Question 1:

Consider 20 DS0 circuits that are multiplexed onto 3 outgoing circuits. The mean arrival rate at each DS0 circuit is 1 call per hour during the busy hour; calls last, on average, 5 minutes. Assume Poisson arrivals, exponentially distributed call durations, and that customers that attempt a call when all circuits are busy are blocked (ignore call retry). The probability of blocked calls is __________. (Use 2 digits to the right of the decimal point.)(hint: DS0 circuit is essentially traditional wired phone circuit. So, the question essentially means there are 20 incoming phone lines, 3 outgoing phone lines)

Question 2:

Customers arrive at a two-chair shoeshine stand at a rate of 10 customers per hour. The average length of a shoeshine is 5 minutes. There is only one attendant, so that one chair is used as a waiting position. Customers who find both chairs occupied go away. Assume Poisson arrivals and exponential service times. The queuing model that is appropriate here is _______

Question 3:

In question 2, the probability that the waiting chair will be occupied is________ . (Use two digits to the right of the decimal point.)(Hint: first figure out what is the state of the system (a.k.a. the number of the users in the queuing system) when the waiting chair is occupied. Then, you can compute the probability of that state)

Question 4:

In question 2, the mean number of customers served per hour is ________. (Use two digits to the right of the decimal point.) Question 5 Now, let us modify question 2 by assuming there are 2 attendants at the stand. The mean number of customers serviced per hour is . (Use two digits to the right of the decimal point.)

Question 5

Now, let us modify question 2 by assuming there are 2 attendants at the stand. The mean number of customers serviced per hour is .________ (Use two digits to the right of the decimal point.)