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 (=1/20=0.05),and 0.1 orders are fulfilled per day(=1/10=0.1).Thus, the occupation rate of this system =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: 0.52 /(10.5)= 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 8 working days to design a hardware and The company receives orders for designing a new circuit every 40 working days on average. What is then the average amount of time an order takes to be fulfilled (W)? to answer complete the following equations.

........... =

........... =

........... =

........... = Lq

........... = Wq

........... = W