II. Discrete Event Simulation Systems DESS

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II. Discrete Event Simulation Systems (DESS)

• M. Peter Jurkat
• CS452/Mgt532 Simulation for Managerial Decisions
• The Robert O. Anderson Schools of Management
• University of New Mexico

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How Various Models are Studied
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Basic ExampleSingle Server Queue (SSQ)

• Components
• Single server (S) is idle or busy
• Queue (Q) can also be a storage (e.g.,
  garage)
• Entities to be served which
• Arrive at server,
• wait in queue if server busy, and
• then are served in turn and depart
• Complex systems often consist of many servers and
  queues (e.g., intersection, manufacturing
  facility, computer network)
• In some applications server(s) go to entities
  (shop floor machine repair) entities queued are
  physically spread out

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Definition and Scope

• DESS consists of entities (E), e.g., UML classes,
  and objects w/ attributes (A) values (V)
  servers (S) other resources (Qs, storage
  facilities, etc.)
• In GPSS entities are transactions (x-acts)
• Events (maybe documented in an UML event table)
• Process consists of entities moving through
  system from server to server, being affected by
  these servers, and possibly being stored and/or
  affecting other parts of the system
• Entities originate (enter the system) at sources
  and terminate (leave) at sinks

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Definition and Scope (cont.)

• System described by variables, IVs and DVs, which
  are classified as
• Endogenous values determined by system
• Exogenous values determined outside of system
• Parameters values set by investigator
  (exogenous)
• State minimal set of variables from whose values
  the system can be completely described (SV)
• Event is an activity which changes the state of
  the system (i.e., changes the value of one or
  more of the state variables)
• Discrete event implies events only occur at
  specific times between which system remains in a
  given state

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Example Event Table for SSQ
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Stochastic DES

• Will concentrate on stochastic systems gt
  probability distributes govern
• type of events (e.g., which checkout counter to
  queue at, whether to chance lines)
• intervals between events (e.g., arrivals)
• duration of events (e.g., service times)
• For SSQ events are next arrival (can occur at
  random time interval) and service completion (can
  take randomly long)
• Other IVs unique to system being modeled
• DVs (system measures) somewhat standard

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Random Variation in Simulation

• If randomness sufficiently regular then model
  with probability distribution
• Distribution table of possible outcomes and
  their probability
• Values of probabilities either observed or
  postulated
• To select event get uniform random number in
  interval 0,1 on vertical axis and move to right
  first cumulative bar encountered is that of the
  event (inverse function method)

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Outcomes or System Measures (DVs)

• Since inputs can be stochastic, output measures
  are likely to be statistical
• Averages, variances/standard deviations, and/or
  proportions of
• Storage levels, inventory/queue levels (e.g.,
  number of entities in system)
• Entity times in system (e.g., waiting time plus
  service time) or in Q, flow rate
• Value added times, processing times
• Resource utilizations (e.g., proportion of time
  server is busy)
• Yield, output, products completed, entities
  served
• Usual 7 standard set of seven DVs on pp30-33
  and others
• Since results of stochs can be different for
  identical parameters, cannot tell if differences
  are due to parameters variation or statistical
  variation
• Implies that if two systems are to be compared,
  statistical tests for significant differences can
  be used to overcome human judgment limitations

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Simulation Representation

• Simulation Table
• 2-D array which supports computation and display
  of system variable values
• Rows may represent event occurrence times,
  entities, etc.
• Columns usually represent input, intermediate,
  and output variables entries in the table are
  their values
• Example Banks et al, Example 2.1, Table 2.10
  (p31) and supporting tables 2.2-2.9 (p25)
• Made operational in Banks2t10-SSQ.xls
• Spreadsheet ok for simple, often unrealistic
  systems but cannot easily model complex ones
  need software that supports greater capability
• See Banks et al, Chapter 4 for survey

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Interlude 1 Time out to learn GPSS

• Introduction to GPSS
• 532-02-IntroToGPSS.ppt
• Banks et al, Section 4.5, p112-117
• see Figure 4.10, p114 for block diagram
• GPSS/H differs
• GPSS-ShortIntro.doc
• See Schriber (1991)
• Reference and Tutorial Manuals of GPSS World
• Run Banks4Example2-1.gps - SSQ compare results
  to usual 7 on pp32-33

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Two Server Queuing System

• If queue before each server then system consists
  of two SSQs unless queue switching is allowed
  need to specify logic and probability of
  switching
• For single queue and two servers need to specify
  which server is used when system is empty and a
  new arrival occurs
• See Abel Baker Call Center system in Banks et al,
  Example 2.2 (p35-39)
• Run Banks4Example2-2.gps Abel-Baker Call Center
  compare Caller Delay to p38

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Assignment

• Abel-Baker do the following exercises using GPSS
  examples will be considered in a laboratory
  session
• Make 10 runs with 100 calls and 10 runs with 400
  calls and for each run determine the 7 output
  measures on pp30-33 - Measures 3 and 4 should be
  calculated for Able and Baker individually -
  record results in Excel and use two population
  tests on each measure to see if there is a
  difference (t-test for averages and z-test for
  proportions)
• Investigate the difference between random
  assignment of calls if both are idle as compared
  to always having Abel take the call two
  populations, sample 10 replications of 400
  callers each and test differences

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Extra Credit Assignment(could be used for DESS
project with sufficient enhancements)

• ECA 1 Add Charlie, a third call taker to the
  Abel-Baker Call Center. Charlie has a service
  distribution one minute longer than Baker at each
  of the four probabilities. Investigate the
  difference between a random and hierarchical call
  assignment.
• ECA 2 Investigate to what extent Java has built
  in classes/class libraries for list processing
  with which queues and event lists could be
  implemented. Use these with the code in Section
  4.4 to create a running simulation of the grocery
  checkout counter.

