CAPACITY & PERFORMANCE EVALUATION (CPE)METODA ANALISA KINERJA SISTEMSYSTEM PERFORMANCE ANALYSIS METHODOLOGY

Kinerja Server TunggalSingle Server Performance

Throughput X Banyaknya transaksi yg dapat diselesaikan dalam selang waktu tertentuNumber of transactions can be completed during certain time interval

System workload N Banyaknya beban (transaksi) yg ada dalam sistem dalam selang waktu tertentuTotal workload (queued transactions) in the system during certain time interval

Response time R Waktu yg diperlukan untuk menyelesaikan satu transaksi sejak memasuki sistem hingga selesai Amount of time needed to complete a transaction since entering the system up to well done

Formula (1): R = N / X Coba ini: R= 3.092000 N= 100.0000 32.34Try this N= 3.5000 X= 80.0000 0.043750

X= 17.0000 R= 3.092000 52.56

Banyaknya siklus CPU yang digunakan untuk memprosesNumber of CPU cycle consumed for certain process

CPU busy U atau Utilisasi - adalah nisbah CPU-time yg dikonsumsi selama selang waktu tertentuor Utilization - is ratio of consumed CPU-time against calendar time frame

Formula (2):

Service time S CPU-time yg diperlukan untuk menyelesaikan satu transaksiCPU-time needed to complete a transaction

© 2003 Deru Sudibyo

==> X= ==> R= ==> N=

CPU-time TCPU

U = TCPU / T

Formula (3): U = S * X Coba ini S= 0.085000 X= 17.0000 144.50%Try this S= 0.085000 U= 80.00% 9.4118

X= 17.0000 U= 100.00% 0.058824

Kinerja Server MajemukMulti Server PerformanceUntuk sejumlah c CPU server, formula (1) dapat diturunkan menjadi sebagai berikutFor c number of server CPUs, formula (1) can be derived as follow:

Formula (4) U = N * m * S / (c * R) dimana R response timewhere N system workload

m kerapatan page-in selama menyelesaikan sekali transaksipagi-in frequency during performing a transaction

S service timec banyaknya CPU

number of CPUsU utilisasi atau tingkat kesibukan CPU

utilization or level of CPU busy

Coba ini: N= 30.0000 U= 100.00%Try this: S= 0.058800 c= 8 51.597000 sec

m= 234.0000

N= 35.0000 R= 6.100000S= 0.082500 c= 5 94.67%m= 10.0000

Model Linier untuk CPU dan I/O Majemuk Linear Model for Multi CPU and Multi I/O Services

==> U= ==> X= ==> S=

==> R=

==> U=

Utilisasi sistem yang dilayani oleh sejumlah c buah CPU dan k buah saluran I/O dengan asumsi semuanya seragam. Model ini diturunkan oleh Boyse dan Warn, sebagai berikut:

System utilization which is served by c number of equal CPUs and k number of equal I/O channels. This model was derived by Boyse and Warn:

Formula (5) Fungsi min() ini untuk menghindari U > 100% seperti yang mungkin terjadi pada formula (4)Function of min() is to avoid possibility U > 100% as one probably happen with formula (4)

where

Coba ini: k= 19 3.700000Try this: S= 0.185600 c= 2 45.38%

Model Exponensial untuk CPU dan I/O Majemuk Exponential Model for Multi CPU and Multi I/O Services

System utilization which is served by c number of equal CPUs and k number of equal I/O channels. This model is more realistic than the linear one.

