Queuing theory is used to determine optimal service levels by using mathematical formulas and simulations to calculate variables like wait times and average service times based on arrival rates and facility capacities. It was originally developed for telephone systems but is now used in various contexts like manufacturing, transportation, and more. Key aspects of queuing systems include arrival patterns, service disciplines, number of service channels, service times, system capacities, and customer abandonment behavior. Common queuing models include the single-channel M/M/1 model and multiple-channel M/M/s models.

1. Antrian (Queuing)M. Sitepu1Antrian

2. Queuing is techniques developed by the study of people standing in line to determine the optimum level of service provision. In queuing theory, mathematical formulae, or simulations, are used to calculate variables such as length of time spent standing in line and average service time, which depend on the frequency and number of arrivals and the facilities available. The results enable decisions to be made on the most cost-effective level of facilities and the most efficient organization of the process. Early developments in queuing theory were applied to the provision of telephone switching equipment but the techniques are now used in a wide variety of contexts, including machine maintenance, production lines, and air transportation.M. Sitepu2Antrian

3. Queuing theory deals with problems that involve queuing (or waiting). Some examples of queuing include:Banks or supermarkets—customers waiting for service

4. Computers—users waiting for a response

5. Public transportation—riders waiting for a bus/train

6. Failure situations—machinery owners waiting for a failure to occurQueues form because resources are limited. In fact, it makes economic sense to have queues.In designing queuing systems, a balance is needed between service to customers (which means short queues and implies many servers) and cost (too many servers waste funds).Most queuing systems can be divided into individual sub-systems, consisting of entities queuing for some activity.M. Sitepu3Antrian

7. Queuing theory applies to any system in equilibrium, as long as nothing in the black box is creating or destroying tasks (arrivals=departures).M. Sitepu4Antrian

8. Queuing theory mathematics gets very complicated because it applies probability and statistics to queuing systems.What is the probability that the arriving task will find a device busy?On average, how many tasks are ahead of the task that just entered the system?The Early DerivationsA single server queue is a combination of a servicing facility that accommodates one customer at a time (server) + a waiting area (queue).These components together are called a system.M. Sitepu5Antrian

9. The early queuing work treated the system as a single homogeneous “server,” without regard to discrete components or types of workloads. These systems were called M/M/1 queues.Later, this work was expanded to include multiple homogeneous servers inside the black box.Queuing MethodsFour types of queuing techniques commonly implementedFirst in First Out (FIFO).Weighted Fair QueuingCustom QueuingPriority QueuingM. Sitepu6Antrian

10. First In First Out (FIFO)Packets are transmitted in the order in which they arrive.Single Queue, Packet droppingWeighted Fair Queuing (WFQ)Packets are classified into different "conversation messages“

11. Each queue has some priority value or weight assigned to it.

12. Low volume traffic is given higher priority over high volume traffic

13. After accounting for high priority traffic the remaining bandwidth is divided fairly among multiple queues (if any) of low priority traffic.M. Sitepu7Antrian

14. Custom QueuingSeparate queues maintained for separate classes of traffic.

15. The algorithm requires a byte count to be set per queue.

16. That many bytes rounded of to the nearest packet is scheduled for delivery.

17. This ensures that the minimum bandwidth requirement by the various classes of traffic is met.

18. CQ round robins through the queues, picking the required number of packets from each.

19. If a queue is of length 0 then the next queue is serviced.M. Sitepu8Antrian

20. Priority Queuing4 traffic priorities Defined.- high, medium, normal and low.

21. Incoming traffic is classified and enqueued in either of the 4 queues.

22. Classification criteria

23. Unclassified packets are put in the normal queue.

24. The queues are emptied in the order of - high, medium, normal and low. In each queue, packets are in the FIFO orderM. Sitepu9Antrian

25. Queuing Networks After much more work in the queuing theory field (approximately 20 years), a new technique was developed that divided computer system into networks of queues.MVAThis new technique is called Mean Value Analysis. It allowed a computer system to be segregated by workload classes(transactions, arrival rates, numbers of clients) as well as components (CPU, disk, etc.)Systems were also delineated as being “open” or “closed.”M. Sitepu10Antrian

26. Mean value analysis is an iterative approach of solving three primary equations for class “r” workload at queue “i.”The three equations provide solutions for the residence time (response time, per class, per queue), the throughput, and the queue length (number of class “r” tasks at queue “i”).Software and hardware contention can be modeled using these techniques.M. Sitepu11Antrian

27. Model AntrianSederhana1.Pendahuluan2.Struktur Model Antrian (The Structure of Queuing Model)3. Single-Channel Model4. Multiple-Channel Model5. Model BiayaMinimum (Cost Minimization Models)6. Non-Poisson Model7. Model Self Service Facilities8. Model Network (Queuing Network)M. Sitepu12Antrian

28. 1. PendahuluanSistem antrian sangat diperlukan ketika para pelanggan (konsumen) menungguuntukmendapatkanjasapelayananContohpenggunaansistemantriandalammelancarkanpelayanankepadapelangganataukonsumen :Mahasiswamenungguuntukregistrasidanpembayaranuangkuliah

29. Pelangganmenunggupelayanandidepankasir

30. Para calonpenumpang KA menunggupelayanandiloketpenjualantiket

31. Para pengendarakendaraanmenungguuntukmendapatkanpelayananpengisianbahanbakardi SPBUTeoriantriandiciptakanoleh A.K. Erlang (ahlimatematikDenmark) padatahun 1909.M. Sitepu13Antrian

32. 2. Struktur Model Antrian (The Structure of Queuing Model)Gambar 1. Struktur sistem antrianM. Sitepu14Antrian

33. Gambar 1 menunjukkan struktur umum suatu model antrian yang memiliki 2 komponen :1) Garis tungguatauantrian (queue)2) Fasilitaspelayanan (servicefacility)Gambar 2. Pelayanan nasabah di bankM. Sitepu15Antrian

34. M. Sitepu16Antrian

35. ProsedurteknikantrianLangkah 1 : Tentukansistemantrianapa yang harusdipelajari.Langkah 2 : Tentukan model antrian yang sesuaidalammenggambarkansistem.ContohdalamkasuspompabensindiSPBU,terdapattiga model yang dapat digunakan :tigapompauntuk premium dengansatugaristunggu

36. tigapompauntuk premium denganmasing-masingmemilikigaristunggu