Data Structures( 数据结构 ) Course 5:Queue

Data Structures(Data Structures( 数据结数据结构构 ))

Course 5:QueueCourse 5:Queue

2西南财经大学天府学院

VocabularyVocabulary

queue 队列 enqueue 进队 dequeue 出队 queue front 队头 queue rear 队尾 Queuing theory 排队论


5.1 5.1 Queue OperationsQueue Operations

A 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.

front rear

Remove(dequeue)

A computer queue

(Enqueue)


Enqueue: Enqueue inserts an element at the rear of the queue.

plum kiwi

front rear EnqueueEnqueueplum grape

front rear

kiwi

grapedata

Queue OperationQueue

Dequeue: Dequeue deletes an element at the front of the queue.

kiwi

front rearDequeueDequeueplum grape

front rear

kiwi

plumdata

Queue Operation Queue

grape


Queue Front: Queue front examines the element at the front of the queue.

plum grape

front rear

kiwi

Queue

plum grape

front rear

kiwi

Queue

Queuefront

Queuefront

plum data

Operation

Queue Rear: Queue rear examines the element at the rear of the queue.

plum grape

front rear

kiwi

Queue

plum grape

front rear

kiwi

Queue

Queuerear

Queuerear

grape

data

Operation


5.2 5.2 Queue Linked List Queue Linked List DesignDesign

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 .


plum kiwi grape figfront rear

Conceptual queue

plum kiwi grape fig

front rear

4

front rear

Physical queue

front rearcount data next

Head structure Node structure


Queue AlgorithmsCreate queue: set the metadata pointers to null and the count to 0.

? ? ?

front rearcount

Before

0

front rearcount

After

No queue

Algorithm createQueue (ref queue <metadata>1 queue.fornt = null2 Queue.rear = null3 Queue.count = 0End createQueue

Algorithm createQueue (ref queue <metadata>1 queue.fornt = null2 Queue.rear = null3 Queue.count = 0End createQueue


Enqueue: 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.

0

front rearcount

plumnextdata

plumnextdata

newPtr newPtr

1

front rearcount

Before AfterInsert into empty queue


plum

nextdata

1

front rearcount

kiwi

nextdata

newPtr

plumnextdata

2

front rearcount

kiwinextdata

newPtr

Before

After

Insert into queue with data

Algorithm enqueue (ref queue<metadata> dataIn <dataType>1 If (queue full) 1 return false2 End if3 Allocate (newPtr)4 newPtr->data = dataIn5 newPtr->next = null pointer6 If (queue.count zero) // inserting into null queue 1 queue.front = newPtr7 Else // insert data 1 queue.rear->next = newPtr8 End if9 Queue.rear = newPtr10 Queue.count = queue.count + 111 Return trueEnd enqueue

Algorithm enqueue (ref queue<metadata> dataIn <dataType>1 If (queue full) 1 return false2 End if3 Allocate (newPtr)4 newPtr->data = dataIn5 newPtr->next = null pointer6 If (queue.count zero) // inserting into null queue 1 queue.front = newPtr7 Else // insert data 1 queue.rear->next = newPtr8 End if9 Queue.rear = newPtr10 Queue.count = queue.count + 111 Return trueEnd enqueue

There are four ways to test if the queue is null 1.Front null2.Rear null3.Count 04.Emptyqueue


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.

plumnextdata

1

front rearcount

0

front rearcount

deleteLoc(recycled)

BeforeAfter

Delete only item in queue


plumnextdata

2

front rearcount

kiwinextdata

Before

plumnextdata

1

front rearcount

kiwinextdata

(recycled)

deleteLoc After

Algorithm dequeue (ref queue <metadata> ref item <dataType>)1 If (queue.count is 0) 1 return false2 End if3 Item = queue.front->data4 deleteLoc = queue.front5 If (queue.count 1)

// Delete only item in queue 1 queue.rear = null pointer6 End if7 Queue.front = queue.front->next8 Queue.count = queue.count – 19 Recycle (deleteLoc)10 Return trueEnd dequeue