Formula (6) U = d * S / c

for n = 1, 2,…, c

for n = c+1, c+2, … k

Coba latihan ini dan bandingkan dengan kalkulator anda ###

Try this exercise and compare with your calculator ###

###

U = Min(u,1)

u = k / [c * (1 + SIO/S)]SIO=

==> U=

Utilisasi sistem yang dilayani oleh sejumlah c buah CPU dan k buah saluran I/O dengan asumsi semuanya seragam. Model ini lebih mendekati kenyataan ketimbang model linier

dimana d diperoleh dengan perhitungan sebagai berikut: where d is obtained from the following calculation:

┌ C(n,k) * S/SIO

│ rn = │ │ n! * C(n,k) * S └ _____________ cn-c * c! * SIO

k

p0 = 1/[1 + S rn] n=1

for n = 1, 2, .., k S= 0.185600 ###

3.700000 ###

c= 5 0.050162162 ###

k= 49 8.85428E-19 ###14.80296938 ###1.681971118

d= 8.800965261

U= 32.67%

Paling baik untuk berlatih formula ini adalah dengan cara membuat program sederhana. The best way to practise this formula is by writing a simple program

Nisbah PengamatanCapture Ratio

Dimana merupakan utilisasi yg diukur pada tingkat program aplikasi is utilization measured at application program level

merupakan utilisasi yg diukur pada tingkat OSis utilization measured at OS level

pn = rn * p0 SIO=

k

Lq = S [n - c] * pn

n=c+1

S/SIO=

p0=

Lq=

Tq=Tq = Lq*[S + SIO] / [k - Lq]

d = k / [Tq + S + SIO]

Untuk meningkatkan ketelitian pengukuran, sebaiknya perhitungan utilisasi dikoreksi dengan nilai nisbah pengamatan. Karena tidak semua siklus CPU terukur dan termanfaatkan oleh program aplikasi. OS sendiri juga membenani sistem. Nilai nisbah pengamatan adalah:

To improve accuracy of measurement when calculating system utilization, suggested to adjust it with capture ration. Because not all CPU cycle are measurable and consumed by application programs. OS overhead is also a workload of the system. Value of capture ratio is:

CR = UAPPL / UOS UAPPL

UOS

1. Angka-angka yang Diperoleh dari Alat-alat Pemantau

Cobalah contoh ini:

Formula (7) R = ?

Coba contoh ini:

Formula (8) X = ?

PENERAPAN CPE UNTUK PERENCANAAN SISTEM

Di lapangan, pada kenyataannya angka-angka utilisasi, response time, throughput dan beban kerja lain sistem tidak perlu dihitung lagi. Ada program khusus seperti RMF maupun produk-produk program canggih lainnya yang sudah menyediakan angka-angka tersebut secara otomatis. Bahkan angka-angka tersebut lebih teliti karena pengukuran langsung, ketimbang pendugaan dengan rumus-rumus statistik pada sheet sebelumnya. Yang penting, bagaimana memanfaatkan angka-angka tersebut untuk mengatur dan merencanakan kapasistas sistem anda. Berikut ini penjelasan sederhana tentang bagaimana penerapan di lapangan.

Response time, R Waktu yg diperlukan untuk menyelesaikan satu transaksi sejak memasuki sistem hingga selesai. Angka dari alat pemantau biasanya terinci untuk tiap jenis beban. Untuk keperluan pengaturan kinerja, kita bisa pilih beban mana yg akan dianalisa. Tetapi untuk keperluan perencanaan, angka ini harus satu, yaitu angka rata-rata keseluruhan sistem. Maka harus dihitung sendiri angka rata-rata R terboboti. Pilih hanya selang waktu yang paling sibuk. Faktor pembobot yang paling berkaitan adalah pemakaian CPU time.

R1 R2 R3 R4

t1 t2 t3 t4

n n R = S(ti * Ri) / S ti

i=1 i=1

CPU busy, U Atau utilisasi - adalah nisbah CPU-time yg dikonsumsi selama selang waktu tertentu. Biasanya, angka tunggal untuk keseluruhan sistem sudah dilaporkan oleh alat pemantau, sehingga tidak perlu dirata-ratakan lagi.

Throughput, X Banyaknya transaksi yg dapat diselesaikan dalam selang waktu tertentu. Bisanya angka ini seperti R, menyebar terinci pada setiap beban. Maka cara mendapatkannyapun dengan merata-ratakan seperti R di atas.

