# 1: B asic S imu lati on Modeling

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1 Network Simulation Chapter 1: Basic Simulation Modeling Prof. Dr. Jürgen Jasperneite 1 Contents The Nature of Simulation Systems, Models and Simulation Discrete Event Simulation Simulation of a Single-Server Queueing System Steps in a Simulation Study 2 Prof. Dr. Jürgen Jasperneite 1

2 Goal of this chapter Understand simulation as a tool to investigate something What is something? > Notion of a system and its model Different system/model types require different simulation methods 3 Contents The Nature of Simulation Systems, Models and Simulation Discrete Event Simulation Simulation of a Single-Server Queueing System Steps in a Simulation Study 4 Prof. Dr. Jürgen Jasperneite 2

3 The Nature of Simulation Simulation: Imitate the operations of a facility or process, usually via computer What s being simulated is the system To study system, often make assumptions/approximations, both logical and mathematical, about how it works These assumptions form a model of the system If model structure is simple enough, could use mathematical methods to get exact information on questions of interest analytical solution 5 The Nature of Simulation (cont d) But most complex systems require models that are also complex (to be valid) Must be studied via simulation evaluate model numerically and collect data to estimate model characteristics Example: Manufacturing company considering extending its plant Build it and see if it works out? Simulate current, expanded operations could also investigate many other issues along the way, quickly and cheaply 6 Prof. Dr. Jürgen Jasperneite 3

4 The Nature of Simulation (cont d) 1: Basic Simulation Modeling 7 Some (not all) application areas Designing and analyzing manufacturing systems Evaluating military weapons systems or their logistics requirements Determining hardware and software requirements for a computer system Designing and operating transportation systems such as airports, freeways, ports, and subways Evaluating designs for service organizations such as call centers, fast-food restaurants, hospitals, and post offices Reengineering of business processes Determining ordering policies for an inventory system Analyzing financial or economic systems Determining hardware requirements or protocols for communications networks Field effect Transistor 1: Basic Simulation Modeling 8 Prof. Dr. Jürgen Jasperneite 4

5 Simulation of a filter 1: Basic Simulation Modeling 9 Mechatronic Systems 1: Basic Simulation Modeling 10 Prof. Dr. Jürgen Jasperneite 5

6 Network Simulation 1: Basic Simulation Modeling 11 Contents 1: Basic Simulation Modeling The Nature of Simulation Systems, Models and Simulation Discrete Event Simulation Simulation of a Single-Server Queueing System Steps in a Simulation Study 12 Prof. Dr. Jürgen Jasperneite 6

7 SYSTEMS, MODELS, AND SIMULATION System: A collection of entities (people, parts, messages, machines, servers, ) that act and interact together toward some end (Schmidt and Taylor, 1970) In practice, depends on objectives of study Might limit the boundaries (physical and logical) of the system Judgment call: level of detail (e.g., what is an entity?) Usually assume a time element dynamic system State of a system: Collection of variables and their values necessary to describe the system at that time Might depend on desired objectives, output performance measures Bank model: Could include number of busy tellers, time of arrival of each customer, etc. CPU scheduling: length of the job queue. 13 SYSTEMS, MODELS, AND SIMULATION Types of systems Discrete State variables change instantaneously at separated points in time E.g. Bank model: State changes occur only when a customer arrives or departs Continuous State variables change continuously as a function of time E.g. Airplane flight: State variables like position, velocity change continuously Many systems are partly discrete, partly continuous 14 Prof. Dr. Jürgen Jasperneite 7

8 SYSTEMS, MODELS, AND SIMULATION Ways to study a system 15 SYSTEMS, MODELS, AND SIMULATION Classification of simulation models Static vs. dynamic Deterministic vs. probabilistic (stochastic) Continuous vs. discrete Most operational models are dynamic, stochastic, and discrete will be called discrete-event simulation models. 16 Prof. Dr. Jürgen Jasperneite 8

9 Contents The Nature of Simulation Systems, Models and Simulation Discrete Event Simulation Simulation of a Single-Server Queueing System Steps in a Simulation Study 20 DISCRETE-EVENT SIMULATION Discrete- event simulation: Modeling of a system as it evolves over time by a representation where the state variables change instantaneously at separated points in time More precisely, state can change at only a countable number of points in time These points in time are when events occur Event: Instantaneous occurrence that may change the state of the system e.g. CPU- Scheduling: arrival of a job, beginning of a new execution, departure of a job Can in principle be done by hand, but usually done on computer Later on we will carry out a small hand simulation. 21 Prof. Dr. Jürgen Jasperneite 9

10 Time-Advance Mechanisms Simulation clock: Variable that keeps the current value of (simulated) time in the model Must decide on, be consistent about, time units Usually no relation between simulated time and (real) time needed to run a model on a computer Two approaches for time advance Next-event time advance (usually used) described in detail below Fixed-increment time advance (seldom used) Generally introduces some amount of modeling error in terms of when events should occur vs. do occur Forces a tradeoff between model accuracy and computational efficiency 22 Time-Advance Mechanisms (cont d.) More on next-event time advance Initialize simulation clock to 0 Determine times of occurrence of future events event list Clock advances to next (most imminent) event, which is executed Event execution may involve updating event list Continue until stopping rule is satisfied (must be explicitly stated) Clock jumps from one event time to the next, and doesn t exist for times between successive events periods of inactivity are ignored 23 Prof. Dr. Jürgen Jasperneite 10

