35.1 Queue OperationsA queue is a linear list in which data can be inserted at one end, called the rear, and deleted from the other end, called the front. It is a first in-first out (FIFO) data structure.Remove(dequeue)(Enqueue)frontrearA computer queue
4Dequeue: Dequeue deletes an element at the front of the queue. Enqueue: Enqueue inserts an element at the rear of the queue.grapedataEnqueueplumkiwiplumkiwigrapefrontrearfrontrearQueueQueueOperationDequeue: Dequeue deletes an element at the front of the queue.plumdataDequeueplumkiwigrapekiwigrapefrontrearfrontrearQueueOperationQueue
5Queue Rear: Queue rear examines the element at the rear of the queue. Queue Front: Queue front examines the element at the front of the queue.plumdataQueuefrontplumkiwigrapeplumkiwigrapefrontrearfrontrearOperationQueueQueueQueue Rear: Queue rear examines the element at the rear of the queue.grapedataQueuerearplumkiwigrapeplumkiwigrapefrontrearfrontrearOperationQueueQueue
65.2 Queue Linked List Design Data structure: For the linked list implementation of a queue, we use tow types of structures: a head and a node.Queue head: The queue head contains the two pointers and a count of the queue.Queue data node: The queue data node contains the user data and a link field pointing to the next node .
7front rear front count rear data next plum kiwi grape fig front rear Conceptual queuefrontrear4plumkiwigrapefigfrontrearPhysical queuefrontcountreardatanextHead structureNode structure
8Queue AlgorithmsCreate queue: set the metadata pointers to null and the count to 0.No queuefrontcountrearfrontcountrear???BeforeAfterAlgorithm createQueue (ref queue <metadata>queue.fornt = nullQueue.rear = nullQueue.count = 0End createQueue
9Enqueue: Three conditions need to be considered: 1.insert into an empty queue.2. Insert into a queue with data.3. Insertinto a queue when there is no memory left in the heap.frontcountrearfrontcountrear1datanextdatanextnewPtrplumplumnewPtrAfterBeforeInsert into empty queue
10plum next data front rear count kiwi plum next data 1 front rear count Algorithm enqueue (ref queue<metadata>dataIn <dataType>If (queue full)1 return falseEnd ifAllocate (newPtr)newPtr->data = dataInnewPtr->next = null pointerIf (queue.count zero)// inserting into null queue1 queue.front = newPtrElse // insert data1 queue.rear->next = newPtrQueue.rear = newPtrQueue.count = queue.count + 1Return trueEnd enqueueplumnextdata1frontrearcountkiwinewPtrThere are four ways to test if the queue is null 1.Front null2.Rear null3.Count 04.EmptyqueueBeforeplumnextdata2frontrearcountkiwinewPtrAfterInsert into queue with data
11Dequeue: 1. Ensure that the queue contains data. 2 Dequeue: 1. Ensure that the queue contains data. 2. Pass the data back through the parameter list and then set the front pointer to the next item in the queue. 3. If the queue is now empty, set the rear pointer to null.plumnextdata1frontrearcountfrontcountrear(recycled)deleteLocBeforeAfterDelete only item in queue
12plum next data front rear count kiwi front count rear data data next 2frontrearcountkiwiAlgorithm dequeue (ref queue <metadata>ref item <dataType>)If (queue.count is 0)1 return falseEnd ifItem = queue.front->datadeleteLoc = queue.frontIf (queue.count 1)// Delete only item in queue1 queue.rear = null pointerQueue.front = queue.front->nextQueue.count = queue.count – 1Recycle (deleteLoc)Return trueEnd dequeueBeforefrontcountrear1datanextdatanextplumkiwi(recycled)AfterdeleteLoc
13Retrieving Queue Data: the logic of retrieving data is the same to that of dequeue except that the data are not deleted from the queue.Algorithm queueFront ( val queue <metadata>,ref dataOut <dataType>)If (queue.count is 0)1 return falseEnd ifdataOut = queue.front->dataReturn trueEnd queueFront
14Empty Queue: it returns true if the queue is empty and false if the queue contains data. Algorithm emptyQueue ( val queue <metadata>)Return (queue.count equal 0)End emptyQueueFull Queue: By allocating a node and then releasing the memory we can determine whether there is room for at least one more node.Algorithm fullQueue ( val queue <metadata>)Allocate (tempPtr)If (allocate successful)1 recycle (tempPtr)2 return falseElse1 return trueEnd ifEnd fullQueue
15Queue Count: it returns the number of elements currently in the queue by returning the count found in the queue head node.Algorithm Queuecount ( val queue <metadata>)Return (queue.count)End queueCountDestroy Queue: it deletes all data in the queue and recycles their memory.Algorithm destroyQueue ( ref queue <metadata>)pWalker = queue.frontLoop (pWalker not null)1 deletePtr = pWalker2 pWalker = pWalker.next3 recycle (deletePtr)End loopQueue.front = nullQueue.rear = nullQueue.count = 0returnEnd destroyQueue
165.3 Queuing TheoryQueuing theory is a field of applied mathematics that is used to predict the performance of queues.A Single-server queue can provide service to only one customer at a time.Example: the hot-food vendor.A Multi-server queue can provide service to many customers at a time.Example: a bank in which there is one line with many bank tellers providing service.