X1 X2 X3 X4

t1 t2 t3 t4

n n X = S(ti * Xi) / S ti

i=1 i=1

CPU service time, S Jumlah CPU-time yg dimanfaatkan untuk melayani satu transaksi. Tergantung alatnya, angka ini ada yang dilaporkan apa adanya, ada pula yang dilaporkan berupa angka service rate (misal dalam RMF). Karena service rate/detik = 1/S, maka tinggal membalik angka itu saja.

2. Angka-angka Pabrikan

Konsumsi processor power untuk sistem dirumuskan sebagai berikut:

Formula (9)

3. Langkah-langkah Perhitungan Kapasitas

Langkah 1

335.0000

Jumlah CPU-time yg dimanfaatkan untuk melayani satu transaksi. Tergantung alatnya, angka ini ada yang dilaporkan apa adanya, ada pula yang dilaporkan berupa angka service rate (misal dalam RMF). Karena service rate/detik = 1/S, maka tinggal membalik angka itu saja.

I/O service time, SIO Mirip S tetapi bukan CPU-time, melainkan cycletime-nya IOP atau I/O channel dan seluruh prosesor yang terkait dengan operasi I/O atau network. Kita sebut saja I/O time, sehingga SIO adalah jumlah I/O-time yg dimanfaatkan untuk melayani I/O satu transaksi. Tergantung alatnya, angka ini ada yang dilaporkan apa adanya, ada pula yang dilaporkan berupa angka service rate (misal dalam RMF, tapi hanya untuk disk). Karena I/O service rate/detik = 1/SIO, maka tinggal membalik angka itu saja.

Page-in rate, m Jumlah pemanggilan kembali isi memori yang telah disapu ke penampungan selama melayani satu transaksi. Ini mengambarkan bahwa terjadi secara serempak dan tidak semua mendapat pelayanan. Karena memori tidak cukup menampung yang antre, maka disapu ke penampungan (auxiliary storage). Untuk sistem non-mainframe, angka ini kebanyakan tidak dilaporkan.

Interval, tINTV Interval atau selang waktu yang digunakan oleh alat pemantau untuk menggali informasi kinerja sistem. Meskipun angka ini ditetapkan dalam parameter alat pemantau, namun pelaksanaannya pasti ada sedikit penyimpangan. Alat pemantau yang baik pasti melaporkan angka tINTV ini agar laporannya bisa dianalisa lanjut.

Processor power, PMAX Konstanta pabrikan tentang besarnya tenaga prosesor. P adalah maximum banyaknya service unit (SU) yang bisa diberikan dalam setiap detik CPU-time. Dalam terminologi IBM dinamakan SRM constant. Bila angka pabrikan tidak dalam satuan SU/CPUsec, agar dikonversi dulu menjadi angka ini.

P = 1 / (S * TCPU) PMAX adalah P pada saat utilisasi U = 100%, atau TCPU = tINTV.

Setelah mendapatkan angka-angka yang cukup akurat dari laporan alat pemantau, perhitungan pendugaan kapasitas bisa dimulai.

Kumpulkan pemantauan kinerja sistem dalam kurun yang cukup panjang. Laporan hanya untuk saat-saat tersibuk, dan harus dipisahkan antara saat tersibuk online dan tersibuk batch. Untuk mainframe OS/390 atau z/OS lebih mudah karena SMF melakukannya secara otomatis.

Berikut ini contoh hasil pengumpulan laporan pemantauan berkala dalam 12 kurun. Anggap saja selama 12 bulan dan angka setiap bulannya merupakan hasil perhitungan rata-rata terboboti seperti dalam formula (7) dan (8) dari laporan harian. Silakan dicoba mengganti angka2 contoh ini dengan data anda.

