Judul: The Expected Value of the Queueing Length on the M/M/1 Queue Model Which Can be Repaired by Considering the Damage Level
Abstrak: Suatu antrean terjadi karena jumlah pelanggan yang datang melebihi jumlah fasilitas yang disediakan. Sistem dapat diandalkan saat server mungkin mengalami kegagalan atau kerusakan dan server dapat segera diperbaiki. Pada karya ilmiah ini, ditinjau sistem antrean M/M/1 yang dapat diperbaiki dengan mempertimbangkan tingkat kerusakan, dengan proses kedatangan pelanggan berdistribusi Poisson. Saat server mengalami kerusakan pada waktu kosong atau waktu sibuk, server segera menuju proses perbaikan. Setelah periode perbaikan selesai, server kembali dengan kondisi baru dan dapat melanjutkan sistem. Kemudian, dengan menyelesaikan persamaan diferensial untuk fungsi pembangkit peluang pada peluang steady-state, formulasi dari nilai harapan panjang antrean pada sistem dapat diperoleh. Simulasi numerik pengaruh parameter terhadap nilai harapan panjang antrean menunjukkan bahwa perubahan panjang antrean dan laju waktu perbaikan sensitif terhadap laju pelayanan, serta panjang antrean rata-rata dipengaruhi oleh laju tingkat kerusakan pada waktu sibuk dan laju waktu perbaikan., A queue occurs because the number of customers who come exceeds the number of provided facilities. The system can be relied on when the server may experience failure or damage, but it can be repaired immediately. In this manuscript, the M/M/1 queuing system that can be repaired by considering the level of damage is reviewed, where the customers arrival process is Poisson distributed. When the server crashes at an idle time or busy time, the server immediately goes to the repairing process. After the repairing process is over, the server returns with a new condition and the server’s operation can be continued. Furthermore, by solving the differential equation for the probability generating function at steady-state probability, the formulation of the expected value of the queue length in the system can be obtained. Numerical simulation of the effect of parameters on the expected value of queue length shows that changes in queue length and repairing time are sensitive to service rates, and the average queue lengths usually are affected by damage rates at busy times and repairing times rate.
Keyword: queue, probability generating function, expected value, repairable system

Judul: Analisis Model Antrean Berulang M/G/1 dengan Prioritas Preemptive Resume dan Collisions pada Kerusakan Server dan Penundaan Perbaikan
Abstrak: Sistem antrean M/G/1 adalah sistem antrean dengan proses kedatangan pelanggan berdistribusi Poisson, waktu layanan pelanggan berdistribusi umum, dan server tunggal. Pada karya ilmiah ini, terdapat dua jenis pelanggan yaitu pelanggan positif dan negatif. Pelanggan positif akan dilayani seperti biasa oleh server dan diambil dari antrean sesuai dengan disiplin yang ditentukan, sedangkan pelanggan negatif yang tidak mendapat pelayanan mengakibatkan kerusakan pada server dan dapat menghapus pelanggan yang ada dalam layanan pada sistem. Disiplin antrean yang digunakan dalam model ini adalah disiplin prioritas preemptive. Dengan menyelesaikan persamaan diferensial untuk fungsi pembangkit peluang dalam kondisi steady-state, diperoleh peluang lama server sedang menganggur, sibuk melayani pelanggan, menunggu perbaikan, dan sedang dalam perbaikan, serta ukuran kinerja lainnya. Kemudian, diperoleh juga nilai harapan periode sibuk., The M/G/1 queue system is a queue system with arrival process of customers follows Poisson process, customer service time has a general distribution, and has single server. In this manuscript, there are two types of customers, namely positive and negative customers. The positive customers are treated in the normal way by a server and are taken from a queue according to the specified queueing system, while the negative customer, which does not receive service, causes the server breakdown and removes the customer being in service from the system. The queue discipline used in this model is preemptive resume priority. By solving the differential equation for the probability generating function in steady-state condition, the probability that the server is idle, busy serving a customer, waiting for repair and under repair, and other performance measure was obtained. Finally, the expected value of busy period was obtained as well.
Keyword: expected value, Poisson, probability, retrial queue

Judul: Waxes, policosanols and aldehydes in sugarcane (Saccharum officinarum L.) and okinawan brown sugar (kokuto)
Abstrak: Waxes, long chain alcohols and aldehydes were found in several variants of sugarcane (Saccharum officinarum L.) and Kokuto, a non-centrifuged Okinawan cane brown sugar. Long chain alcohols, policosanols, have been reported to have beneficial effect to human health. The composition of wax in sugarcane was analyzed using HPLC with an evaporative light scattering detector. Sugarcane wax composed of 55–60% aldehydes, sterol esters and wax esters, 32–40% alcohols, and small amounts of triacylglycerols, acids and sterols. Extraction of policosanols performed effectively with hexane and methanol (20:1 v/v), while that of long chain aldehydes was with chloroform and methanol (2:1 v/v). Their composition was determined using GC with a flame ionization detector, whereas their compounds were identified using GC-MS. Sugarcane rinds contained up to 500 mg policosanols and 600 mg aldehydes per 100 g sample of Ni 22 cultivar. The content of policosanol and long chain aldehyde in Kokuto was influenced by its production systems. Compositional analysis of the end product confirmed the presence of policosanols and aldehydes up to 85 mg and 8 mg respectively per 100 g sample of Kokuto A, a product of brown sugar manufacture with open pan heating system. Octacosanol and octacosanal were found to be the major wax components in both sugarcane and Kokuto samples. This study revealed significant difference in content and composition of waxes, policosanols and long chain aldehydes between sugarcane parts, cultivars and harvesting times; also between Kokuto types and production methods.
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