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Learning Outcomes

Learning Outcomes. Mahasiswa akan dapat menjelaskan pengertian atrian, system antrian, struktur dan analisis pola kedatangan pada sistem antrian. Outline Materi:. Pengertian Antrian Sistem Antrian Struktur dasar model antrian Bentuk-bentuk model antrian Analisis pola kedatangan Contoh .

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Learning Outcomes

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  1. Learning Outcomes • Mahasiswa akan dapat menjelaskan pengertian atrian, system antrian, struktur dan analisis pola kedatangan pada sistem antrian.

  2. Outline Materi: • Pengertian Antrian • Sistem Antrian • Struktur dasar model antrian • Bentuk-bentuk model antrian • Analisis pola kedatangan • Contoh ..

  3. Pengertian • Istilah “antrian” atau disiplin “garis tunggu” atau “waiting lines” menunjukan pada kondisi dimana kedatangan dipilih untuk dilayani. Prosedur yang umum diguna-kan adalah kedatangan menempati garis tunggu atas dasar yang : “datang pertama dilayani pertama” (FCFS), walaupun beberapa prioritas dapat mengubah pola pelayanan ini, namum analisis ini tidak mempertimbangkan kemungkinan itu.

  4. Waiting Lines • First studied by A. K. Erlang in 1913. • Analyzed telephone facilities. • Body of knowledge called queuing theory. • Queue is another name for waiting line. • Decision problem: • Balance cost of providing good service with cost of customers waiting.

  5. Waiting Line Examples Situation Arrivals Servers Service Process Bank Customers Teller Deposit etc. Doctor’s Patient Doctor Treatmentoffice Traffic Cars Traffic Controlledintersection Signal passage Assembly line Parts Workers Assembly

  6. Waiting Line Components • Arrivals: Customers (people, machines, calls, etc.) that demand service. • Service System: Includes waiting line and servers. • Waiting Line (Queue): Arrivals waiting for a free server. • Servers: People or machines that provide service to the arrivals.

  7. Sistem Antrian

  8. Car Wash Example

  9. Waiting Line Terminology • Queue: Waiting line. • Arrival: 1 person, machine, part, etc. that arrives and demands service. • Queue discipline: Rules for determining the order that arrivals receive service. • Channels: Parallel servers. • Phases: Sequential stages in service.

  10. Input Characteristics • Input source (population) size. • Infinite: Number in service does not affect probability of a new arrival. • A very large population can be treated as infinite. • Finite: Number in service affects probability of a new arrival. • Example: Population = 10 aircraft that may need repair. • Arrival pattern. • Random: Use Poisson probability distribution. • Non-random:Appointments.

  11. Number of events that occur in an interval of time. Example: Number of customers that arrive each half-hour. Discrete distribution with mean =  Example: Mean arrival rate = 5/hour . Probability: Time between arrivals has a negative exponential distribution. Poisson Distribution

  12. Waiting Line Characteristics • Line length: • Limited: Maximum number waiting is limited. • Example: Limited space for waiting. • Unlimited: No limit on number waiting. • Queue discipline: • FIFO (FCFS): First in, First out.(First come, first served). • Random:Select next arrival to serve at random from those waiting. • Priority: Give some arrivals priority for service.

  13. Bentuk-bentuk Model Antrian • Single channel, single phase. • One server, one phase of service. • Single channel, multi-phase. • One server, multiple phases in service. • Multi-channel, single phase. • Multiple servers, one phase of service. • Multi-channel, multia-phase. • Multiple servers, multiple phases of service.

  14. Service system Served units Arrivals Queue Service facility Ship unloading system Ships at sea Empty ships Waiting ship line Dock Single Channel, Single Phase

  15. Single Channel, Multi-Phase Service system Served units Arrivals Queue Service facility Service facility McDonald’s drive-through Cars in area Cars& food Waiting cars Pay Pick-up

  16. Service system Served units Service facility Queue Arrivals Service facility Example: Bank customers wait in single line for one of several tellers. Multi-Channel, Single Phase

  17. Service system Served units Service facility Service facility Queue Arrivals Service facility Service facility Example: At a laundromat, customers use one of several washers, then one of several dryers. Multi-Channel, Multi-Phase

  18. Random: Use Negative exponential probability distribution. Mean servicerate =  6 customers/hr. Mean service time = 1/ 1/6 hour = 10 minutes. Non-random:May be constant. Example: Automated car wash. Analisis Pola Pelayanan

  19. Assumptions in the Basic Model • Customer population is homogeneous and infinite. • Queue capacity is infinite. • Customers are well behaved (no balking or reneging). • Arrivals are served FCFS (FIFO). • Poisson arrivals. • The time between arrivals follows a negative exponential distribution • Service times are described by the negative exponential distribution.

  20. Steady State Assumptions • Mean arrival rate , mean service rate , and the number of servers are constant. • The service rate is greater than the arrival rate. • These conditions have existed for a long time.

  21. Terima kasih Semoga berhasil

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