Judul: Nilai Harapan Waktu Tunggu Pelanggan pada Antrean M/G/2 dengan Server Heterogen di Bawah Disiplin Layanan Terkendali
Abstrak: Sistem antrean M/G/2 adalah suatu sistem antrean dengan proses kedatangannya menyebar Poisson, waktu layanan pelanggan terdistribusi umum, dan banyak server yang digunakan adalah dua server. Pada karya ilmiah ini, dua server yang digunakan dalam layanan adalah server yang heterogen yaitu server-1 memiliki pelayanan yang lebih cepat dibandingkan dengan server-2. Disiplin antrean yang digunakan dalam model ini adalah disiplin layanan terkendali di mana aturan First Come First Served (FCFS) dilanggar oleh sistem. Ukuran kinerja yang dibahas adalah nilai harapan waktu tunggu pelanggan di dalam sistem. Langkah awal untuk menentukan nilai harapan waktu tunggu adalah mencari peluang stasioner untuk antrean M/G/2 dengan disiplin layanan terkendali. Selanjutnya, menyelesaikan fungsi pembangkit peluang banyaknya pelanggan dengan menggunakan peluang stasioner tersebut, maka diperoleh nilai harapan waktu tunggu banyaknya pelanggan di dalam sistem. Akhirnya dengan menggunakan teorema Little’s Law didapatkan fungsi nilai harapan waktu tunggu pelanggan., The M/G/2 queue system is a system with arrival process of customers follows Poisson distribution, customers service time has a general distribution, and has two servers. In this manuscript, the two servers used in the service are heterogeneous, namely server-1 has a faster service rate than server-2. The queuing discipline used in this model is a controlled service discipline in which the First Come First Served (FCFS) rule is violated by the system. The performance measure discussed is expected value of the customer waiting time in the system. The initial step to determine the expected value of waiting time was to find stationary probability for M/G/2 queuing system with controlled service discipline. Then, by completing the probability generating function for the number of customers using the stationary probability, the function of the expected value of the number customers in system was obtained. Finally, by using the Little’s Law theorem the function of the expected value of customers waiting time was obtained.
Keyword: expected value, heterogeneous servers, stationary probability, queue

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: Insecticidal Activity of Essential Oils Leaves of Cinnamomum spp. (Lauraceae) against Crocidolomia pavonana and Their Phytotoxicity on Broccoli Seedlings
Abstrak: Essential oils from leaves of 13 species of Cinnamomum were tested for their insecticidal activity on the cabbage head caterpillar Crocidolomia pavonana with leaf immerse method. The results showed that the treatment with 1% (w/v) essential oils leaves of C. celebicum, C. multiflorum, C. sintoc, and C. verum caused 21.45, 93.65, 60.30, and 76.10% mortality, respectively. Based on the results of phytotoxicity and insecticidal activity tests, C. multiflorum oil was further tested at 6 concentration levels. In all treatments, larval mortality has occurred at 24 hours after treatment (HAT) and increased at 48 HAT. LC50 of C. multiflorum oil at 24 and 48 HAT was 0.504 and 0.396%, respectively. The treatment with C. multiflorum oil at ≤0.31% did not inhibit the development of C. pavonana larvae. Determination of the chemical constituents of Cinnamomum oils were carried out by gas chromatography-mass spectrometry (GCMS). Totally, 345 compounds were identified. Methyleugenol constituted the main component (49.4%) of leaf essential oil of C. multiflorum and was assumed to be responsible for the insecticidal activity of the oil against C. pavonana larvae. LC50 of pure methyleugenol obtained at 0.365% (48 HAT) and 0.363% (72 HAT). The results showed that C. multiflorum was more effective with LC50 value equivalent to methyleugenol content of 0.32% (24 HAT) and 0.24% (48 HAT).
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