The management of the EE-Cole-Eye Sandwich Truck could not find a fast enough sandwich maker, so they changed their business strategy: they found a vacant store they could afford and opened the EE-Cole-Eye Sandwich Shop. Unfortunately, they could only afford a very small space: there was only room for 4 people to wait in line in the shop. Figure 3 shows the transition graph for the number of customers in the shop. The inter-arrival time and the sandwich-making time are exponentially distributed.

Let pi_n(n = 0; 1; 2; 3; 4) be the steady state probability that there are n customers in the shop. Solve the set of equations to determinepi_n. Assume lambda = 1/30and mu = 1/29(Enter 4 decimal places).

What isPi₀?

What is Pi_1?

What is Pi₂?

What is Pi₃?

What is Pi₄?

They replaced the original sandwich maker with a new sandwich maker whose average sandwich-making time was 25 seconds (The original sandwich maker took 29 seconds on average to make a sandwich. What is the average number of customer in the shop at any given time? (Enter 3 decimal places)

When there are 4 people in the shop, no new customer can enter. Assume that customers that arrive when the shop is full go away, without waiting outside for someone to leave the shop. Those people represent lost sales.

What is the fraction of customers that do not get their sandwiches? (Enter as a decimal, round to 3 decimal places)