Power PMAX =

6

Interval Resp.time Utilisasi ThruputR U X

1 15.0450 2.002300 60.000% 480.23002 14.8730 2.004630 62.000% 470.45003 15.0010 2.004986 61.000% 468.43004 14.9670 2.005321 64.000% 475.40005 14.7840 2.018625 67.500% 491.23406 14.7820 2.051946 70.200% 513.45507 14.3890 2.092395 71.900% 550.45608 14.4782 2.107058 80.000% 601.34569 15.0032 2.187599 82.000% 599.4500

10 14.9780 2.258318 84.000% 613.731011 14.7380 2.428865 87.000% 612.234012 14.8360 2.589000 90.000% 625.4570

Rata-rata 14.8229 2.145920 73.300% 541.8227

Langkah 2

N = R * X P

1 961.5645 9.02700000 89.77212 943.0782 9.22126000 82.15533 939.1956 9.15061000 82.57694 953.3296 9.57888000 76.01205 991.6170 9.97920000 71.15566 1,053.5817 10.37696400 65.85167 1,151.7714 10.34569100 68.38738 1,267.0699 11.58256000 60.66389 1,311.3560 12.30262400 55.5845

10 1,385.9995 12.58152000 55.426511 1,487.0337 12.82206000 52.589712 1,619.3082 13.35240000 50.1493

Indikator 1 1 1Rata-rata 1,172.0754 10.86006408 67.5271

Langkah 3 (Akhir)

#CPU c =

Kurun tINTV

Menghitung angka-angka statistik yang diperlukan berdasarkan masukan data di atas. Yang paling diperlukan disini adalah CPU-time TCPU = tINTV * U, dan pemakaian power (P) merujuk formula (9). Beberapa yang lain disertakan untuk analisa pelengkap jika diperlukan.

Kurun t TCPU = tINTV * U = 1/(S * TCPU)

Fokus utama dalam perhitungan kapasitas adalah pada angka yang paling penting bagi pengguna, yaitu response time, R. Selanjutnya dicari hubungan fungsional yang mencerminkan fungsi bagi response time.

R S/U

1 2.002300 0.00205667 0.001399342 2.004630 0.00212903 0.001529073 2.004986 0.00216951 0.001521264 2.005321 0.00214597 0.001652655 2.018625 0.00208637 0.001765456 2.051946 0.00208462 0.001907647 2.092395 0.00196579 0.001836918 2.107058 0.00177900 0.002070789 2.187599 0.00178334 0.00226001

10 2.258318 0.00170714 0.0022664511 2.428865 0.00170460 0.0023887112 2.589000 0.00165933 0.00250495

Penyimpulan 1

1.265756457.1646170.886411 akurat

500.0000 1.83556968

1,002.5658

Penyimpulan 2

Fokus utama dalam perhitungan kapasitas adalah pada angka yang paling penting bagi pengguna, yaitu response time, R. Selanjutnya dicari hubungan fungsional yang mencerminkan fungsi bagi response time.

Dari formula (4) diperoleh R = (N*m/c) * S/U. Sedangkan formula (6), jika R = TQ + S + SIO, maka R = (k/c) * S/U. Tampak ada hubungan fungsi R = b * (S/U), dimana b = (k/c) = (N*m/c). Merujuk formula (9) bahwa S = 1/(P * TCPU), maka R dapat dinyatakan R = b / (P * TCPU * U). Jika 1/(P * TCPU * U) dan S/U kita anggap sebagai satu peubah bebas, maka hubungannya dengan R bisa dianggap hubungan linier. Selanjutnya kita cari penyelesaian hubungan linier R = a + b * (S/U) + e dan R = a + b / (P * TCPU * U) + e dengan analisis regresi sederhana.

Kurun t 1/(P * TCPU * U)

Menyelesaikan hubungan fungsi (1), R = a + b /(P * TCPU * U) + e dan menghitung indikator korelasinya. Koefisien a merupakan nilai awal dan b laju perkembangannya. Dengan analisa regresi linier diperoleh:

Nilai awal, a =Laju, b =

Korelasi, r =

Jika indikasi korelasi yang diperoleh di atas cukup akurat (e boleh dianggap 0), maka fungsi (1) bisa digunakan untuk mensimulasi response time R yang anda kehendaki dengan merubah angka PMAX seolah memilih prosesor yang tepat. Silakan dicoba memilih PMAX.

