1 cs 132 spring 2008 chapter 8 queues. 2 queue a data structure in which the elements are added at...
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CS 132 Spring 2008Chapter 8
Queues
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Queue
A data structure in which the elements are added at one end, called the rear, and deleted from the other end, called the front or first
First In First Out (FIFO)
Operations common to previous data structures:– initializeQueue: initializes the queue to an empty state– destroyQueue: removes all the elements from the queue, leaving
the queue empty– isEmptyQueue: checks whether the queue is empty--if the queue is
empty, it returns the value true; otherwise, it returns the value false– isFullQueue: checks whether the queue is full--if the queue is full,
it returns the value true; otherwise, it returns the value false
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New Operations
front: returns the front (first) element of the queue
back: returns the rear (last) element of the queue
addQueue: adds a new element to the rear of the queue; the queue must exist and must not be full
deleteQueue: removes the front element of the queue
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Array Implementation
list: the array of elements
queueFront: the first (front) element
queueRear: the last (rear) element
Dequeue:– retrieve the first element via front
– remove it via deleteQueue
Enqueue (traditional term): – addQueue to the rear
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A Queue
A B C D E
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What are the elements in the queue?
What is returned by front()?
What is returned by back()?
What is the effect of addQueue('X')?
What is the effect of deleteQueue()?
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An Empty Queue
Note: when the first element is added, it will be put in slot 0.
To add an element:– increment queueRear – put the new element in list[queueRear]
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Adding to a Queue
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Deleting from a Queue
What now?
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Conceptually: a Circular Queue
Idea: reuse slots that have been vacated by deleteQueueWhat do we have that allows us to wraparound, going from 99+1 to 0?
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Queues as Circular Arrays
What happens if we add an element 'z'?
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Queues as Circular Arrays
It looks the same as an empty queueSolutions: 1. maintain a count of the number of elements 2. let queueFront be the position preceding the first element and leave it empty
Choose option #1
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private:
{
int maxQueueSize;
int count;
int queueFront;
int queueRear;
Type *list
}
[maxQueueSize-1]
Implementation
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Initialize Queue
template<class Type>void queueType<Type>::initializeQueue(){ queueFront = 0; queueRear = maxQueueSize - 1; count = 0;}
Note: queueRear does not point to an element when the first element is added, it will be put in slot 0
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What about a linkedQueue?
queueFront queueRear
private:
{
nodeType<Type> queueFront;
nodeType<Type> queueRear;
}
How would addQueue(50) work?
deleteQueue?
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Application of Queues: Simulation
Major application of queues
Build a computer model and "test" different policies
Text example: the manager of a local movie theater wants to know whether to go from 1 cashier to 2
What are the considerations?– the cost of the cashier– how much an extra cashier reduces average wait time
What happens when a customer arrives?– she gets in line– waits for the next available server– is served– goes into the theater
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NewCustomer
Server
CustomerCustomer
One Server
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Two Servers with Two Queues
NewCustomer
Server
CustomerCustomer
Server
Customer
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Three Servers with a Single Queue
NewCustomer
Server
Customer
Customer
(arriving)
Server
CustomerCustomer Customer
Server
Customer
(leaving)
(next)
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Movie Theater Simulation
What do we want to track? how many customers were served
the sum of their waiting times
Assumptionswhen the first customer arrives, all servers are free
when a customer arrives, if there is a free server, she moves to it, otherwise gets in the wait queue
when a customer is done, the first person in line moves to the free server
What do we need to know# servers
transaction time for each customer
average time between customers (arrival rate)(assume customers arrive according to a Poisson distribution)
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Movie Theater Simulation
Time-driven simulationrun for a number of clock periods (e.g. 6000 1 minute periods)
track the number of customers served and their cumulative waiting time
When a customer starts being served: the time she waited is added to the cumulative waiting time
the server initializes its remaining transaction time
Each period the simulationincrements the clock
decrements the remaining transaction time for each server
updates the waiting time for each customer in line
checks to see if anyone arrived
checks to see if there is a free server
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Procedural Bones
//set simulationTime, numberOfServers, transactionTime, timeBetweenCustomerArrival
//process simulationTime periods
for(clock = 1; clock <= simulationTime; clock++)
{
//update remaining server transaction time
//update the waiting time for each customer
//check to see if a customer arrives
//check for a free server
}
//print results
How would we think of this from an object-oriented perspective?
