1. WOOD 492 MODELLING FOR DECISION SUPPORT Lecture 27 Simulation

2. Review Simulated a single server queue with Next-event increment method State of the system at each time t – N(t) = number of customers in the queue at time t Random events in the simulation: –Arrival of customers (mean inter arrival times are 1/3 hour) –Serving the customers (mean service times are 1/5 hour) System transition formula: –Arrival: reset N(t) to N(t)+1 –Serve customer: reset N(t) to N(t)-1 Next-event increment has two steps: 1.Advance time to the time of the next event 2.Update N(t) Nov 9, 2012Wood 492 - Saba Vahid2 Example 16

3. Example 17: drive-in restaurant simulation A drive-in restaurant has one queue and two servers for bringing the food to the cars The cars arrive every 1 to 4 minutes according to the probabilities in the table below. CDF (same as F(x)) values are given in the last column. Cars wait for the first server who’s free or has been free the longest The servers have different times for serving cars –Server 1: uniform distribution between 2 to 4 minutes –Server 2: uniform distribution between 3 to 5 minutes Nov 9, 2012Wood 492 - Saba Vahid3

4. Uniform distribution Nov 9, 2012Wood 492 - Saba Vahid4

5. Simulating the drive-in system Use Next-event increment method Assume at t=0 there are 2 cars in line and both servers are busy State of the system = N(t) = number of cars in the line Potential events: –Arrival of cars (arrival) –Car served by server 1 (exit to 1) –Car served by server 2 (exit to 2) System transition formula: –Arrival: N(t)=N(t-1)+1 –Exit to 1 or exit to 2 : N(t)=N(t-1)-1 Simulation clock: moves to the next event time, decided by a random draw and inverse CDF transformation Nov 9, 2012Wood 492 - Saba Vahid5 Example 17

6. Final comments Exam on November 19 th, 9:00 am, same room as usual Grades will be posted at my door about one week later Check the course website for any potential updates Quiz 5 answers posted online Some extra simulation and network problems will be uploaded next week Friday, 16th 10 to 12 office hours room 2026 Nov 9, 2012Wood 492 - Saba Vahid6