PMAX baru = maka R baru =

beban RAM, N =

Menyelesaikan hubungan hubungan (2), R = a + b * S/U + e dan menghitung indikator korelasinya. Koefisien a merupakan nilai awal dan b laju perkembangannya. Dengan analisa regresi linier diperoleh:

3.764354-834.554114-0.861157 akurat

0.00091362U baru, U = 39.531% rata-rata semula adalah:

berarti turun sebesar:

4. TambahanCatatan

Email

Khusus untuk OS/390

Nilai awal, a =Laju, b =

Korelasi, r =

Jika dari korelasinya, hubungan fungsi (2) akurat, maka U = S * b/(R - a). Merujuk formula (9), S = 1/(P * TCPU), maka diperoleh hubungan fungsi (3), U = b / [(R - a) * P * TCPU]. U dalam fungsi ini bisa digunakan untuk menduga utilisasi prosesor dengan PMAX baru kelak, yaitu:

S baru, SMIN =

Akurasi dari penyimpulan-penyimpulan di atas, sangat tergantung dari normalitas data laporan yang anda kumpulkan. Tentu, makin banyak data yang dianalisa, makin normal sebarannya. Berarti makin akurat hasilnya. Secara awam anda bisa menguji seberapa akurat analisa ini dengan cara memasok PMAX baru = PMAX semula dan perhatikan hasilnya. Jika angka R dan U baru yang diperoleh ada perubahan, berarti analisa tidak akurat. Malahnya, tidak adanya perubahan tidak menjamin analisa akurat, sampai anda buktikan data yang dipasok normal dan koreaslinya mengindikasikan minimal "cukup akurat". Jika ada pertanyaan atau koreksi, silakan email saya.

Deru Sudibyo

Pertimbangan khusus untuk OS/390 maupun z/OS, angka R dapat diambil langsung dari laporan RMF monitor I topik "WORKLOAD ACTIVITY" di bagian total keseluruhan workload-policy. Info R ada di kolom TRANS.-TIME baris ACTUAL. Biasanya angka ini cukup besar karena merupakan rata-rata R untuk seluruh beban termasuk batch job. Jika hanya menginginkan R aplikasi interaktif online, harus dipilih loporan pada interval online saja, tapi harus yang paling padat. Info kepadatan transaksi, X bisa diperoleh dari baris END/S pada kolom TRANSACTIONS. Service time memang tidak langsung, tapi tinggal menghitung TOT - IOC pada kolom SERVICE, hasilnya adalah service rate. S = 1/(servicerate). I/O service time bisa menggunakan IOC pada kolom SERVICE, maupun RESP pada kolom DASD-I/O. Page-in rate juga bahkan tersedia dalam satu kolom terpisah. Utilisasi, U diperoleh dari laporan CPU ACTIVITY.

1. Angka-angka yang Diperoleh dari Alat-alat Pemantau

UNTUK PERENCANAAN SISTEM

Di lapangan, pada kenyataannya angka-angka utilisasi, response time, throughput dan beban kerja lain sistem tidak perlu dihitung lagi. Ada program khusus seperti RMF maupun produk-produk program canggih lainnya yang sudah menyediakan angka-angka tersebut secara otomatis. Bahkan angka-angka tersebut lebih teliti karena pengukuran langsung, ketimbang pendugaan dengan rumus-rumus statistik pada sheet sebelumnya. Yang penting, bagaimana memanfaatkan angka-angka tersebut untuk mengatur dan merencanakan kapasistas sistem anda. Berikut ini penjelasan

