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Queues provide services in computer science, transport, and operations research where various entities such as data, objects, persons, or events are stored and held to be processed later. In these contexts, the queue performs the function of a buffer. Another usage of queues is in the implementation of breadth-first search.
In the study of queue networks one typically tries to obtain the equilibrium distribution of the network, although in many applications the study of the transient state is fundamental. Queueing theory is the mathematical study of waiting lines , or queues . [ 1 ]
While priority queues are often implemented using heaps, they are conceptually distinct from heaps. A priority queue is an abstract data type like a list or a map; just as a list can be implemented with a linked list or with an array, a priority queue can be implemented with a heap or another method such as an ordered array.
Representation of a FIFO queue with enqueue and dequeue operations. Depending on the application, a FIFO could be implemented as a hardware shift register, or using different memory structures, typically a circular buffer or a kind of list. For information on the abstract data structure, see Queue (data structure).
Imagine an application that had no easy way to measure response time. If the mean number in the system and the throughput are known, the average response time can be found using Little’s Law: mean response time = mean number in system / mean throughput. For example: A queue depth meter shows an average of nine jobs waiting to be serviced.
One example application of the double-ended priority queue is external sorting. In an external sort, there are more elements than can be held in the computer's memory. The elements to be sorted are initially on a disk and the sorted sequence is to be left on the disk. The external quick sort is implemented using the DEPQ as follows:
Its amortized time is O(1) if the persistency is not used; but the worst-time complexity of an operation is O(n) where n is the number of elements in the double-ended queue. Let us recall that, for a list l, |l| denotes its length, that NIL represents an empty list and CONS(h, t) represents the list whose head is h and whose tail is t.
An application then registers a software routine that "listens" for messages placed onto the queue. Second and subsequent applications may connect to the queue and transfer a message onto it. The queue-manager software stores the messages until a receiving application connects and then calls the registered software routine.