tech support staff: 11 people variously qualified

for the three different product lines

 Work eight-hour days plus 30 minutes off for lunch  Some people only qualified on one line  Some people qualified on two or maybe all three lines  Detailed staffing description and schedule ...

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Technical-Support Staff Schedules

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New Modeling Issues (cont’d.)

• Three-way decisions

 Entity or call can go to one of three places in model based on call type

• Similarly, tech-support calls can go to one of three places based on product type  Capability available in Decide module
• Sets

 Groups of similar objects  Can be referenced by a common set name and index (1, 2, 3, …) into the set

• Can also be referenced by original name, independent of set  Technical-support staff requires sets
• An object can be a member of more than one set  Sets data module Docsity.com

New Modeling Issues (cont’d.)

• Variables and Expressions

 Can be referenced in model by name  Can be one- or two-dimensional arrays, indexed by one or two integers  User-defined Variables

• Store some numerical value (not a formula)
• Can be initialized in Variable data module
• Can be used, reassigned during the simulation run by any entity  User-defined Expressions
• A name defined by a mathematical expression
• This name can be references anywhere in the model
• Can use constants, Variables, Attributes, system state variables, values from distribution – connected via mathematical operations Can use Expression Builder to help define
• Defined in Expression data module (Advanced Process panel) Docsity.com

Key Output Performance Measures

• Count balks — no. of attempted incoming calls

sent away due to all 26 trunk lines being busy

 Will not model reneging — customers in queue leaving the system if they get sick of waiting

• Total time in system, by customer type
• Time waiting for a real person, by customer type
• Contact time, by customer type
• Number of calls waiting, by customer type
• Personnel utilization

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Animation Requirements

• No entity movement to animate here
• Can still display queues
• To see how well staffing matches up with load,

craft appropriate plots vs. time

 Number of calls balked  Lengths of queues  Number of idle staff

• Strategy to improve performance — alter the

staffing schedule, see if it produces a better

matchup of the plots

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Arena Modeling Panels

• Basic Process panel

 Highest level of modeling

• Advanced Process panel

 More detailed (and different) modeling capabilities

• Advanced Transfer panel

 Material-handling, entity-movement capabilities

• Blocks, Elements panels

 Lowest level of modeling capabilities – the underlying SIMAN simulation language itself  Other panels are created using modules from these panels  Occasionally needed, but not very often

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Building the Model

• Defining the Data
• Submodel Creation
• Divide model in sections or submodels

 Increment the Time Period  Create Arrivals and Direct to Service  Technical Support Calls  Technical Support Returned Calls  Sales Calls  Order-Status calls

• We’ll discuss each of these in turn …

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