Waktu yg diperlukan untuk menyelesaikan satu transaksi sejak memasuki sistem hingga selesai. Angka dari alat pemantau biasanya terinci untuk tiap jenis beban. Untuk keperluan pengaturan kinerja, kita bisa pilih beban mana yg akan dianalisa. Tetapi untuk keperluan perencanaan, angka ini harus satu, yaitu angka rata-rata keseluruhan sistem. Maka harus dihitung sendiri angka rata-rata R terboboti. Pilih hanya selang waktu yang paling sibuk. Faktor pembobot

R5 R6 R7

t5 t6 t7

Atau utilisasi - adalah nisbah CPU-time yg dikonsumsi selama selang waktu tertentu. Biasanya, angka tunggal untuk keseluruhan sistem sudah dilaporkan oleh alat pemantau, sehingga tidak perlu dirata-ratakan lagi.

Banyaknya transaksi yg dapat diselesaikan dalam selang waktu tertentu. Bisanya angka ini seperti R, menyebar terinci pada setiap beban. Maka cara mendapatkannyapun dengan merata-ratakan seperti R di atas.

X5 X6 X7

t5 t6 t7

Jumlah CPU-time yg dimanfaatkan untuk melayani satu transaksi. Tergantung alatnya, angka ini ada yang dilaporkan apa adanya, ada pula yang dilaporkan berupa angka service rate (misal dalam RMF). Karena service rate/detik = 1/S,

2. Angka-angka Pabrikan

Konsumsi processor power untuk sistem dirumuskan sebagai berikut:

3. Langkah-langkah Perhitungan Kapasitas

Jumlah CPU-time yg dimanfaatkan untuk melayani satu transaksi. Tergantung alatnya, angka ini ada yang dilaporkan apa adanya, ada pula yang dilaporkan berupa angka service rate (misal dalam RMF). Karena service rate/detik = 1/S,

Mirip S tetapi bukan CPU-time, melainkan cycletime-nya IOP atau I/O channel dan seluruh prosesor yang terkait dengan operasi I/O atau network. Kita sebut saja I/O time, sehingga SIO adalah jumlah I/O-time yg dimanfaatkan untuk melayani I/O satu transaksi. Tergantung alatnya, angka ini ada yang dilaporkan apa adanya, ada pula yang dilaporkan berupa angka service rate (misal dalam RMF, tapi hanya untuk disk). Karena I/O service rate/detik = 1/SIO, maka tinggal

Jumlah pemanggilan kembali isi memori yang telah disapu ke penampungan selama melayani satu transaksi. Ini mengambarkan bahwa terjadi secara serempak dan tidak semua mendapat pelayanan. Karena memori tidak cukup menampung yang antre, maka disapu ke penampungan (auxiliary storage). Untuk sistem non-mainframe, angka ini

Interval atau selang waktu yang digunakan oleh alat pemantau untuk menggali informasi kinerja sistem. Meskipun angka ini ditetapkan dalam parameter alat pemantau, namun pelaksanaannya pasti ada sedikit penyimpangan. Alat pemantau

ini agar laporannya bisa dianalisa lanjut.

Konstanta pabrikan tentang besarnya tenaga prosesor. P adalah maximum banyaknya service unit (SU) yang bisa diberikan dalam setiap detik CPU-time. Dalam terminologi IBM dinamakan SRM constant. Bila angka pabrikan tidak dalam satuan SU/CPUsec, agar dikonversi dulu menjadi angka ini.

pada saat utilisasi U = 100%, atau TCPU = tINTV.

Setelah mendapatkan angka-angka yang cukup akurat dari laporan alat pemantau, perhitungan pendugaan kapasitas bisa

Kumpulkan pemantauan kinerja sistem dalam kurun yang cukup panjang. Laporan hanya untuk saat-saat tersibuk, dan harus dipisahkan antara saat tersibuk online dan tersibuk batch. Untuk mainframe OS/390 atau z/OS lebih mudah

Berikut ini contoh hasil pengumpulan laporan pemantauan berkala dalam 12 kurun. Anggap saja selama 12 bulan dan angka setiap bulannya merupakan hasil perhitungan rata-rata terboboti seperti dalam formula (7) dan (8) dari laporan harian. Silakan dicoba mengganti angka2 contoh ini dengan data anda.

