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Bina Nusantara Model Antrian (Waiting Line Models ) Pertemuan 18: Mata kuliah: K0194-Pemodelan Matematika Terapan Tahun: 2008.

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Presentation on theme: "Bina Nusantara Model Antrian (Waiting Line Models ) Pertemuan 18: Mata kuliah: K0194-Pemodelan Matematika Terapan Tahun: 2008."— Presentation transcript:

1 Bina Nusantara Model Antrian (Waiting Line Models ) Pertemuan 18: Mata kuliah: K0194-Pemodelan Matematika Terapan Tahun: 2008

2 Bina Nusantara Learning Outcomes Mahasiswa akan dapat menjelaskan pengertian atrian, system antrian, struktur dan analisis pola kedatangan pada sistem antrian.

3 Bina Nusantara Outline Materi: Pengertian Antrian Sistem Antrian Struktur dasar model antrian Bentuk-bentuk model antrian Analisis pola kedatangan Contoh..

4 Bina Nusantara 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.

5 Bina Nusantara First studied by A. K. Erlang in –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. Waiting Lines

6 Bina Nusantara BankCustomersTellerDeposit etc. Doctor’sPatientDoctorTreatment office Traffic CarsTrafficControlled intersection Signalpassage Assembly linePartsWorkersAssembly Situation Arrivals ServersService Process Waiting Line Examples

7 Bina Nusantara 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. Waiting Line Components

8 Bina Nusantara Sistem Antrian

9 Bina Nusantara Car Wash Example

10 Bina Nusantara 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. Waiting Line Terminology

11 Bina Nusantara 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. Input Characteristics

12 Bina Nusantara 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

13 Bina Nusantara 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. Waiting Line Characteristics

14 Bina Nusantara 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. Bentuk-bentuk Model Antrian

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

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

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

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

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

20 Bina Nusantara 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.

21 Bina Nusantara 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.

22 Bina Nusantara


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