The purpose of this homework is to run a simulation of different queuing policies, and observe their impact on average waiting time. Imagine that we have five interchangeable service stations (airline check-in counters; store check-out counters; DMV service windows; immigration posts in an international airport; etc). Arriving passengers (or clients or citizens or visitors) are lined up in FIFO queues, and you have to decide how to organize these queues and associated queuing policies:

i) round robin (1, 2, 3, 4, 5, 1, 2, 3, 4, 5, 1, 2, ...).

ii) arriving passenger is placed in a shortest queue.

Inputs to the simulation:

The duration of the simulation measured in minutes (D: make it arbitrarily long, do not worry about it being or not being realistic). The average arrival rate measured in minutes (A: arrivals are random, but on average there is one new passenger every A minutes), The average service rate measured in minutes (S: service rates are random, but on average they need about S minutes of service). For the sake of this study, make sure to crowd the system, by choosing S >> 5*A, without causing an overflow of your queues. Also choose D to be long enough to get rid of any transitory effects.

Outputs of the Simulations for queuing policy:

The duration of the simulation (which may be longer than the input parameter, as when check-in closes, there may be passengers in the waiting queues and service stations). The maximum length of the queue for each queue. The average and maximum waiting time for each queue. The rate of occupancy of each service station (percentage of time each station was busy). If you want: show the real-time evolution of the queues during the run-time simulation.