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Agner Krarup Erlang , a Danish engineer who worked for the Copenhagen Telephone Exchange, published the first paper on queueing theory in 1909. [ 3 ] Agner Krarup Erlang, seorang Denmark insinyur yang bekerja di Kopenhagen Telepon Exchange, menerbitkan makalah pertama tentang teori queueing pada tahun 1909. [3]

David G. Kendall introduced an A/B/C queueing notation in 1953. David G. Kendall memperkenalkan percobaan A / B / C queueing notasi pada tahun 1953. Important work on queueing theory used in modern packet switching networks was performed in the early 1960s by Leonard Kleinrock . Penting bekerja pada teori queueing modern yang digunakan dalam packet switching jaringan dilakukan pada awal tahun 1960-an oleh Leonard Kleinrock.

[ edit ] Application to telephony [Sunting] Aplikasi untuk telepon

The public switched telephone network ( PSTN ) is designed to accommodate the offered traffic intensity with only a small loss. The publik beralih jaringan telepon (PSTN) dirancang untuk mengakomodasi lalu lintas intensitas yang ditawarkan dengan hanya kerugian kecil. The performance of loss systems is quantified by their grade of service , driven by the assumption that if sufficient capacity is not available, the call is refused and lost. [ 4 ] Alternatively, overflow systems make use of alternative routes to divert calls via different paths — even these systems have a finite traffic carrying capacity. [ 4 ] The kinerja sistem kehilangan dihitung oleh pelayanan kelas, didorong oleh asumsi bahwa jika kapasitas yang memadai tidak tersedia, panggilan tersebut akan ditolak dan kalah. [4] Atau, sistem overflow menggunakan rute alternatif untuk mengalihkan panggilan melalui jalan yang berbeda – bahkan sistem ini memiliki kapasitas lalu lintas terbatas. [4]

However, the use of queueing in PSTNs allows the systems to queue their customer’s requests until free resources become available. Namun, penggunaan queueing di PSTNs memungkinkan sistem antrian permintaan pelanggan mereka sampai sumber daya tadi tersedia gratis. This means that if traffic intensity levels exceed available capacity, customer’s calls are here no longer lost; they instead wait until they can be served. [ 5 ] This method is used in queueing customers for the next available operator. Ini berarti bahwa jika tingkat intensitas lalu lintas melebihi kapasitas tersedia, pelanggan telepon di sini tidak lagi hilang; mereka alih-alih menunggu sampai mereka dapat dilayani. [5] Metode ini digunakan dalam antrian pelanggan untuk operator yang tersedia berikutnya.

A queueing discipline determines the manner in which the exchange handles calls from customers. [ 5 ] It defines the way they will be served, the order in which they are served, and the way in which resources are divided between the customers. [ 5 ] [ 6 ] Here are details of four queueing disciplines: Sebuah disiplin queueing menentukan cara di mana pertukaran menangani panggilan dari pelanggan. [5] ini mendefinisikan cara mereka akan dilayani, urutan di mana mereka melayani, dan bagaimana sumber daya yang dibagi antara para pelanggan. [5] [6] Berikut adalah rincian dari empat queueing disiplin:

First in first out Pertama keluar pertama
This principle states that customers are served one at a time and that the customer that has been waiting the longest is served first. [ 6 ] Prinsip ini menyatakan bahwa pelanggan dilayani satu per satu waktu dan bahwa pelanggan yang telah menunggu lama dilayani pertama. [6]
Last in first out Terakhir di pertama keluar
This principle also serves customers one at a time, however the customer with the shortest waiting time will be served first. [ 6 ] Also known as a stack . Prinsip ini juga melayani pelanggan satu per satu waktu, namun pelanggan dengan waktu tunggu terpendek akan dilayani pertama. [6] Juga dikenal sebagai stack.
Processor sharing Processor berbagi
Customers are served equally. Pelanggan dilayani sama. Network capacity is shared between customers and they all effectively experience the same delay. [ 6 ] Kapasitas jaringan dibagi antara pelanggan dan mereka semua pengalaman efektif penundaan yang sama. [6]
Priority Prioritas
Customers with high priority are served first. [ 6 ] Pelanggan dengan prioritas tinggi dilayani pertama. [6]

Queueing is handled by control processes within exchanges, which can be modelled using state equations. [ 5 ] [ 6 ] Queueing systems use a particular form of state equations known as Markov chains which model the system in each state. [ 5 ] Incoming traffic to these systems is modelled via a Poisson distribution and is subject to Erlang’s queueing theory assumptions viz. [ 4 ] Queueing ditangani oleh proses kontrol dalam pertukaran, yang dapat dimodelkan dengan menggunakan persamaan negara. [5] [6] queueing sistem menggunakan bentuk tertentu persamaan negara yang dikenal sebagai rantai Markov model mana sistem di setiap negara. [5] Incoming lalu lintas ke sistem ini dimodelkan melalui Poisson distribution dan tunduk pada teori queueing Erlang’s asumsi yaitu. [4]

  • Pure-chance traffic – Call arrivals and departures are random and independent events. [ 4 ] Pure-kesempatan lalu lintas – Call kedatangan dan keberangkatan yang acak dan peristiwa independen. [4]
  • Statistical equilibrium – Probabilities within the system do not change. [ 4 ] Statistik kesetimbangan – Probabilitas dalam sistem tidak berubah. [4]
  • Full availability – All incoming traffic can be routed to any other customer within the network. [ 4 ] Kendali ketersediaan – Semua masuk lalu lintas dapat dialihkan ke pelanggan lain dalam jaringan. [4]
  • Congestion is cleared as soon as servers are free . [ 4 ] Kemacetan akan dihapus sesegera server gratis. [4]

Classic queueing theory involves complex calculations to determine call waiting time, service time, server utilisation and many other metrics which are used to measure queueing performance. [ 5 ] [ 6 ] Teori queueing klasik melibatkan perhitungan kompleks untuk menentukan waktu menunggu panggilan, waktu layanan, pemanfaatan server dan metrik lainnya yang digunakan untuk mengukur kinerja queueing. [5] [6]