1) A “server” links county roads and interstates which can hold 20 vehicles. During peak hours, the vehicles can enter interstate at 1 vehicle every 15 seconds. Vehicles arrive at “server” at 1 vehicle every 20 seconds. Assume that this “server” is an M/M/1 server system, calculate:
a) The probability of having 6 or more vehicles on the server.
b) Percent of time “server” is full and empty.
c) Expected number of vehicles on “server” in peak hour.
2) (Continue from Problem 1) Because the entering of vehicles from the “server” disturbing the flow on freeway and cause enormous delays on freeway, “server” metering is implemented to control the rate of vehicles entering into the interstate. By installing a signal timing device, the vehicle entering rate is controlled at 1 per 12 seconds constantly.
Assume that this “server” is not capacitated, i.e. there is no limit on how many vehicles can wait on the “server”, simulate the server system operation in one peak hour and determine
a) Total time of vehicles spend in the server system,
b) Average time of each vehicle spend in the server system.