Servicetime I/O servicetime Page-inS m0.001234 0.2378000.001320 0.2978000.001323 0.3897000.001373 0.3523000.001408 0.3987000.001463 0.4210000.001413 0.4980000.001423 0.5023000.001462 0.5689300.001434 0.6000000.001483 0.6234000.001493 1.3893240.001403 0.523271 0.000000

m k

6.074885 697 0.0000000000###5.990396 843 0.0000000000###5.903985 1,081 0.0000000000###5.881237 989 0.0000000000###5.854252 1,151 0.0000000000###5.605611 1,216 0.0000000000###5.544884 1,524 0.0000000000###5.608557 1,699 0.0000000000###5.612596 1,919 0.0000000000###5.726685 2,114 0.0000000000###5.749259 2,200 0.0000000000###5.781229 5,029 0.0000000000###

1 1 05.777798 1,705 0.00000000

SIO

Menghitung angka-angka statistik yang diperlukan berdasarkan masukan data di atas. Yang paling diperlukan disini P) merujuk formula (9). Beberapa yang lain disertakan untuk

TQ = f * c / N = U*c*(1+SIO/S) =k*S/(c*U)-S-SIO

angka yang paling penting bagi pengguna, yaitu response . Selanjutnya dicari hubungan fungsional yang mencerminkan fungsi bagi response time.

yang semula: 2.14592009perbaikan: 14.46%

yang semula: 1,172.0754perbaikan: 14.46%

angka yang paling penting bagi pengguna, yaitu response . Selanjutnya dicari hubungan fungsional yang mencerminkan fungsi bagi response time.

. Sedangkan formula (6), jika R = TQ + S + SIO, maka R = (k/c) * S/U. Tampak = (k/c) = (N*m/c). Merujuk formula (9) bahwa S = 1/(P * TCPU), maka R

* U) dan S/U kita anggap sebagai satu peubah bebas, maka hubungannya dengan R bisa dianggap hubungan linier. Selanjutnya kita cari penyelesaian hubungan linier R = a + b *

dengan analisis regresi sederhana.

CPU * U) + e dan menghitung indikator korelasinya. Koefisien a laju perkembangannya. Dengan analisa regresi linier diperoleh:

Jika indikasi korelasi yang diperoleh di atas cukup akurat (e boleh dianggap 0), maka fungsi (1) bisa digunakan untuk yang anda kehendaki dengan merubah angka PMAX seolah memilih prosesor yang tepat.

S/U + e dan menghitung indikator korelasinya. Koefisien a laju perkembangannya. Dengan analisa regresi linier diperoleh:

73.300%46.070%

4. Tambahan

U = S * b/(R - a). Merujuk formula (9), S = 1/(P * TCPU), maka ]. U dalam fungsi ini bisa digunakan untuk menduga utilisasi

Akurasi dari penyimpulan-penyimpulan di atas, sangat tergantung dari normalitas data laporan yang anda kumpulkan. Tentu, makin banyak data yang dianalisa, makin normal sebarannya. Berarti makin akurat hasilnya. Secara awam anda bisa menguji seberapa akurat analisa ini dengan cara memasok PMAX baru = PMAX semula dan perhatikan hasilnya. Jika angka R dan U baru yang diperoleh ada perubahan, berarti analisa tidak akurat. Malahnya, tidak adanya perubahan tidak menjamin analisa akurat, sampai anda buktikan data yang dipasok normal dan koreaslinya mengindikasikan minimal "cukup akurat". Jika ada pertanyaan atau koreksi, silakan email saya.

