How to Change Customer Class While Queueing

Ciw allows customers to change their class while waiting in the queue. It does this by sampling times that the customer will wait in their current class before changing to other classes.

To do this a dictionary of class_change_time_distributions is defined. This is a dictionary of dictionaries, mapping pairs of customer classes to distribution objects:

>>> import ciw
>>> class_change_dist_dict = {
...     'Class 0': {'Class 1': ciw.dists.Exponential(rate=5)}
... }

In the above example, the time a customer of class 'Class 0' will wait before becoming a customer of class 'Class 1' will be samples from an Exponential distribution with rate 5. Any other pairs of classes are assumed not to change into one another if they are not present in the dictionary.

This class_change_time_distributions matrix is applied to every node in the queueing network.

As an example, consider an M/M/1 queue with three classes of customer, C0, C1 and C2. Each class arrives with Exponential inter-arrival rates 2, 4 and 6 respectively; and have Exponential service rates 5, 5, and 4 respectively. Now say that:

• C0 customers will change to C2 customers if they have waited in the queue for longer than 0.5 time units.

• C1 customers will change to C2 customers Exponentially at rate 1.

This is input into the simulation as follows:

>>> import ciw
>>> N = ciw.create_network(
...     arrival_distributions={
...         'C0': [ciw.dists.Exponential(rate=2)],
...         'C1': [ciw.dists.Exponential(rate=4)],
...         'C2': [ciw.dists.Exponential(rate=6)]},
...     service_distributions={
...         'C0': [ciw.dists.Exponential(rate=5)],
...         'C1': [ciw.dists.Exponential(rate=5)],
...         'C2': [ciw.dists.Exponential(rate=6)]},
...     number_of_servers=[1],
...     class_change_time_distributions={
...         'C0': {'C2': ciw.dists.Deterministic(value=0.5)},
...         'C1': {'C2': ciw.dists.Exponential(rate=1)}
...     }
... )

As a further example, consider a one node queue with two servers, with two classes of customer, P0 and P1. Both arrive with Exponential inter-arrival rate of 5, both Exponential service rates of 6, and P1 has priority over P1. However P1 customers will change class, and hence change priority, if they have been waiting over 1.5 time units:

>>> N = ciw.create_network(
...     arrival_distributions={
...         'P0': [ciw.dists.Exponential(5)],
...         'P1': [ciw.dists.Exponential(5)]},
...     service_distributions={
...         'P0': [ciw.dists.Exponential(6)],
...         'P1': [ciw.dists.Exponential(6)]},
...     number_of_servers=[2],
...     priority_classes={
...         'P0': 0,
...         'P1': 1},
...     class_change_time_distributions={
...         'P1': {'P0': ciw.dists.Deterministic(1.5)}
...     }
... )

Running this for a while:

>>> ciw.seed(0)
>>> Q = ciw.Simulation(N)
>>> Q.simulate_until_max_time(100)
>>> recs = Q.get_all_records()

We will see than no P1 customer will have a waiting time longer than 1.5 time units, as they will have switched to P0 at this point:

>>> len([r.waiting_time for r in recs if r.customer_class == 'P1'])
421
>>> [r for r in recs if r.customer_class == 'P1' and r.waiting_time >= 1.5]
[]

Under no class changing, we would expect roughly equal amounts of customers of Class 0 and Class 1, as they have the same arrival rates. However, as many Class 1 customers are changing to Class 0 customers, the ratio is now skewed:

>>> number_P0 = len([r for r in recs if r.customer_class == 'P0'])
>>> number_P1 = len([r for r in recs if r.customer_class == 'P1'])
>>> number_P0, number_P1
(563, 421)