Customers arrive randomly to an airport shoe-shine stand at a rate of 8 per hour. The average length of a shoe shine is 12 minutes. There are two attendants. Arriving customers who find both chairs occupied by other customers will wait only if NO customers are waiting. Assume that service times are exponentially distributed and that the calling population is infinite. (a) VWhat is the queuing model? (b) To the nearest third decimal place, what is the expected total time in steady state that a customer spends at the stand? O (M/M/2): (GD/2/infinity), 18.333 minutes O (M/G/2): (GD/infinity/infinity), 0.467 hours none of the other choices O (M/M/2) : (GD/3/infinity), O.233 hours

1. The DMV Licensing office has a single line for customers waiting for the next available clerk. There are two clerks who work at the same rate. On average customers arrive every 8 minutes and the average service rate is 5 per hour for each of the two clerks. The arrival rate of customers follows a Poisson distribution, while the service time follows an exponential distribution. a.) What is the service rate? (please include units) b.) What is the arrival rate? (please include units)

Assume trucks arriving for loading/unloading at a truck dock from a single server waiting line. The mean arrival rate is three trucks per hour, and the mean service rate is six trucks per hour. Use the Single Server QueueExcel template to answer the following questions. Do not round intermediate calculations. Round your answers to three decimal places.   What is the probability that the truck dock will be idle?   What is the average number of trucks in the queue?  truck(s) What is the average number of trucks in the system?  truck(s) What is the average time a truck spends in the queue waiting for service?  hour(s) What is the average time a truck spends in the system?  hour(s) What is the probability that an arriving truck will have to wait?   What is the probability that more than two trucks are waiting for service?

Customers in a small retail store arrive at the single cashier on average every 6 minutes. The average service time for the cashier is 5 minutes.Arrivals tend to follow a Poisson distribution, and service times follow anexponential distribution. We need to analyze this waiting-line system. (g) Should the retail store consider creating a second cashier lane?(h) A cash machine manufacturer has offered an advanced system that willreduce service time to 2 minutes per customer. The cost of the newmachine would be the same as opening a second cashier lane, so theowner has decided to buy the new system only if it reduces wait timesover the two-cash option. Evaluate the two options (advanced cash or atwo-cash system) and suggest which option you would choose.