Exercise 2 (5 Marks) A company designs customized clectronie hardware for a range of customers in the high-tech electronics industry. The company receives orders for designing a new circuit every 20 working days on average. It takes a team of engineers on average 10 working days to design hardware This problem can be mapped to an M/M/I model assuming that the arrival of designs follows a Poisson process that the distribution of times for designing a circuit follows an exponential distribution and that new design requests are handled. on a FIFO manner. Note that even though the team includes several people, they act as a monolithis entity and therefore it should be treated as a single server. We will hereby take the working day as a time unit. On average, 0,05 orders are received per day 1/20 005 and 0.1 orders are fulfilled per dayu-1/100.1). Thus, the occupation rate of this system -0.05 0.1 05. Using the formulas for M/M/I models, we can deduce that the average length of the queue Leis 0.5 1-0.5 0.5 orders. From there we can conclude that the average time an order spends on the queue is Wq -0.5/0.05-10 days. Thus, it takes on average order W-10.1 0.05-20 working days for an order to be fulfilled. Question Consider now the case where the engineering team in the previous example takes 5 working days to design a hardware and The company receives orders for designing a new circuit every 8 working days on average. What is then the average amount of time an order takes to be fulnlled (W)? Exercise 2 (5 Marks) A company designs customized electronic hardware for a range of customers in the high-tech electronics industry. The company receives orders for designing a new circuit every 20 working days on average. It takes a team of engineers on average 10 working days to design hardware. This problem can be mapped to an M/M/1 model assuming that the arrival of designs follows a Poisson process that the distribution of times for designing a circuit follows an exponential distribution and that new design requests are handled. on a FIFO manner. Note that even though the team includes several people, they act as a monolithic entity and therefore it should be treated as a single server. We will hereby take the working day as a time unit. On average, 0.05 orders are received per day (n=1/20=0.05), and 0.1 orders are fulfilled per day(u=1/10=0.1). Thus, the occupation rate of this system p=0.05/0.1=0.5. Using the formulas for M/M/1 models, we can deduce that the average length of the queue Lq is: 0.5/(1-0.5-0.5 orders. From there we can conclude that the average time an order spends on the queue is Wq -0.5/0.05=10 days. Thus, it takes on average order W =1/(0.1- 0.05)=20 working days for an order to be fulfilled. Question Consider now the case where the engineering team in the previous example takes 5 working days to design a hardware and The company receives orders for designing a new circuit every 8 working days on average. What is then the average amount of time an order takes to be fulfilled (W)