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Object-Oriented Approach: what pieces (objects) do we need to build?
NewCustomer
Server
Customer
Customer
(arriving)
Server
CustomerCustomer Customer
Server
Customer
(leaving)
(next)
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Object-Oriented Approach
Objects (classes)– customer– server– server list– customer queue
What are their properties and methods?
Customer properties– id– when she arrived– how long her transaction will take– how long she has waited in line
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Object-Oriented Approach
serverType properties– whether free or busy
– the current customer
– remaining transaction time
serverTypeList properties– how many servers
– the list
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Movie Theater Simulation
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Movie Theater Simulation
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waitingCustomerQueueType
A queue of customers (suppose clock= 12)
queueRear queueFront
What happens with a clock tick?
cust#: 5:arrT: 9transT: 6waitT: 3
cust#: 4arrT: 7transT: 5waitT: 5
cust#: 3arrT: 5transT: 5waitT: 7
queueRear queueFront
Is it different from the normal queue?
Its type is customertype
Additional operation: update the waiting time
cust#: 5:arrT: 9transT: 6waitT: 3 4
cust#: 4arrT: 7transT: 5waitT: 5 6
cust#: 3arrT: 5transT: 5waitT: 7 8
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waitingCustomerQueueType
Is it different from the normal queue?
Its type is customerType
Additional operation: update the waiting time
(How) can we use the existing queueType?
Inheritance!!
What functions will need to be added?updateWaitingQueue to add one to each person's waiting time
What functions will be different?the constructor
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waitingCustomerQueueType
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updateWaitingQueue()
How can we add one to the waiting time for each customer?
Clumsy:– dequeue each person and add one to her waiting time
– add the updated customer to the end of the queue
Problem: how do we know when to stop– add a dummy customer to the end before you start
– stop when you reach her
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updateWaitingQueue()
Before:
queueRear queueFront
cust#: 5:arrT: 9transT: 6waitT: 3
cust#: 4arrT: 7transT: 5waitT: 5
cust#: 3arrT: 5transT: 5waitT: 7
cust#: 5:arrT: 9transT: 6waitT: 3
cust#: 4arrT: 7transT: 5waitT: 5
cust#: 3arrT: 5transT: 5waitT: 7
cust#: -1arrT: 0transT: 0waitT: 0
(add one to waitT)
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updateWaitingQueue()void waitingCustomerQueueType::updateWaitingQueue()
{
customerType cust;
cust.setWaitingTime(-1);
int wTime = 0;
addQueue(cust);
while(wTime != -1)
{
cust = front();
deleteQueue();
wTime = cust.getWaitingTime();
if(wTime == -1)
break;
cust.incrementWaitingTime();
addQueue(cust);
}
}
Can you think of a better way?
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Poisson Distribution
A good way to model events that occur "on the average"
E.g. suppose a bus arrives once every 10 minutes
The probability of a bus arrives in 1 minute is ~1/10
If λ is the probability an event occurs in an interval, the
probability that it occurs y times is
P(y) = λ ye- λ/y!
Busses Probability
0 (0.1)0 e -0.1 /0! =.9
1 (0.1)1 e -0.1 /1! =.09
2 (0.1)2 e -0.1 /2! =.0045
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Poisson Distribution
Using this to generate arrivals for the movie theater– generate a number between 0 and 1
– see if it is > e- λ (the probability of 0 arrivals)
no arrival arrival
|_________________________| 0 e- λ 1
bool isCustomerArrived(double arvTimeDiff)
{
double value;
value = static_cast<double> (rand()) / static_cast<double>(RAND_MAX);
return (value > exp(- 1.0/arvTimeDiff));
}
static_cast<double>? converts the expression to double