CX 4010 / CSE 6010 Assignment 2: Queueing Network Simulation solution




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1 Discrete Event Simulation Application
To complete this assignment, develop a discrete event (as opposed to a time-stepped) simulation
that models a simple manufacturing system. This simulation is known as a queueing model in the
literature. Queueing models are widely studied and used to model systems such as customers
using a facility (e.g., a department store or restaurant), air and road transportation systems,
computer networks and computer systems, and manufacturing systems, to mention a few. All of
these systems involve customers (e.g., people, aircraft, vehicles, data packets, computer jobs,
parts) that must travel from one station to another and receive “service” or “processing” at each
station. Each station can only process one of these entities (e.g., a customer) at a time. Customers
wanting to use a facility that is busy handling another customer must wait in a queue until the
station is ready to process the next customer.
Here, you will simulate the operation of a simple manufacturing system represented as a “tandem
queue” as shown above. Specifically, the system of interest is an assembly line where parts are
generated at a source, and move through three stations, A, B, and C in succession. Parts leaving
station C move to a “sink” where they exit the system. At any instant, a station is either busy
processing a part or is idle. If the station is idle when the part arrives, it begins processing the
part. If the station is busy, the part is placed in a queue where it will wait until the station can
process it. Parts are removed from the queue in first-in-first-out (FIFO) order.
Each part maintains certain attributes as it travels through the system. Specifically, when created
each part is assigned an attribute indicating the amount of time required to service the part at
each station (this service time is the same for all three stations). The service time should be
selected from an exponential distribution with mean value of S. Assume that the time between
the generation of successive parts at the source, i.e., the interarrival time, is also exponentially
distributed with mean A.
Your simulation should compute the average amount of time a part remains in the system as well
as the average of the total waiting time experienced by each part in traveling through the three
stations. These values should be printed at the end of the simulation run. In your experiments,
assume the average service is 10.0 units of time, and run your simulation for 10,000 units of
simulation time.
Your software must adhere to the following rules concerning the implementation:
1. You must implement an event-driven, discrete event simulation, not a time-stepped
2. Use a double precision floating point number to represent simulation time.
A B C source sink
3. Storage for events must be allocated dynamically by calling malloc(), and the storage
released when you are done using the memory by calling free(). Programs that have
memory leaks or dangling pointers will be considered erroneous!
4. Similarly, malloc() must be used for each part to create storage that holds
information concerning that part. This storage should be allocated when the part is
created at the source and released when the part reaches the sink.
5. Your simulator must implement the future event list as a priority queue constructed as a
linear linked list sorted according to simulation time.
6. Each event and part must be implemented using a C struct. Each event must include a
timestamp value and any parameters you deem necessary to characterize the event. Each
part will have attributes and statistics associated with the part stored in the structure.
7. To generate random numbers from an exponential distribution with mean U, create a
function double urand(void) that returns a random number uniformly distributed
over the interval [0,1) (note it cannot return the value 1.0), then define double
randexp() that returns -U*(log(1.0–urand())) where log() is the C
function defined in <math.h> to compute a natural logarithm.
The software is composed of two parts. You will work in teams of two students each to complete
this assignment, with one student responsible for implementing each part. The first part involves
developing a software library that will used to create discrete event simulations in general,
independent of the particular application. It should include a priority queue, a library module
implementing first-come-first-serve (FIFO) queues, and a random number generation function.
The second part includes the main processing loop for the discrete event simulation that
repeatedly removes the smallest time-stamped event and calls an event handler function to
process that event. This code also should also print the results of the simulation once the
execution has been completed.
The interface between the two parts of the simulation must be clearly documented in a .h file.
This file should include only that information necessary to use the software module, and provide
no information concerning details of the internal implementation of the module.
Your software must be well modularized with a clear application program interface (API)
defined and documented in your code. The programmer using the software modules you create
should not need to know anything about how you implemented these functions, only the
interface for using them. Specifically, you must design the priority queue as a distinct “module,”
with a well-defined interface that should include functions to (1) create a new (empty) priority
queue, (2) insert a timestamped event, and (3) remove the smallest timestamped event from the
queue. Similarly, the FIFO queue should have functions to (1) create a new FIFO queue, (2) add
an item to the queue, and (3) remove the next item from the queue.
2 Student Taking CX 4010
If you are a CX 4010 student, you must:
1. Implement the simulation and generate a print out to demonstrate to the TA that your
program is functioning correctly. To accomplish this, generate a short simulation and
print out a series indicating what events are processed in the simulation, and argue why it
is correct.
2. Complete a series of runs increasing the arrival rate (1 / A). Vary the arrival rate to fully
explain the behavior of this system for different workloads. Generate a graph showing the
average time in the system and queueing delay of parts as a function of the arrival rate. In
your report explain any anomalies or unexpected results in your plot. Pay special
attention to your results when the arrival rate becomes large.
3. Turn in your report including your results, and all software in a single zip file. Your
software must be well documented and include comments so the code is easy to
understand. You should include a README file with instructions on how to compile and
run your program on the jinx cluster.
3 Students Taking CSE 6010
If you are a CSE 6010 student you must:
1. Complete the steps described above for students taking CX 4010.
2. Examine the literature on queueing networks to determine what waiting time should be
obtained for the case of a single queue/server. Create a simulation for a single queue, and
compare your results with the theoretical results that should be obtained by plotting both
on a single graph. Write up your results, including references to the relevant literature.
3. Write a program to measure the average time to perform a single insert followed by a
single remove operation in the priority queue containing N events where each event has a
timestamp uniformly distributed between 0.0 and 1.0. The new event should have a
timestamp also uniformly distributed over the same interval. Show a graph indicating the
execution time as N increases. This program should follow the following steps:
Initialize the priority queue to contain N events
start timer
loop a large number of times
insert into priority queue
delete from priority queue
stop timer
print average time for one iteration of the loop
4 CX 4010 Students (Extra Credit)
Complete the assignment required for CSE 6010 students described above.
5 Reminder: Collaboration Policy
A reminder you must adhere to the Georgia Tech honor code, and the collaboration policy stated
in the course syllabus. Specifically, you are encouraged to discuss the problem and possible
solutions with other students (as well as the TA/instructor), however, all code that you turn in
must be completely your own work. Disseminating your code to other students (not in your
team) is strictly prohibited. Further, downloading code from the web or other sources other than
examples provided in class for use in this assignment is also prohibited.