Case Study: Optimizing Check-Out Processes for a Large Retailer Introduction: This case study analyzes the check-out processes at a large retall store with the objective of determining the most efficient queue system. The two queue models under consideration are: 1. A single queue system where the first person in line goes to the first avallable cashier (e.g., Marshalls) and that has five cashiers available; 2. Five separate queues with one cashier assigned to each line (e.g., Waimart). Store Background: The store has a total of five cashlers on duty. The rate of customer arrivals for check-out is 990 people per hour, while each cashler can serve an average of 200 people per hour. Both interarival times and service times are assumed to follow an exponential distribution. Inputs: Derintions of terms: lambde tambda w arrival rate mei mu = service rate 5. number of servers to = average number in the queue L. average number in the system Wq: average wat in the queve lambda/mu W = average wait in the system P(0) =itrobability of tere customers in the sintem P(Selar) = probability that an arriving cwatomer has to wait Ourputs: 1. At first, let us assume a system with one single line leading to the five cashiers. [4) (10 Points) What type of queue is this? M/M/1 M/M/5 M/G/1 M/G/5 2. What is the expected number of people in the system (including people waiting in (10 Points) line and being served)? The value must be a number 3. What is the expected time people need to wait between the time they join the line (10 and the time they leave the store in minutes? Points) The value must be a number 4. What proportion of the time are the cashiers idle? (provide your answer as a number between 0 and 1 ) Case Study: Optimizing Check-Out Processes for a Large Retailer Introduction: This case study analyzes the check-out processes at a large retall store with the objective of determining the most efficient queue system. The two queue models under consideration are: 1. A single queue system where the first person in line goes to the first avallable cashier (e.g., Marshalls) and that has five cashiers available; 2. Five separate queues with one cashier assigned to each line (e.g., Waimart). Store Background: The store has a total of five cashlers on duty. The rate of customer arrivals for check-out is 990 people per hour, while each cashler can serve an average of 200 people per hour. Both interarival times and service times are assumed to follow an exponential distribution. Inputs: Derintions of terms: lambde tambda w arrival rate mei mu = service rate 5. number of servers to = average number in the queue L. average number in the system Wq: average wat in the queve lambda/mu W = average wait in the system P(0) =itrobability of tere customers in the sintem P(Selar) = probability that an arriving cwatomer has to wait Ourputs: 1. At first, let us assume a system with one single line leading to the five cashiers. [4) (10 Points) What type of queue is this? M/M/1 M/M/5 M/G/1 M/G/5 2. What is the expected number of people in the system (including people waiting in (10 Points) line and being served)? The value must be a number 3. What is the expected time people need to wait between the time they join the line (10 and the time they leave the store in minutes? Points) The value must be a number 4. What proportion of the time are the cashiers idle? (provide your answer as a number between 0 and 1 )