An example of a Simulation

1. An example of a Simulation Simulation of a bank: Three tasks or processes: • Customer arrives • Customer served • Customer leaves Customer Leaves Customer Arrives Customer Served UniS - Based on Slides by Micro Analysis & Design

2. An example of a Simulation Let’s describe task 1 Customer Arrives • Arrival rate – rate that customers arrive at bank 1 customer every 3 minutes or so i.e. Inter-arrival rate IAT = 3 • Time period customers can arrive Bank Hours: 9 to 5 Customer Arrives UniS - Based on Slides by Micro Analysis & Design

3. An example of a Simulation Task 2 Customer Served • Time to serve a customer Approx 6 minutes per customer Select sample from for example a normal distribution mean = 6 and standard deviation = 2 Choice of distribution ? Customer Served UniS - Based on Slides by Micro Analysis & Design

4. An example of a Simulation Task 3 Customer Leaves • Record the time customer leaves • No further interest in customer Customer Leaves UniS - Based on Slides by Micro Analysis & Design

5. An example of a Simulation What else affects this flow of customers? Number of bank staff on duty Lunchtime crowd Customer Arrives Customer Served Customer Leaves UniS - Based on Slides by Micro Analysis & Design

6. An example of a Simulation What information would be useful to collect? • Employee utilisation • Waiting times • Length of queue Is there a way to get this information? Customer Leaves Customer Arrives Customer Served UniS - Based on Slides by Micro Analysis & Design

7. An example of a Simulation To performing this analysis without micro-simulation: • Only use mean times or averages rates or • Run the experiment in real life. • Using micro-simulation every individual is computed taking account of stochastic behaviour – hence more realistic analysis possible - e.g maximum delay not obtained from an average Customer Leaves Customer Arrives Customer Served UniS - Based on Slides by Micro Analysis & Design

8. Essentials of Discrete-Event Micro-Simulation • Tasks • Events – start and end of tasks • Entities • Entity flow • Resources • Queues • Clock • Scenario events UniS - Based on Slides by Micro Analysis & Design

9. Tasks or processes • The building block of any discrete-event simulation • A task represents a single step in the process that makes up the discrete event simulation • A task may require a certain amount of time in order to execute • Tasks & Events have three main parts: • Pre-condition or Release condition • Start condition or Beginning effect • End condition or Ending effect • Events trigger subsequent actions UniS - Based on Slides by Micro Analysis & Design

10. Conditions • Release condition • The conditions that need to be satisfied so this task may begin • Beginning effect • Things that take place when this task begins execution • Ending effect • Things that take place this task completes execution • You are responsible for writing code to achieve these logical conditions UniS - Based on Slides by Micro Analysis & Design

11. Task Flow • For every discrete-event simulation, there is a basic entity flow • Here is an example of the flow of a bank: • When one task completes the following can happen to the entity at same simulation time: • Nothing • Join a queue • Another activity starts • Several activities start simultaneously Customer Leaves Customer Arrives Customer Served UniS - Based on Slides by Micro Analysis & Design

12. Resources • In any process some tasks require a resource to be available in order to begin execution • Example: A task may require the availability of a trained operator in order for that task to begin • Many processes are constrained by limited resources • Without resources, steps in the process may be held up until those resources are available • Without resources, the flow of the entities might change UniS - Based on Slides by Micro Analysis & Design

13. Entities • Entities flow through a simulation and are involved in the execution of any task • Examples of entities: • Customers in a bank • Cars going through a toll both • Parts being manufactured • When an entity arrives at a task the system: • Checks the release condition and if accepted • Executes the beginning effect • Waits the appropriate amount of time (simulation time or clock time) • Executes the ending effect UniS - Based on Slides by Micro Analysis & Design

14. Queues • What happens when the release condition of a task is not met (such as when all bank staff are busy)? • The entity must wait in a queue until the release condition is met • Sometimes, the behavior of the queue is important • FIFO (e.g. queue for bank staff) • LIFO (e.g. stocked shelves) • Sorted based on priority (e.g. A&E Department) Customer Served Queue UniS - Based on Slides by Micro Analysis & Design

15. The Simulation Clock • Since we are interested in time based behaviour, a clock is needed to keep the system in synchronism • As events in your simulation occur, the simulation clock will advance based upon how long each task or process takes – not fixed small steps as in continuous dynamic systems UniS - Based on Slides by Micro Analysis & Design

16. How a Simulation is Executed • As a simulation executes, all scheduled events are kept in an event queue or time line • The simulation begins by taking the first event that is scheduled to occur from the event queue (e.g. start the first task) • That event may place other events later in the event queue, ordered of time • When that event is completed, the simulation takes the next event from the queue, updates the clock, and processes that event UniS - Based on Slides by Micro Analysis & Design

17. Running a Simulation Let’s step through a simulation of a bank. Using the task rules we defined for customer served • Here are other rules to follow • Bank is open for 8 hours (480 minutes) • Customers arrive about every 3 minutes • It takes around 6 minutes to serve a customer • We have 2 bank staff on duty UniS - Based on Slides by Micro Analysis & Design

18. Running a Simulation Using this diagram below let’s step through this simulation Customer Served Customer Leaves Customer Arrives Queue TimeTaskStaffPeople Waiting 0Customer Arrives 2 0 UniS - Based on Slides by Micro Analysis & Design

19. Simulation What else affects this flow of customers? • Number of bank staff on duty • Lunchtime crowd Customer Arrives Customer Served Customer Leaves UniS - Based on Slides by Micro Analysis & Design

20. Scenario Events • What happens if we want to: • Model customers arriving faster at lunchtime? • Put another bank teller on duty at lunchtime? • Events that don’t necessarily fall into any one task can be defined as a scenario events • Scenario events are defined by • The time when the scenario event occurs • What happens UniS - Based on Slides by Micro Analysis & Design