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Interlude 2 Statistical Testing

• Single model tests and confidence intervals for
• Mean t-test (includes test for the mean of
  differences in paired samples from two
  populations)
• Variance c2-test
• Proportion z-test
• Distributions c2-test
• Two models tests for differences in
• Means paired and unpaired t-test
• Variances F-test
• Proportions z-test

• More than two models
• Means ANOVA
• Proportions c2-test
• See
• TestingHypotheses.doc,
• StatisticalTestingInExcel.xls
• SPSS (ASM Computer Lab)
• Box, Hunter, and Hunter (1978)
• All except paired sample tests assume independent
  sample points

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Interlude 3 Excel

• See Liengme (2003), ExcelTutorial.doc
• For next assignments review/learn
• rand() for uniform random number in (0,1) in
  formulas
• vlookup() function for selecting event
• random number with given statistical distribution
  using Analysis ToolPak Random Number Generation
  procedure (Excel -gt Tools -gt Data Analysis -gt
  Random Number Generation)

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How Various Models are Studied
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Monte Carlo Simulation

• Although all stochastic simulations are Monte
  Carlo simulations, the term is often reserved for
  static (a single event) system
• Parameters are varied randomly
• Spreadsheet implementation often successful
• Examples
• Company profits next quarter w/ interest rates,
  demand, supply prices as parameters
• Success of venture w/ sales, degree of
  technological success, feature implementation as
  parameters
• Measures of systems w/ no analytic description
• Spreadsheet example MonteCarlo-NewFab.xls
• Multiple samples of single population usually
  show results as confidence intervals

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Assignment

• Elevator Banks Exercise 2.8 this may be easier
  to do by hand rather than programming all
  formulas into a spreadsheet can use Excel for
  random numbers generation and calculation (use
  vlookup() function as in Banks2t10-SSQ.xls)

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Newsboy Problem

• Order once for a given selling period
• Examples
• Perishable items (e.g., food, newspapers)
• Spare parts while factory setup exists
• Seasonable items
• DV Profit Revenue from Sales
• - Cost of Goods
• - Excess Demand Lost Sales
• Revenue from Salvage
• Stochastic demand, type of sales situation
• See Banks et al, Example 2.3, pp40-43

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Assignment

• Mothers Day Cards Banks Exercise 11.10
• For now, develop the simulation only the
  expected total profit with an estimated error
  will be considered later
• This may best be done with Excel

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How Various Models are Studied
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Inventory Systems

• Static one order for a single selling period
  called newsboy problem stochastic demand
• Dynamic
• Stocking for extended selling period
  stochastic demand
• Reorders can be periodic or at random times
• Reorders can be specified amount or enough to
  achieve a given inventory level (warehouse
  capacity?)
• Backorders may or may not be allowed if not
  sales are lost or reorder costs are at retail
• Usual DV is total cost or profit over given time
  for long time periods use discounted cash flow

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(M, N) Inventory System

• Reorders occur at a given intervals N units long
  lead time may be zero or greater
• Reorders are enough to bring inventory level up
  to M units after backorders satisfied
• Events
• Demand for items from inventory
• Review of inventory position
• Order and receipt of order from supplier
• Stochastic demand, lead time
• See Banks et al, Example 2.4, in
• Banks4Exmpl2-4Inv.gps

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Assignment

• Inventory Policy Banks Exercise 11.6a
• For now just create the simulation and make the
  four required replications.
• Banks4Example2-4Inventory.gps implements an (M,
  N) inventory model similar to that described in
  Example 2.4 starting on page 44. Start with this
  program and modify it to
• (1) add a reorder point as required by Exercise
  11.6 and (2) code/procedures to account for
  costs as specified in Exercise 11.6.
• This problem will be considered in a computer
  laboratory session.

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Discrete Event Simulation Systems

• Creation of simulation table, clock, list (queue)
  processing, and output measures has long been
  automated in simulation software
• See Banks et al, Chapters 3 and 4, for the
  principles behind such software and current
  implementation
• Section 4.4 provides some Java classes

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DESS Implementation

• Based on classifying activities into
• B types (bound to occur) and
• C types (will occur based on conditions)
• FEL (future event list) whenever one or more
  events are to occur
• Add them and their times to the FEL
• Sort all events in the FEL by their times in
  increasing order
• Three phases in each cycle
• Phase A remove the next event(s) to occur from
  the FEL and set the simulation clock to the time
  of its/their occurrence
• Phase B execute all B type events (may change
  system state)
• Phase C execute all C type events if their
  conditions are true may need to recycle through
  Phase B and C
• FEL and general list processing is hard to
  implement in a spreadsheet use special purpose
  software