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: Nilai Harapan Panjang Antrean pada Model M/M/2 dengan Server Heterogen dan Multiple Vacation
Abstrak: Model M/M/2 dengan server heterogen dan multiple vacation adalah model antrean dengan proses kedatangan pelanggan mengikuti proses Poisson, laju pelayanan berdistribusi eksponensial, dan terdapat dua server heterogen dengan laju pelayanan berbeda. Vacation adalah periode acak tidak tersedianya server ketika tidak ada pelanggan dalam antrean pada saat penyelesaian layanan. Pada karya ilmiah ini, kedua server diperbolehkan mengambil periode vacation ketika server tidak menemukan pelanggan dalam antrean. Pada akhir periode vacation, pelayanan akan dimulai kembali jika terdapat setidaknya satu pelanggan dalam antrean. Jika tidak, server akan memasuki periode vacation kembali dan demikian seterusnya. Mekanisme seperti ini disebut sebagai multiple vacation. Ukuran kinerja yang dibahas yaitu nilai harapan panjang antrean. Langkah awal yang dilakukan yaitu menentukan rate matriks dan peluang stasioner model dengan metode solusi matriks geometrik. Kemudian, dengan dekomposisi stokastik bersyarat, diperoleh panjang antrean bersyarat. Akhirnya, dengan formulasi nilai harapan jumlah peubah acak yang saling bebas, diperoleh nilai harapan panjang antrean untuk model., The M/M/2 model with heterogeneous servers and multiple vacations is a queuing model with the customer arrival process following the Poisson process, the service rate is exponentially distributed, and there are two heterogeneous servers with different service rates. Vacation is a random period of server unavailability when there are no customers in line at the time of service completion. In this manuscript, each server is allowed to take a vacation when the server finds no customer waiting in the line. At the end of a vacation period, service will restart if there is at least one customer in the queue. Otherwise, the server will enter the vacation period again and so on. This mechanism is known as multiple vacation. The performance measure discussed is the expected value of the queueing length. The first step is to determine the rate matrix and the stationary probability of the model using the geometric matrix solution method. Then, by conditional stochastic decomposition, the conditional queue length is obtained. Finally, by using expected value formulation for sum of independent random variables, the expected value of the queueing length for the model is obtained.
Keyword: queue, conditional stochastic decomposition, expected value, multiple vacations

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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