11 Time-Advance Mechanisms (cont d.) Next-event time advance for a single-server queue t i = time of arrival of i-th customer (t 0 = 0) A i = t i t i-1 = interarrival time between (i-1)st and i- th customers (usually assumed to be a random variable from some probability distribution) S i = service-time requirement of i-th customer (another random variable) D i = delay in queue of i-th customer C i = t i + D i + S i = time i-th customer completes service and departs e j = time of occurrence of the j-th event (of any type), j = 1, 2, 3, 24 Components and Organization of a Discrete-Event Simulation Model Each simulation model must be customized to target system But there are several common components, general organization System state variables to describe state Simulation clock current value of simulated time Event list times of future events (as needed) Statistical counters to accumulate quantities for output Initialization routine initialize model at time 0 Timing routine determine next event time, type; advance clock Event routines carry out logic for each event type Library routines utility routines to generate random variates, etc. Report generator to summarize, report results at end Main program ties routines together, executes them in right order 26 Prof. Dr. Jürgen Jasperneite 11

12 Components and Organization of a Discrete-Event Simulation Model (cont d.) A B 27 Components and Organization of a Discrete-Event Simulation Model (cont d.) A B 28 Prof. Dr. Jürgen Jasperneite 12

13 Components and Organization of a Discrete-Event Simulation Model (cont d.) More on entities Objects that compose a simulation model Usually include customers, parts, messages, etc. may include resources like servers Characterized by data values called attributes For each entity resident in the model there s a record (row) in a list, with the attributes being the columns Approaches to modeling Event-scheduling as described above, coded in general-purpose language Process focuses on entities and their experience, usually requires special-purpose simulation software 29 # events = 10 IA time = constant(2) Service time = constant(1) 1: Basic Simulation Modeling 30 Prof. Dr. Jürgen Jasperneite 13

14 Contents The Nature of Simulation Systems, Models and Simulation Discrete Event Simulation Simulation of a Single-Server Queueing System Steps in a Simulation Study 31 Problem statement Perform a performance evaluation of a checkout counter in a store Objectives: Determine how long do customers have to wait? how many customers are in line? how much of the time is the cashier busy? 32 Prof. Dr. Jürgen Jasperneite 14

15 A simple model Map the real-world system parts to abstract representations System New customers Queue Customer Server Customers leave system 33 Model A simple model - Algorithm 1: Basic Simulation Modeling How does such a checkout queue work? Server is idle (no customer present) If customer arrives, customer is serviced immediately, until completion Server is then busy until customer is completely served Server is busy If customer arrives, the customer joins the end of the queue When server becomes idle (a customer has been finished), server checks the queue If one or more customer waits in queue, the first customer leaves the queue and is now serviced If no customer in queue, the server becomes idle 34 Prof. Dr. Jürgen Jasperneite 15

16 Simulation of a Single-Server Queueing System Recall single-server queueing model Assume interarrival times are independent and identically distributed (IID) random variables Assume service times are IID, and are independent of interarrival times Queue discipline is FIFO Start empty and idle at time 0 First customer arrives after an interarrival time, not at time 0 Stopping rule: When n-th customer has completed delay in queue (i.e., enters service) n will be specified as input 35 Problem Statement 36 Quantities to be estimated Expected average delay in queue ˆ( d n) (excluding service time) of the n customers completing their delays Why expected? Expected average number of customers in queue ˆ( q n) (excluding any in service) A continuous-time average Area under Q(t) = queue length at time t, divided by T(n) = time simulation ends Expected utilization (proportion of time busy) of the server ˆ( u n) Another continuous-time average Area under B(t) = server-busy function (1 if busy, 0 if idle at time t), divided by T(n) Many others are possible (maxima, minima, time or number in system, proportions, quantiles, variances ) Important: Discrete-time vs. continuous-time statistics Prof. Dr. Jürgen Jasperneite 16

17 Intuitive Explaination Given (for now) interarrival times (all times are in minutes): Given service times: n = 6 delays in queue desired Hand simulation: Display system, state variables, clock, event list, statistical counters all after execution of each event Use above lists of interarrival, service times to drive simulation Stop when number of delays hits n = 6, compute output performance measures 37 Status shown is afterall changes have been made in each case 42 Prof. Dr. Jürgen Jasperneite 17

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24 Final output performance measures: Average delay in queue = 5.7/6 = 0.95 min./customer Time-average number in queue = 9.9/8.6 = 1.15 cust. Server utilization = 7.7/8.6 = 0.90 (dimensionless) 55 Contents The Nature of Simulation Systems, Models and Simulation Discrete Event Simulation Simulation of a Single-Server Queueing System Steps in a Simulation Study 56 Prof. Dr. Jürgen Jasperneite 24

25 Steps in a Simulation Study Formulate problem and plan the study Collect data and define a model Design experiments Conceptual Model valid? Construct a computer program and verify Make pilot runs Programmed Model valid? Yes No No Make productionruns Analyze Output data Document, present, anduse results Advantages, Disadvantages of Simulation Advantages Simulation allows great flexibility in modeling complex systems, so simulation models can be highly valid Easy to compare alternatives Control experimental conditions Can study system with a very long time frame Disadvantages Stochastic simulations produce only estimates with noise Simulation models can be expensive to develop Simulations usually produce large volumes of output need to summarize, statistically analyze appropriately 58 Prof. Dr. Jürgen Jasperneite 25

26 Conclusions for Today You know now What is a system, a model, the state of a system? Different types of systems and models deterministic, stochastic, Continuous time/state, discrete time/state Basic Concepts of Discrete Event Simulation 59 Prof. Dr. Jürgen Jasperneite 26

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