Assignment 5: Simulate a store with queues

Grade:	Only compulsory for grade 5.
Preparations:	All net lessons and assignment 4.
Examination:	Mail the solution no later than December 14, 2020.

In this assignment you will write a program that simulates a store, with one or more queues/cashiers: Blue squares are symbolizes cashiers, dark read circles customers being processed and light red circles customers in queue.

You should reuse the queue data structures from Assignment 4.

The aim is to do simulations and make estimates of

• Average waiting time (Time from arriving to queue until leaving the store).
• Maximum waiting time.

Some basic assumptions are

• When a customer has finished collecting items (this is when the customer is created in the simulation), it chooses the shortest queue.
• When a customer has payed it leaves the store, and the cashier expedites the next customer in its queue

Some input parameters of the program are

• The number of queues/cashiers n_q.
• The probability of a customer being created for each time step.
• The probability of different number of items a new customer has n_item ∈ [n_min, n_max]. This is individually set for each customer. The number of items equals the number of time steps a customer will be standing at the cashier when it is served.
• The opening time of the store, t_max is the number of time steps that the simulation is run.

Supplied files and tips

• prand.c, prand.h Poisson distribution, to be used as a probability distribution for defining the number of items (n_item) a new customer has. Example code of usage testPoisson.c. The usage is basically sprand(n_m) and then prand() will return an integer n_item ∈ [0, 3n_m].
• You can use the Poisson distribution code as a random number generator also for determining if a new customer should be created in a time step, or use drand48() or lrand48(). Use the man command in the terminal to get information on how to use. The usage is basically srand48(time(&ttime)); is an initial seed where time_t ttime; and drand48() returns a random double in [0, 1].

Some optional extra features that can be added

• Add various ways to input the parameters of the program; command line arguments, read from a file, get information from stdio
• Generate visualizations of interesting statistics in for example Matlab or Python.
• Verify Little’s Law with your program.