Algorithm dequeue (ref queue <metadata> ref item <dataType>)1 If (queue.count is 0) 1 return false2 End if3 Item = queue.front->data4 deleteLoc = queue.front5 If (queue.count 1)

// Delete only item in queue 1 queue.rear = null pointer6 End if7 Queue.front = queue.front->next8 Queue.count = queue.count – 19 Recycle (deleteLoc)10 Return trueEnd dequeue


Retrieving 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>)1 If (queue.count is 0) 1 return false2 End if3 dataOut = queue.front->data4 Return trueEnd queueFront

Algorithm queueFront ( val queue <metadata>, ref dataOut <dataType>)1 If (queue.count is 0) 1 return false2 End if3 dataOut = queue.front->data4 Return trueEnd queueFront


Empty Queue: it returns true if the queue is empty and false if the queue contains data.Algorithm emptyQueue ( val queue <metadata>)

1 Return (queue.count equal 0)End emptyQueue

Algorithm emptyQueue ( val queue <metadata>)1 Return (queue.count equal 0)End emptyQueue

Full 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>)1 Allocate (tempPtr)2 If (allocate successful) 1 recycle (tempPtr) 2 return false3 Else 1 return true4 End ifEnd fullQueue

Algorithm fullQueue ( val queue <metadata>)1 Allocate (tempPtr)2 If (allocate successful) 1 recycle (tempPtr) 2 return false3 Else 1 return true4 End ifEnd fullQueue


Destroy Queue: it deletes all data in the queue and recycles their memory.

Queue 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>)1 Return (queue.count)End queueCount

Algorithm Queuecount ( val queue <metadata>)1 Return (queue.count)End queueCount

Algorithm destroyQueue ( ref queue <metadata>)1 pWalker = queue.front2 Loop (pWalker not null) 1 deletePtr = pWalker 2 pWalker = pWalker.next 3 recycle (deletePtr)3 End loop4 Queue.front = null5 Queue.rear = null6 Queue.count = 07 returnEnd destroyQueue

Algorithm destroyQueue ( ref queue <metadata>)1 pWalker = queue.front2 Loop (pWalker not null) 1 deletePtr = pWalker 2 pWalker = pWalker.next 3 recycle (deletePtr)3 End loop4 Queue.front = null5 Queue.rear = null6 Queue.count = 07 returnEnd destroyQueue


5.3 5.3 Queuing TheoryQueuing 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.


Two elements to all queuesA 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.


The faster customers arrive and the higher the service time, the longer the queue will be.The ideal is arrival rate matches service time The 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?


ServerQueue

Queuetime

Servicetime

Responsetime

A queuing theory model


5.4 5.4 Queue ApplicationsQueue Applications

Two queue implementations: Queue simulation and categorizing data Queue 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)


Events: 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


Data 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.


2front rearcount

nextcustNum arriveTime

custNum arriveTime startTime svcTime

numCust totSvcTime totWaitTime maxQueueSize

simStats

custStatus

node

head

Figure 5-13 queue data structures


Output: 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.

Simulator

Printstats

Newcustomer

Serverfree

Service complete

Createqueue

Figure 5-14 design for queue simulation


Simulation AlgorithmSimulator

Algorithm taffySimulationData Structures data number <integer> arrivalTime <integer> end data head front <node pointer> count <integer> rear <node pointer> end head node custData <data> next <node pointer> end node

Algorithm taffySimulationData Structures data number <integer> arrivalTime <integer> end data head front <node pointer> count <integer> rear <node pointer> end head node custData <data> next <node pointer> end node

custStatus custNum <integer> arriveTime <integer> startTime <integer> svcTime <integer> end custstatus simStats numCust <integer> totSvcTime <integer> totWaitTime <integer> maxQueueSize <integer> end simstats

custStatus custNum <integer> arriveTime <integer> startTime <integer> svcTime <integer> end custstatus simStats numCust <integer> totSvcTime <integer> totWaitTime <integer> maxQueueSize <integer> end simstats


