A crafter has a booth at the Cary Spring Daze Craft Show. She figures that she will spend an exponentially distributed amount of time with a mean of about 5 minutes talking with each customer who visits the booth. Based on her experience, the time between customers coming to the booth is also exponentially distributed with a mean of about 5 minutes. About half the time, an arriving customer is alone but the other half of the time they are accompanied by another customer. Assume that a pair of customers arriving together will be served individually by the crafter. Also, when the first of a pair has been served, they will wait outside the booth for their partner. Based upon experience the crafter believes that any arriving customers who find 4 customers already in the booth will leave without waiting. Assume that if a pair of customers arrives and there are three customers in the booth, the pair will balk.

a. Assuming the crafter is interested in learning such things as the expected number of customers in the booth and the rate at which customers balk, develop a model for this system. Be sure to define the states of the system, list the system events and give the state transition rate diagram.

b. Solve for the steady state probabilities.

c. What is the throughput rate of the system in steady state? Throughput rate in this case is the rate at which customers leave having talked to the crafter.

d. What is the expected time a customer will spend waiting in queue to talk to the crafter?