TUTORIAL 4

  1. The time required for the transmission of a message in minutes is samples electronically at a communications centre. The last 50 values in the sample are as follows:

7.9364.6122.2074.2785.1324.5995.2242.0031.8572.696

5.2597.5633.9376.9085.0026.2122.7597.1726.5133.326

8.7614.5026.1882.5665.5153.7853.7424.6824.3465.359

3.5355.0614.6295.2986.4923.5024.2663.1291.2983.454

5.2896.8053.8273.9122.9694.6465.9633.8294.4044.924

How are the transmission times distributed? Develop and test an appropriate model.

  1. The time spent in minutes by a customer in a bus stop awaiting to board a bus is

1.0710.6911.8112.8113.757.1916.2512.326.7213.926.626.10

20.219.5814.1311.273.0012.538.0114.467.2814.127.599.33

11.1610.3811.133.564.5717.8511.9716.965.0413.776.6014.34

13.888.9312.729.000.8913.3910.3720.539.923.49

Using appropriate methods, determine how time is distributed.

TUTORIAL 5

  1. Develop a simulation model in ARENA for a Bank with a single teller and customers arriving with an interarrival time uniformly distributed between 1 and 8 minutes. The service time of the teller is uniformly distributed between 1 and 6 minutes. Simulate for 500, 1000, 1500, 2500, and 5000 customers and note down the performance measures. Assume that the server works for 8 hours a day and 6 days a week. Take 5 replications.
  2. What is the effect on the above model if the interarrival time changes to U (1, 10) and service time changes to U (1, 8)? Note the performance measures with the same run parameters.
  3. Analyse the effect on the system in Question 1 if the management decides to install two tellers at a time and

a)Individual queues for each teller

b)Single queue for both the tellers

Based on the simulation results, which type of queue gives better performance?

  1. Parts arrive at two machine system according to an exponential interarrival time distribution with a mean 20 minutes. Upon arrival, the parts are sent to machine 1 and processed. The processing time distribution is TRIA (4.5, 9.3, 11.0) minutes. The parts are then processed at machine 2 with a processing time distribution as TRIA (16.4, 19.1, 21.8) minutes. The parts from machine 2 are directed back to machine 1 to be processed a second time (same processing time). The completed parts then exit the system. Run the simulation for a single replication of 20,000 minutes to observe the average number in the machine queues and the average part cycle time.

TUTORIAL 6

  1. Parts arrive at a single machine system according to an exponential interarrival distribution with mean 20 minutes; the first part arrives at time 0. Upon arrival the parts are processed at the machine. The processing time distribution is TRIA (11, 16, 18) minutes. The parts are inspected and about 25% are sent back to the same machine to be reprocessed (same processing time).

Run the simulation for 20,000 minutes to observe the average and maximum number of times a part is processed, the average number of parts in the machine queue and the average part cycle time (time from a part’s entry to the system to its exit after however many passes through the machine system are required).

  1. Travellers arrive at the main entrance door of an airline terminal according to an exponential interarrival time distribution with mean 1.6 minutes, with the first arrival at time 0. The travel time from the entrance to the check-in is distributed uniformly between 2 and 3 minutes. At the check-in-counter, travellers wait in a single line until one of the five agents is available to serve them. The check-in time in minutes follows a Weibull distribution with parameters β = 7.76 and α = 3.91. Upon completion of their check-in, they are free to travel to their gates.

(a)Create a simulation model, with animation (including the travel time from entrance to check-in) of this system.

(b)Run the simulation for 16 hours to determine the average time in system, number of passengers completing check-in and the average length of the check-in queue.

  1. Using the input analyzer, open a new window. Generate a new data file (use file – Data file- Generate new) containing 50 points for an erlang distribution with parameters: Exp. mean 12, k equal to 3 and offset equal to 5. Once you have the data file, perform a Fit All function to find the best fit from among the available distributions. Repeat the process for 500, 5000 and 25000 data points, using the same erlang parameters. Compare the results of the Fit All for the four different sample sizes.