Statements1 CreateQueue (queue)2 Clock = 13 endTime = 8*604 custNum = 05 Loop (clock <=endTime or moreCusts) 1 newCustomer (queue, clock, custNum) 2 serverFree (queue, clock, custStatus, moreCusts) 3 svcComplete (queue, clock, custStatus, runStats, moreCusts) 4 if ( not emptyQueue (queue)) 1 moreCusts = true 5 end if 6 clock = clock + 16 End loop7 printStats (runStats)8 return end taffySimulation

Statements1 CreateQueue (queue)2 Clock = 13 endTime = 8*604 custNum = 05 Loop (clock <=endTime or moreCusts) 1 newCustomer (queue, clock, custNum) 2 serverFree (queue, clock, custStatus, moreCusts) 3 svcComplete (queue, clock, custStatus, runStats, moreCusts) 4 if ( not emptyQueue (queue)) 1 moreCusts = true 5 end if 6 clock = clock + 16 End loop7 printStats (runStats)8 return end taffySimulation

Algorithm 5-9 queue simulation: driver


New customer

Algorithm newCustomer (ref queue < metadata >, val clock <integer>, ref custNum <integer>)1 Arrival = (random number modulo 4) + 12 If (arrival equal 4) // new customer has arrived 1 custNum = custNum + 1 2 custData.number = custNum 3 custData.arriveTime = clock 4 enqueue (queue, custData)3 End if4 ReturnEnd newCustomer

Algorithm newCustomer (ref queue < metadata >, val clock <integer>, ref custNum <integer>)1 Arrival = (random number modulo 4) + 12 If (arrival equal 4) // new customer has arrived 1 custNum = custNum + 1 2 custData.number = custNum 3 custData.arriveTime = clock 4 enqueue (queue, custData)3 End if4 ReturnEnd newCustomer


Server free

Algorithm serverFree ( ref queue <metadata>, val clock <integer> , ref status <custStastus>, ref moreCusts <Boolean> )1 If (clock > status.startTime + status.svcTime – 1) // server is idle 1 if (not emptyQueue (queue)) 1 dequeue (queue,custData) 2 status.custNum = custData.number 3 status.arriveTime = custData.arriverTime 4 status.startTime = clock 5 status.svcTime = random service time 6 moreCusts = true 2 end if2 End if3 ReturnEnd serverFreestatus

Algorithm serverFree ( ref queue <metadata>, val clock <integer> , ref status <custStastus>, ref moreCusts <Boolean> )1 If (clock > status.startTime + status.svcTime – 1) // server is idle 1 if (not emptyQueue (queue)) 1 dequeue (queue,custData) 2 status.custNum = custData.number 3 status.arriveTime = custData.arriverTime 4 status.startTime = clock 5 status.svcTime = random service time 6 moreCusts = true 2 end if2 End if3 ReturnEnd serverFreestatus


Service complete

Algorithm svcComplete (ref queue <metadata>, val clock <integer>, ref status <custStatus>, ref stats <simStats>, ref moreCusts <Boolean>)1 If (clock equal status.startTime + status.svcTime – 1) //current call complete 1 waitTime = status.startTime – status.arriveTime 2 stats.numCust = stats.numCust + 1 3 stats.totSvcTime = stats.totSvcTime + status.svcTime 4 stas.totWaitTime = stats.totWaitTime + waitTime 5 queueSize = queueCount (queue) 6 if (stas.maxQueueSize < queueSize) 1 stats.maxQueueSize = queueSize 7 end if 8 print ( status.custNum status.arriveTime status.startTime status.svcTime waitTime queueCount(queue)) 9 moreCusts = false2 ReturnEnd svcComplete