17Two elements to all queues A customer is any person or thing needing service. Such as jobs in computer, packages being sent…The service is any activity needed to accomplish the required result.Two factors affect the queueThe arriving rate(比率) is the rate at which customers arrive in the queue for service. Depending on the service being provided, the arrival rate may be random or regular.Service time is the average time required to complete the processing of a customer request.The arriving rate and service time are the factors that most affect the performance of queues.
18The faster customers arrive and the higher the service time, the longer the queue will be. The ideal is arrival rate matches service timeThe importance of queuing theory: it can predict the queue patterns including queue time(that is, the average length of time customers wait in the queue), the average size of the queue, and the maximum queue size. So, we can build a model of queue and used the model to study proposed changes to the system.For example, In the banking queue, if we were able to add automation improvements that would reduce the average service by 15%,how many fewer tellers would we need?
19Queue time Service time Response time Queue Server A queuing theory model
205.4 Queue ApplicationsTwo queue implementations: Queue simulation and categorizing dataQueue simulation: a modeling activity used to generate statistics about the performance of queues.An example: a saltwater taffy store on a beach boardwalk. The store has one window and a clerk can service only one customer at a time. The store also ships boxes of taffy anywhere in the country.The time to serve customers varies between 1 and 10 minutes.(8hs per day, 7 days a week)
21Events:completed process new customer module: determine the arrival of a new customer. The owner found that, on average , a customer arrives every 4 minutes. An arrival rate is simulated by using a random number generator that returns a values between 1 and 4.If = 4, customer arrived; 1,2,3 customer not arrived.server free module: determine whether the clerk is busy or idle. If the clerk is idle, then the next waiting customer in line can be served. If the clerk is busy, then the waiting customers remain in the queue.Completed processing: determine whether it has completed processing for the current customer. Then processing time for the current customer is determined by a random number generator when the processing is started. When customers has been completely served, we gather statistics about sale and set server to an idle state
22Data structures:Four data structure are required for the queue simulationQueue head: It contains two node pointers – front and rear – and a count of the number of elements currently in the queue.Queue node: It contains the customer data and a next node pointer. The customer data consist of a sequential customer number and the arrival time.Current Customer status: We use customer’s number, arrival time, the start time and the processing time to describe customer status.(random generator to calculate)Simulation statistics: It stores the total number of customers processed in the simulation, the total and average service time, the total and average wait time, and the maximum number of customers in the queue at one time.
23front rear count head next node custNum arriveTime startTime svcTime 2frontrearcountheadnextcustNumarriveTimenodecustNumarriveTimestartTimesvcTimecustStatusnumCusttotSvcTimetotWaitTimemaxQueueSizesimStatsFigure 5-13 queue data structures
24Output: the statistics gathered during the simulation and the average queue wait time and average queue service time, the basic statistics for each customer: arrival time, start time, wait time, service time etc.SimulatorCreatequeueNewcustomerServerfreeServicecompletePrintstatsFigure 5-14 design for queue simulation
31For example, given the following list of numbers Categorizing Data: It is often necessary to rearrange data without destroying their basic sequence.For example, given the following list of numbersthen categorize them into four different groups:Group1: less than 10Group2: between 10 and 19Group3: between 20 and 29Group4: 30 and greater
345.8 SummaryA queue is a linear list in which data can only be inserted at one end, called the rear, and deleted from the other end, called the front.A queue is a first in-first out (FIFO) structure.There are four basic queue operations: enqueue, dequeue, queue front, and queue rear.The enqueue operation inserts an element at the rear of the queue.The dequeue operation deletes the element at the front of the queue.The queue front operation examines the element at the front of the queue without deleting it.The queue rear operation examines the element at the rear of the queue without deleting it.
35To implement the queue using a linked list, we use two types of structures: a head and a node. Queuing theory is a field of applied mathematics that is used to predict the performance of queues.Queue applications can be divided into single servers and multi-servers.A single-server queue application provides service to only one customer at a time.A multi-server queue application provides service to only several customers at a time.The two features that most affect the performance of queues are the arrival rate and the service time.The rate at which the customers arrive in the queue for service is known as the arrival rate.Service time is the average time required to complete the processing of a customer request.
36The queue time is the average length of time customers wait in the queue. The response time is a measure of average time from the point at which customers enter the queue until the moment they leave the server. It is queue time plus service time.One application of queues is queue simulation, which is a modeling activity used to generate statistics about the performance of a queue.Another application of queues is categorization. Queues are used to categorize data into different groups without losing the original ordering of the data.Queues can be implemented suing linked lists or arrays.
37ExerciseImagine you have a stack of integers,S ,and a queue of integers,Q. Draw a picture of S and Q after the following operation:PushStack(S,3)PushStack(S,12)Enqueue(Q,5)Enqueue(Q,8)PopStack(S,x)pushStack(S,2)Enqueue(Q,x)Dequeue(Q,y)PushStack(S,x)PushStack(S,y)
38ExerciseWhat would be the contents of queue Q1 and Q2 after the following code is executed and the following data are entered?Q1=createQueueQ2=createQueueLoop (not end of file)read numberenqueue(Q1,number)enqueue(Q2,number)loop (Not empty Q1)dequeue(Q1,x)enqueue(Q2,x)End loopThe data are 5,7,12,4,0,4,6