Queues

Min ChenSchool of Computer Science and Engineering Seoul National University

Data Structure: Chapter 4

Content

Definition of Queues Operators for Queues

Insert Remove Peek

Special Queues Circular Queues Priority Queues

Efficiency of Queues

Definition of Stacks

A Queue is a First-In-First-Out(FIFO) abstract data structure.

In a Queue, new item insert to the rear and the item in the front will be removed first

Rear

Front

Functional Requirements of a Queue

A queue is similar to a stack, except that you join the queue at one end and leave it at the other.

We shall again use an array to storing the items in the queue.

We shall need two pointers, one to indicate where the next item to be placed in the queue should be stored (rear), and another to indicate the location of the next item to be retrieved (front).

Analogy of Queue

Fig.1 Bus Queue: A Typical Queue

Analogy of Queue: Some everyday queues

7

Typical Java Interface for a queue of objects

Abstract Data Type (ADT): don’t care about how to realize, just use it.

public interface QueueInterface{

/** Task: Add item to back */public void enqueue(Object newEntry);/** Task: Removes and returns the front */public Object dequeue();/** Task: Retrieves front of queue without

removing */public Object getFront();/** Task: Determines whether the queue is

empty.*/public boolean isEmpty();/** Task: Removes all entries from the queue.

*/public void clear();

}

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A Simple ExampleQueue of strings after (a) enqueue adds Jim;

(b) Jess;

(c) Jill;

(d) Jane;

(e) Joe;

(f) dequeue retrieves, removes Jim;

(g) enqueue adds Jerry;

(h) dequeue retrieves, removes Jess.

Using a Queue to Simulate a Waiting Line

Using a Queue to Simulate a Waiting Line: Customer Enqueues for Service

Using a Queue to Simulate a Waiting Line: Customer Enqueues for Service 2

Types of Queuing Systems Single queue, single server Single queue, multiple servers:

Improve processes, e.g., most banks use a snake queue instead individual lines at each teller.

2 queues, 2 servers vs. 1 queue, 2 servers ▪ Increase utilization ratio

Electronic Queuing System (see animation)

Multiple queues, single server Intersection Management byTraffic Light (see animation)

Multiple queues, multiple servers

Inpatient customer strategies

Customers who intended to join the line but don’t

Customers who join, then leave Jumping from queue to queue Jumping to newly opened line Follow the employee Two line strategy (bring spouse or

kids), then merge into a faster queueSee Animation

Why Study Queues

People hate to wait in queues – shorter queues may result in increased efficiency.

Some customers leave shopping carts full of groceries at the checkout counters and frozen and cold food are wasted.

Operators for Queues: Insert

Insert: insert a data item to the rear of the queue

Fig.2 Insert Operator in Queues

FrontRear

Program

Operators for Queues: Remove

Remove: Remove a data item at the front of the queue

Fig.3 Remove Operator in Queues

FrontRear

Program

Operators for Queues: Peek

Peek: Get a data item at the front of the queue without removing

Fig.4 Peek Operator in Queues

FrontRear

Special Queues 1: Circular Queues Circular Queues

We shall treat the underlying array as a circular buffer. Problem Statement

FrontRear

No Space

Rear

Fig.5 Insertion of Circular Queues

Circular Queues: Simple Implementation

Items to be enqueued will be written in the array at queue[rear].

Items to be dequeued will be read from queue[front].

After each writing, top is incremented by one.

After each reading, rear is incremented by one.

Incrementing of rear and front is always modulo queue.length.

The priority queue is a data structure that only allows access to the “minimum” item in a set.

Special Queues 2: Priority Queue

Priority Queue: Realization of Network Simulation

Time

Simulation Kernel

Intrpt Code

Module ID

Event ID

Event Type Discrete event

simulation (desired simulation time is used to set priorities)

Special Queues 2: Priority Queue

The items in Priority Queue has priority

Insertion in Priority Queue is different

Fig.6 Insertion of Priority Queues

FrontRear

2199 45

81

7592112214

Implementing Priority Queues

Goals: fast findMin, deleteMin, insert findMin: Identify entry whose key is lowest deleteMin: remove entry whose key is lowest Insert: any entry may be inserted at any time

How should we implement a priority queue? Option 1: a linked list Option 2: a sorted linked list Option 3: a binary search tree Option 4: a balanced binary search tree

Problem rised by Priority Queue

Starving When items with higher priority are

inserted into the queue, the items with lower priority will be starved

Fairness problems should be considered

Efficiency of Queues

In conventional queues, items can be both pushed and popped from a stack in constant O(1) time

For priority queues, insertion runs in O(N) time, whereas deletion takes O(1) time

Thank you!