Algorithm svcComplete (ref queue <metadata>, val clock <integer>, ref status <custStatus>, ref stats <simStats>, ref moreCusts <Boolean>)1 If (clock equal status.startTime + status.svcTime – 1) //current call complete 1 waitTime = status.startTime – status.arriveTime 2 stats.numCust = stats.numCust + 1 3 stats.totSvcTime = stats.totSvcTime + status.svcTime 4 stas.totWaitTime = stats.totWaitTime + waitTime 5 queueSize = queueCount (queue) 6 if (stas.maxQueueSize < queueSize) 1 stats.maxQueueSize = queueSize 7 end if 8 print ( status.custNum status.arriveTime status.startTime status.svcTime waitTime queueCount(queue)) 9 moreCusts = false2 ReturnEnd svcComplete


Algorithm printStats ( stats <simStats> )1 Print (Simulation Statistics: )2 Print (Total customers: stats.numCust)3 Print (Total service time: stats.totSvcTime)4 avrgSvcTime = stats.totSvcTime / stats.numCust5 Print (Average service time: arvgSvcTime)6 avrgWaitTime = stats.totWaitTime / stats.numCust7 Print (Average wait time: avrgWaitTime)8 Print (,Maximum queue size: stats.maxQueueSize)9 returnEnd printstats

Algorithm printStats ( stats <simStats> )1 Print (Simulation Statistics: )2 Print (Total customers: stats.numCust)3 Print (Total service time: stats.totSvcTime)4 avrgSvcTime = stats.totSvcTime / stats.numCust5 Print (Average service time: arvgSvcTime)6 avrgWaitTime = stats.totWaitTime / stats.numCust7 Print (Average wait time: avrgWaitTime)8 Print (,Maximum queue size: stats.maxQueueSize)9 returnEnd printstats

Print stats


Categorizing Data: It is often necessary to rearrange data without destroying their basic sequence. For example, given the following list of numbers

3 22 12 6 10 34 65 29 9 30 81 4 5 19 20 57 44 99

then categorize them into four different groups:

Group1: less than 10

Group2: between 10 and 19

Group3: between 20 and 29

Group4: 30 and greater

3 6 9 4 5 12 10 19 22 29 20 34 65 30 81 57 44 99


Algorithm categorize

1 CreateQueue (q0to9)

2 createQueue (q10to19)


4 createQueue (qOver29)

5 fillQueues (q0t09, q10to19,q20to29, qOver29)

6 printQueues (q0to9, q10to19, q20to29,qOver29)

7 Return

End categorize

Algorithm categorize

1 CreateQueue (q0to9)



4 createQueue (qOver29)

5 fillQueues (q0t09, q10to19,q20to29, qOver29)

6 printQueues (q0to9, q10to19, q20to29,qOver29)

7 Return

End categorize


Algorithm fillQueues (ref q0to9 <metadata>, ref q10to19 <metadata>, ref q20to29 <metadata>, ref qOver29 <metadata>)1 Loop (not EOF) 1 read (number) 2 if (number < 10) 1 enqueue (q0to9, number) 3 elseif (number<20) 1 enqueue (q10to19, number) 4 elseif (number<30) 1 enqueue (q20to29, number) 5 else 1 enqueue (qOver29, number) 6 end if2 End loop3 ReturnEnd fillQueue

Algorithm fillQueues (ref q0to9 <metadata>, ref q10to19 <metadata>, ref q20to29 <metadata>, ref qOver29 <metadata>)1 Loop (not EOF) 1 read (number) 2 if (number < 10) 1 enqueue (q0to9, number) 3 elseif (number<20) 1 enqueue (q10to19, number) 4 elseif (number<30) 1 enqueue (q20to29, number) 5 else 1 enqueue (qOver29, number) 6 end if2 End loop3 ReturnEnd fillQueue


5.8 5.8 SummarySummary

A 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.


To 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.


The 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.


ExerciseExercise

Imagine 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)


ExerciseExercise

What 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 loop

End loop The data are 5,7,12,4,0,4,6

Documents

Data Structures( 数据结构 ) Course 5:Queue