In [3]:

```
from mytypes import Queue
```

In [4]:

```
# A class to represent a single customer in an M/D/1 queue simulation.
# Each customer has three attributes:
#
# - cid: A customer identifier (can be anything, but we will use consecutive integers)
# - arrival_time: The time at which the customer arrived at the queue
# - departure_time: The time at which the customer departed the queue
class Customer(object):
CUSTOMER_ID = 0
def __init__(self, arrival_time):
Customer.CUSTOMER_ID += 1
self.cid = Customer.CUSTOMER_ID
self.arrival_time = arrival_time
self.departure_time = None
@property
def wait(self):
if self.departure_time is None:
return None
else:
return self.departure_time - self.arrival_time
def __str__(self):
return "Customer({}, {})".format(self.cid, self.arrival_time)
def __repr__(self):
return str(self)
```

In [6]:

```
q = Queue()
```

In [7]:

```
q.enqueue(Customer(10))
```

Out[7]:

In [8]:

```
q.enqueue(Customer(15))
```

Out[8]:

In [9]:

```
q.enqueue(Customer(18))
```

Out[9]:

In [10]:

```
q
```

Out[10]:

In [13]:

```
import random
# simulate_md1: Simulates an M/D/1 queue.
#
# In an M/D/1 queue que have:
#
# - Arrivals follow a Markov process (M)
# - The time to service each customer is deterministic (D)
# - There is only one server (1)
#
# The function takes three parameters (plus one optional parameter)
#
# - lambd: The simulation uses an exponential distribution to determine
# the arrival time of the next customer. This parameters is the
# lambda parameter to an exponential distribution (specifically,
# Python's random.expovariate)
# - mu: The rate at which customers are serviced. The larger this value is,
# the more customers will be serviced per unit of time
# - max_time: The maximum time of the simulation
# - verbosity (optional): Can be 0 (no output), 1 (print state of the queue
# at each time), or 2 (same as 1, but also print when
# each customer arrives and departs)
#
# The function returns two lists: one with all the customers that were served
# during the simulation, and one with all the customers that were yet to be
# served when the simulation ended.
#
def simulate_md1(lambd, mu, max_time, verbosity = 0):
md1 = Queue()
# Our return values: the list of customers that have been
# served, and the list of customers that haven't been served
served_customers = []
unserved_customers = []
# The type of simulation we have implemented in this function
# is known as a "discrete event simulation"
# (https://en.wikipedia.org/wiki/Discrete_event_simulation), where
# we simulate a discrete sequence of events: customer arrivals
# and customer departures. So, we only need to keep track of when
# the next arrival and the next departure will take place (because
# nothing interesting happens between those two types of events).
# Then, in each step of the simulation, we simply advance the
# simulation clock to earliest next event. Note that, because
# we have a single server, this can be easily done with just
# two variables.
next_arrival = random.expovariate(lambd)
next_service = next_arrival + 1/mu
# We initialize the simulation's time to the earliest event:
# the next arrival time
t = next_arrival
while t < max_time:
# Process a new arrival
if t == next_arrival:
customer = Customer(arrival_time = t)
md1.enqueue(customer)
if verbosity >= 2:
print("{:10.2f}: Customer {} arrives".format(t, customer.cid))
next_arrival = t + random.expovariate(lambd)
# The customer at the head of the queue has been served
if t == next_service:
done_customer = md1.dequeue()
done_customer.departure_time = t
served_customers.append(done_customer)
if verbosity >= 2:
print("{:10.2f}: Customer {} departs".format(t, done_customer.cid))
if md1.is_empty():
# The next service time will be 1/mu after the next arrival
next_service = next_arrival + 1/mu
else:
# We start serving the next customer, so the next service time
# will be 1/mu after the current time.
next_service = t + 1/mu
if verbosity >= 1:
print("{:10.2f}: {}".format(t, "#"*md1.length))
# Advance the simulation clock to the next event
t = min(next_arrival, next_service)
# Any remaining customers in the queue haven't been served
while not md1.is_empty():
unserved_customers.append(md1.dequeue())
return served_customers, unserved_customers
```

In [15]:

```
simulate_md1(0.167, 0.15, 100, verbosity=2)
```

Out[15]: