辅导案例-EECS2011-Assignment 2

  • July 24, 2020

EECS2011: Fundamentals of Data Structures Assignment 2 Assigned: July 7, 2020; Due: Aug 4, 2020 @ 10:00 a.m. If you are working in a group of two or three, then indicate the associated student IDs and numbers in the Test.java file as a comment in the header. 1 Objectives The queue data structure can be used for modelling and simulating many interesting systems. In many practical systems, some kind of buffers/queues are used to temporarily place tasks or items prior to processing these. Entities arriving first at the buffer are processed first. Since the FIFO service paradigm is quite natural in a broad range of practical systems, queues can be naturally used to model the behaviour of these. In this lab assignment, you will be modelling a simple data network. 2 Introduction to Data Networks Transmitting data through the internet (emails, video/voice streaming, etc.) is a complex process. The internet is essentially a large network composed of intermediate devices that forward transmitted data originating from a source device to a destination device through links as illustrated in Figure 1. These intermediate devices include routers and switches that forward data from incoming links to outgoing links based on their destination. Figure 1: A Simplified Visualization 2.1 A Transportation of People Analogy In order to understand how data is transmitted across the internet from a source to a destination, consider the following analogy. Suppose that 20 people are to be transported from Point A to Point B via cars only. Everyone is leaving from the same place and intend to arrive at the same place. Cars have fixed space (i.e. can only seat a maximum of 5 people). Assume that all 20 people manage to fit into 4 cars. These cars then will use various roads to travel from Point A to Point B. Since the roads are public, these will be shared by other cars as well. Depending on the time of the day, there will be various degrees of traffic on the roads. Certain roads such as the highways allow cars to travel at a faster speed than others. The cross point of roads will be managed by traffic signals. Based on all these factors, the drivers of the four cars may choose 1 different paths (composed of various roads) to reach the final destination (i.e. Point B). All four cars will arrive at Point B but possibly at different times depending on the conditions of the roads travelled and speed limits. 2.2 Similarities between Data Network and Transportation This transportation example has surprisingly many similarities with the process incurred during the trans- mission of data from a source device to a destination device. Suppose that you would like to send an email from your computer (source) to your friend (destination) who resides in another country. In the transmission process, your email is first broken down into smaller entities called packets (analogous to dividing 20 people into 4 cars). These packets then traverse links (analogous to roads) in order to reach the final destination. Different links have different speeds/bandwidths (analogous to speed limits on roads). Since links in the internet are mostly public, your email packets will share the link with other packets from other sources (roads are shared with other people who are driving from other places). Multiple links intersect at a single point (i.e. junction at a road intersection). Intermediate devices such as switches or routers decide on where to forward packets arriving at these junctions. Packets may arrive at different times at a router. When more than one packet arrives at the router, these are stored in a buffer/queue (i.e. cars waiting at a junction). In this lab assignment, the following assumptions are made: data packets are all of the same size, time taken for a router to forward packets to appropriate links is constant and the queue is infinite in length. Based on the congestion properties and conditions of the network, routers may forward packets to different links (i.e. drivers taking different routes). Even though the packets will arrive at the destination, these might arrive at different times based on the conditions of the paths. Figure 2: A Simple Representation of a Router Queue 2.3 Your Task for this Lab Assignment In this lab assignment, you will model various properties of a queue in a single router when packets arrive into the queue at a particular rate and depart from the queue at a particular rate. As depicted in Figure 2, multiple incoming links can converge at the router. Packets arriving through these links are forwarded to appropriate outgoing links by the router. Service time (i.e. the forwarding of packets to appropriate links) is assumed to be constant. Intuitively, it is pretty reasonable to postulate that if the arrival rate of packets into a queue is lower than the service rate, then the queue will be not be congested and the average wait time of a packet in the queue before being processed will not be excessive. On the other hand, when the arrival rate of packets into the queue is greater than the service rate, then the queue will get filled up quickly and each packet in the queue will have to wait for very large periods of time before being served. 2 In this lab assignment, you will compute the average waiting times of packets departing a router queue by simulating the router queue for various packet arrival rates. You will notice that as the arrival rate gets closer to the service rate, the average waiting times of packets in the queue will increase exponentially and explode. This trend has been modelled by a well known law called the Little’s Law. The average waiting time E(S) or sojourn time of a packet in a queue can be related to the arrival rate λ of packets into the queue and service rate µ of the queue which denotes the departure rate of packets from the queue via this equation: E(S) = 1λ ( λ µ + 1 2 ( λ µ ) 2 1−λµ ). You can use your simulations to verify whether the router queue obeys this law. 2.4 Simulation of a Router Queue A router queue can have no packets at a time or some packets waiting to be serviced. Packets arrive at random times. These arrival times depend on the arrival rates of packets. The function public double getRandTime(double arrivalRate) is provided to you in the QueueSimulator.java file. This function returns the duration (seconds) within which the next packet will arrive into the queue for a particular arrival rate λ which is passed as an argument to the function. For instance, suppose λ = 0.1 packets/sec, the function call getRandTime(0.1) may result in 1.344 sec. This means that the next packet will arrive into the queue within 1.344 sec. Hence, packets can be queued into the router according to the times returned by getRandTime. Every packet queued into the router will be processed by the router according to the first come first serve policy. Time taken to serve each packet is assumed to be constant. Suppose the service rate is µ = 10 packets/sec, then the service time is 110 = 0.1 sec. This means that the time required for the router to process every packet at the front of the queue is 0.1 sec. In a simulation, certain metrics about the system are measured throughout the simulation period. We are particularly interested in the average waiting time of departing packets for various combinations of λ and µ. The simulation will run for ρ sec. Time progression currTime in a simulation is based on events occurring in the simulation. Simulation will start at 0 sec. In a router queue, an event will occur if a packet is scheduled to arrive into or depart from the queue. Suppose that a packet is scheduled to arrive into the queue at timeForNextArrival. Suppose that the number of packets in the queue is at least one. Then the first packet in the queue is scheduled to depart from the queue at timeForNextDeparture. The next event that will occur in the simulation is an ARRIVAL if timeForNextArrival < timeForNextDeparture. Otherwise, the next event is a packet DEPARTURE. If there are no packets in the queue, then the only event that can occur next is an ARRIVAL. When an event occurs, the simulator updates the current time variable currTime to the time at which the event occurs. The simulator operates a loop conditioned upon the current simulation time. The loop will terminate when currTime is greater than or equal to the total simulation time simTime allocated to the simulation. At each iteration of the while loop, the simulator will perform operations on two queue data structures. If the current event is an ARRIVAL, the simulator will enqueue a node into the buffer queue (which mimics the router queue) and compute timeForNextArrival. On the other hand, if the current event is a DEPARTURE, then the first node in the buffer queue is dequeued and this node is enqueued into eventQueue. The simulator then computes timeForNextDeparture. All nodes in eventQueue contain information about the arrival time and departure time of a packet into and from the buffer queue. At the end of the simulation, the simulator uses the calcAverageWaitingTime function to dequeue all nodes from eventQueue and compute the average waiting time or sojourn time of packets that have departed the buffer queue. Packets still remaining in the buffer queue are not accounted for in this calculation. The average packet waiting time computed is returned by the function runSimulation which is running the simulation. 3 Materials Provided You will download content in the folder Assignment2 which contains two folders (code and expOutput) onto your workspace. Folder code contains a skeleton of function implementations and declarations. Your task is to expand these functions appropriately in the SinglyLinkedList.java, LinkedListQueue.java, Data.java, and QueueSimulator.java files. Test.java evokes all the functions you will have imple- mented and is similar to the file that will be used to test your implementations. Use Test.java file to test 3 all your implementations. Folder expOutput contains outputs expected for function calls in Test.java (for part 2 the answers should be fairly close to the expected output (to one decimal place) with the exception of λ = 10packets/sec). Note that we will NOT use function calls with the same parameters for grading your lab assignment. Do NOT change the name of these files or functions. 4 Grading: Final Mark Composition It is IMPORTANT that you follow all instructions provided in this assignment very closely. Otherwise, you will lose a significant amount of marks as this assignment is auto-marked and relies heavily on you accurately following the provided instructions. Following is the mark composition for this assignment (total of 40 points): • Successful compilation of all program files i.e. the following command results in no errors (3 points): javac Queue.java SinglyLinkedList.java LinkedListQueue.java Data.java QueueSimulator.java Test.java • Successful execution of the following commands: (2 points) java Test 1 java Test 2 • Output from Part 1 matches expected output (7 points) • Output from Part 2 matches expected output (to one decimal place for the first four outputs of the runSimulation function) (18 points) • Code content (10 points) Sample expected outputs are provided in folder expOutput. We will test your program with a set of completely different data files. Late submissions will not be accepted. All late submissions will be assigned a grade of 0/40. 5 Implementation of the Simulation Program You will be using queue ADT as a basic building block for this lab assignment. Your simulation program will make use of the queue ADT to model a queue in a router. This queue is assumed to be infinite in length (i.e. no restriction on the size of the queue). Packets will arrive into the queue at rate λ. Time taken to serve these packets (i.e. forward to the appropriate link) is fixed as dictated by the service rate µ. Part 1: Defining Functions Associated with a Queue In this part, function implementations of enqueue, and dequeue will be tested. The Queue interface is provided in Queue.java file. These functions are to be defined in the LinkedListQueue.java file. Prior to implementing the LinkedListQueue class, you will need to define the SinglyLinkedList class in SingleLinkedList.java file. This class is composed of a local private Node class that consists of a generic element E and a reference to the next Node. It should also support the following interface functions: • public Node(E e, Node n); • public E getElement(); • public Node getNext(); • public void setNext(Node n); 4 where the constructor initializes the local fields with the arguments passed, getElement returns the generic element stored in the node, getNext returns the reference to the next node locally stored and setNext changes the reference stored in the local variable next. After this private class is defined, you can proceed to defining the SinglyLinkedList. Here you will need to keep track references to the first and last nodes along with the size of the linked list as private field variables. The following functions will be defined to support operations on the linked list: • public SinglyLinkedList(); • public int size(); • public boolean isEmpty(); • public E first(); • public E last(); • public void addFirst(E element); • public void addLast(E element); • public E removeFirst(); where you will define the constructor to initialize the private field variables, size returns the number of nodes in the linked list, isEmpty returns TRUE if the linked list has no nodes and FALSE otherwise, first returns the content stored in the node at the front of the linked list, last returns the content stored in the node at the end of the linked list, addFirst adds a node containing element to the front of the linked list, addLast adds a node containing element to the end of the linked list and removeFirst removes the node at the front of the linked list. The SinglyLinkedList class will then be utilized to implement the Queue interface in LinkedListQueue.java. Here you will implement the interface functions defined in the Queue.java file. • public LinkedListQueue(); • public int size(); • public boolean isEmpty(); • public E first(); • public void enqueue(E node); • public E dequeue(); where constructor will initialize the private field variables (e.g. linked list), size returns the number of nodes in the queue, isEmpty checks whether the queue has any nodes, first returns the element stored at the front of the queue, enqueue inserts a node to the back of the queue, and dequeue removes a node from the front of the queue. The element stored in each node is defined to be of generic type. For this lab assignment, we will utilize a specific element of type Data which is defined in the Data.java file. It is composed of the two private field variables of type double that are called arrivalTime and departureTime. Operations on these variables will be conducted via the following functions: • public Data(); • public void setArrivalTime(double a); • public void setDepartureTime(double d); • public double getDepartureTime(); • public double getArrivalTime(); where the constructor initializes the private field variables to 0, setArrivalTime sets the arrivalTime variable to be the argument passed into the function, setDepartureTime sets the departureTime variable to be the argument passed into the function, getDepartureTime returns the value stored in the departureTime variable and getArrivalTime returns the value stored in thearrivalTime variable. This part of the lab assignment will be tested via the following commands: 5 • java Test 1 Outputs from these tests should match the content of Part1.txt which is the result of the parameters passed from function calls in Test.java. Part 2: Implementing the Router Queue Simulator You will build a queue simulator that computes the average waiting time of data packets departing from a router queue. You will analyze the impact of various packet arrival rates on average waiting times. In this implementation, you will define the class called QueueSimulator and three functions. The QueueSimulator class stores all parameters and ADTs associated with a simulation via field variables. These consist of the following field variables: double currTime, double arrivalRate, double serviceTime, double timeForNextArrival, double timeForNextDeparture, double totalSimTime, LinkedListQueue buffer, LinkedListQueue eventQueue and Event e;. currTime keeps tracks of the time progression of a simulation. arrivalRate and serviceTime store λ and 1µ respectively. timeForNextArrival stores the time at which the next packet will arrive into the buffer queue. timeForNextDeparture will keep track of the time at which a packet will de- part from the buffer queue. totalSimTime denotes the total time duration for which the simulation is run for. It is assumed that the buffer is initially empty and packets start entering the queue only when the simulation begins. buffer is a LinkedListQueue data structure that will mimic an actual queue in a router. eventQueue is another queue that is used to store information about packets entering and exiting the buffer queue. Event is an enum with two constants: ARRIVAL and DEPARTURE. e is used to store information about the next event that will occur in the simulation. Three functions which are to be implemented for this part are: • public QueueSimulator(double aR, double servT, double simT); • public double runSimulation(); • public double calcAverageWaitingTime(); The service rate is denoted by µ is fixed and denotes the rate at which packets depart from the queue. The arrival rate of packets into the queue can vary depending on the congestion in the network. Suppose that the service rate is µ = 10 packets/sec (i.e. the service time for a packet is fixed and therefore if µ = 10 packets/sec then it takes the router 110 = 0.1 sec to process a packet (also known as service time)). Packets will arrive into a queue at random times. However, on average, these packets arrive at a rate λ. A simulation is evoked via the creation of a new QueueSimulator instance. The simulation is initialized by the constructor QueueSimulator. Three arguments arrivalRate, serviceTime and simTime are passed into this function. arrivalRate is λ, serviceTime is 1µ and simTime is ρ. The arrival time of the first packet into the queue is computed via the getRandTime function and this value is stored in the timeForNextArrival member. The departure time of the first packet from the queue is computed by adding the fixed service time to the previously computed packet arrival time and this value is stored into the timeForNextDeparture member. The next function runSimulation will launch a while loop and progress through the simulation by performing appropriate enqueueing or dequeueing operations based on the current event. Packets are enqueued into buffer in the form Node. The arrival time of the packet into buffer is recorded in the arrivalTime member of the Data variable which is the E member of the Node struct. When a packet is dequeued from buffer, its departure time is recorded in the departureTime member of the Data variable and this node is then enqueued into the eventQueue queue which records all packets departing the buffer queue. When the simulation runs for ρ seconds, it exits the while loop and evokes calcAverageWaitingTime to compute the average waiting time of packets that have already departed from the buffer queue. This value is printed to the console. This part of the assignment will be tested via the following commands: • java Test 2 Outputs from these tests should match the content ((to one decimal place for the first four outputs of the runSimulation function)) in Part2.txt which is the result of the parameters passed from function calls 6 in main. You can test if your implementation is correct by printing out the arrival time and departure time of packets when these are removed from buffer queue. 6 Code Submission ENSURE that your work satisfies the following checklist: • You submit before the deadline • All files and functions retain the same original names • Your code compiles without error (if it does not compile then your maximum grade will be 3/40) 7

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