A. Northbound trucks leaving Helmand Province with USMC communications equipment must go through a washing process before getting underway, so as to prevent Tajikistan from getting "too sandy."  Trucks are ready to wash at a sustained rate of one every 2 hours (exponentially distributed), and a washdown takes 4 hours (exponentially distributed).  There are 10 wash stations that operate in parallel, with 10 wash technicians (hosers) manning the wash stations.  Whenever all 10 wash stations are simultaneously idle, the hosers smoke a communal hookah together until the next truck arrives for a wash.

1. This is a X/Y/Z/W kind of queue (give X, Y, Z, and W).

2. Give rho for this system.

3. Is this queue stable?

4. On average, how long do the hosers smoke the hookah?

5. On average, how many hookah smoking breaks to the hosers enjoy per day?

6. On average, how long is the work period between smokes?

7. On average, how many trucks get washed between smokes?

C. (Use QTS)  Summon up the model SENSITIVITY OF M/G/1 TO THE SERVICE-TIME COEFFICIENT OF VARIATION in QTS.  Recall that CoV = stddev(service time)/mean(service time), the ratio of the service time's standard deviation to its mean.  Make rho = .9, and run the model.

1. For CoV = 1.0, L should be 9.0.  Why does this make sense?

2. For CoV = 0, how does this queue operate?

3. For CoV's other than 1.0, does Little's Law apply?  If so, why isn't the L = 9.0 for all values of CoV?

4. Calculate L-Lq for several values of CoV.  Comment.