1. Consider a single-server queue operating on discrete time slots, with Bernoulli arrivals and departures in each time slot. The departure rate is = 0.75. Plot the expected delay of a job as a function of the arrival rate . You have to run the simulations long enough, for example at least for 106 time slots. (Hints: use Littles law to calculate the expected delay, but you have to simulate the queue dynamics to get the expected queue length first.) Note: Choose one programming language to do the simulation from C/C++, Matlab, Python, and Java. Report (in a format of one single PDF) should include the plot, and simulation code and annotations.

There are some example but u have to convert those into a code

= 0.75

Expected Delay, D = 1 (1 )

Where = (1 ) (1 ) For = 0.75, as < ,

assuming = 0.35 = 0.35(10.75) 0.75(10.35)

= 0.35 (0.25) 0.75(0.65) = 0.088/0.488

P = 0.180

Therefore, Expected Delay, D = 1 0.35 0.180 (10.180)