Jackson network in a random environment: strong approximation

We consider a Jackson network with regenerative input flows in which every server is subject to a random environment influence generating breakdowns and repairs. They occur in accordance with two independent sequences of i.i.d. random variables. We establish a theorem on the strong approximation of the vector of queue lengths by a reflected Brownian motion in positive orthant.

Prediction of Aircraft Waiting Time at Airport During Immediate Response to Disaster

Air transportation is especially critical to the immediate response that must be providedafter a natural disaster strikes a region. Airport operations are hindered by fluctuating waiting timesacross different operation types because of bottlenecks caused by unexpected amounts of aid goods,aircraft, and emergency workers. To address this problem, this study proposes a model forestimating the waiting time of an aircraft at an airport during the immediate response phase after adisaster. The proposed framework was developed by applying an open Jackson network with firstcomefirst-served, priority, and mixed-queuing disciplines. These disciplines are compared througha numerical example based on data acquired from the Great East Japan Earthquake of 2011. Theresults indicate that the mixed-queuing discipline reduces the waiting time for higher-priorityoperators, with permissible waiting times for lower-priority operators. The results of this studyreveal that various disaster response operations should be prioritized ahead of a natural disasteroccurring, such that the waiting times for those operators involved in life-saving activities can bereduced.

Customer and Cost Sharing in a Jackson Network

In this paper we consider a Jackson network of independent service stations. To improve upon the total expected queue length, the stations may redistribute the total arrival rate of customers over all queues. We investigate this situation by means of arrival rate games. These are cooperative TU cost games in which the stations are the players and the total cost of a coalition is linear in the total expected queue length. We show that these games are totally balanced; cooperation is beneficial to all stations. Further, we provide a tailor-made cost allocation rule that belongs to the core of the game.

ANALISA ANTRIAN PENGERJAAN BENANG HEAT TECHNOLOGY DENGAN METODE JACKSON NETWORK DI PT. KURABO MANUNGGAL TEXTILE INDUSTRIES

ABSTRAK PT.Kurabo Manunggal Textile Industries adalah salah satu perusahaan yang bergerak dibidang textile, dimana sebagian besar produksinya adalah benang heat technology. Masalah yang sering dihadapi adalah kurang efektifnya tenaga kerja dan mesin produksi, sehingga terjadinya bottleneck pada area packing. Untuk mencapai efisiensi kerja maka bottleneck harus diminimalkan dengan cara menyeimbangkan jumlah operator dan kecepatan mesin. Pada penelitian kali ini, penulis menganalisa sistem antrian yang ada pada area packing dengan metode Jackson Network, dan dengan menghitung performance mesin machconer dengan metode Overall Equipment Effectiveness. Hasil pengolahan data menunjukkan bahwa didapatkan waktu baku yang diperlukan untuk antrian sebesar 40 detik/bale jadi paling banyak 1 orang dapat melayani 3 sampai 4 mesin, dan untuk biaya layanan benang heat technology sebesar Rp 13.856,04/hari. Sementara biaya menunggu waktu packing sebesar Rp 83.810,69/hari. Sedangkan untuk nilai Overall Equipment Effectiveness diperoleh rata-rata sebesar 83,32%. Peneliti juga melakukan asumsi simulasi antrian dengan waktu standar yang telah ditetapkan oleh perusahaan yaitu sebesar 2400 detik/bale. Dengan menggunakan asumsi waktu standar didapatkan hasil 26 bale/hari tanpa adanya over time. Selain itu, dengan melakukan perbandingan dan eksisting didapatkan perbedaan yaitu untuk rata-rata jumlah bale didapatkan 6 bale/hari, tidak ada waktu menunggu, jarak antrian lebih cepat 1515,789 detik, dan untuk lama packing lebih cepat 570 detik serta tidak ada over time. Kata kunci: Antrian, Jackson Network, Overall Equipment Effectiveness