You arrive at a movie theater only to notice that there's only one person selling tickets. Fortunately you have packed your jacket with enough candy to choke a horse and filled your camel back with "soda." You now must rely on your cunning knowledge of queuing theory to determine your chances of making the show before the ever impressive preview- mercials. As you approached, you noticed the average number of customers in line (waiting to be served) was 8.1 people, yet every once in a while (15% of the time you determine) there is nobody in line or being served. People are clearly arriving randomly, but on average every 35 seconds.
Once that last fact was clear you close your eyes (for effect) and start writing on the sidewalk with your chalk you take everywhere the following:
a. The utilization of the server is ___________%
b. The average service time is ___________ seconds.
c. The amount of time I can expect to wait in line before being served is ________ seconds.
d. The total amount of time I can expect to wait to get through both the line and service is ________ seconds.
a. Utilization = % of time server is busy
= 100% - 15% (time when nobody is waiting in line or being ...
Solution to a classic M/M/1 queuing model