SIMULATION

USE WOLFRAM MATHEMATICA

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Question 1 Tshepiso owns a Muffler shop. His mechanic, Samkelo is able to install new mufflers at an average of 3 per hour or about 1 every 20 minutes according to an exponential distribution. The distribution of interarrival times (in minutes) of customers needing this service is assumed to follow a Gamma(a; 8) distribution with a = 3 and B = 9. If a customer arrives while Samkelo is busy, he/she should join the queue. However, if there are already at least 6 customers in the queue, a new customer arrival may decide to or not to join the queue with probability 0.4. But if a customer joins the queue, it is assumed that they will stay in the queue until served. Develop a simulation model for this queuing system. Clearly define any variables that you may use and give corresponding initial values where necessary. Assume that the maximum length of the simulation is 2 000 hours. Run your code and comment on the efficiency of the system. HINT: Modify the queuing system code for M/M/1 model in your study guide to reflect what is in this question. Question 1 Tshepiso owns a Muffler shop. His mechanic, Samkelo is able to install new mufflers at an average of 3 per hour or about 1 every 20 minutes according to an exponential distribution. The distribution of interarrival times (in minutes) of customers needing this service is assumed to follow a Gamma(a; 8) distribution with a = 3 and B = 9. If a customer arrives while Samkelo is busy, he/she should join the queue. However, if there are already at least 6 customers in the queue, a new customer arrival may decide to or not to join the queue with probability 0.4. But if a customer joins the queue, it is assumed that they will stay in the queue until served. Develop a simulation model for this queuing system. Clearly define any variables that you may use and give corresponding initial values where necessary. Assume that the maximum length of the simulation is 2 000 hours. Run your code and comment on the efficiency of the system. HINT: Modify the queuing system code for M/M/1 model in your study guide to reflect what is in this