Pertimbangan khusus untuk OS/390 maupun z/OS, angka R dapat diambil langsung dari laporan RMF monitor I topik "WORKLOAD ACTIVITY" di bagian total keseluruhan workload-policy. Info R ada di kolom TRANS.-TIME baris ACTUAL. Biasanya angka ini cukup besar karena merupakan rata-rata R untuk seluruh beban termasuk batch job. Jika hanya menginginkan R aplikasi interaktif online, harus dipilih loporan pada interval online saja, tapi harus yang paling padat. Info kepadatan transaksi, X bisa diperoleh dari baris END/S pada kolom TRANSACTIONS. Service time memang tidak langsung, tapi tinggal menghitung TOT - IOC pada kolom SERVICE, hasilnya adalah service rate. S = 1/(servicerate). I/O service time bisa menggunakan IOC pada kolom SERVICE, maupun RESP pada kolom DASD-I/O. Page-in rate juga bahkan tersedia dalam satu kolom terpisah. Utilisasi, U diperoleh dari laporan CPU ACTIVITY.

1. Information collected from Monitor Tool Reports

Try example below:

Formula (7) R = ?

Try example below:

Formula (8) X = ?

APPLICATION OF CPE FOR SYSTEM PLANNING

In fact, values of utilization, response time, throughput and other system workload indicators, don't need to be calculated any more. There are lots of sophisticated tools that can obtain those values automatically. Even more accurate because they directly measure, instead of estimation using statistical formulas as presented on the previous sheet. The important thing is how to use those values to manage and plan your system capacity. Below is a brief hint how to do it.

Response time, R Amount of time needed to complete a transaction since entered to the system. Usually, monitor tool provides R value in detail for each particular workload. For tuning, R can be selected only from certain workload we concern to. For capacity planning, however, R must represent the whole system. Hence, we need to calculate the weighted average R value of whole system workload Keep in mind that all observation must be within peak time only period. The most relevant weight factor is CPU time.

R1 R2 R3 R4

t1 t2 t3 t4

n n R = S(ti * Ri) / S ti

i=1 i=1

CPU busy, U Or - Utilization - is a ratio of consumed CPU-time during certain time interval. A single value of U is usually provided in certain monitor tool report.

Throughput, X Number of transactions completed during certain time interval. As R info, usually X is reported in detail for each particular workload. To get a single info, do the same way as R, calculate weighted average.

X1 X2 X3 X4

t1 t2 t3 t4

n n X = S(ti * Xi) / S ti

i=1 i=1

CPU service time, S Number of CPU-time to serve a single transaction. Some tools report S directly in seconds or milliseconds. Some others are service rate in service units (SU). Since service rate/sec = 1/S, so S can be easily obtained. For example, service rate = 1000 SU/sec, then S = 0.001 sec.

I/O service time, SIO Service time of I/O. The unity is not CPU seconds instead, but cycletime of IOP or I/O channel and all other processors involve during I/O operation whether to I/O or network devices. From the view of device-RAM interaction, it can be considered as I/O response time. Just say I/O time, hence SIO is a number of I/O-time to serve a single I/O operation of a certain transaction. Depend on the tool, some reported in time unity, and some others in rate. Since I/O service rate/sec = 1/SIO, hence SIO can be obtained in the same way as S.

2. Manufacturer Information

Processor power is formulated as follow:

Formula (9)

3. Capacity Analysis Stages

Stage 1

335.00006

Period Interval Resp.time Utilization ThruputR U X

1 15.0450 2.002300 60.000% 480.23002 14.8730 2.004630 62.000% 470.45003 15.0010 2.004986 61.000% 468.4300

Service time of I/O. The unity is not CPU seconds instead, but cycletime of IOP or I/O channel and all other processors involve during I/O operation whether to I/O or network devices. From the view of device-RAM interaction, it can be considered as I/O response time. Just say I/O time, hence SIO is a number of I/O-time to serve a single I/O operation of a certain transaction. Depend on the tool, some reported in time unity, and some others in rate. Since I/O service rate/sec = 1/SIO, hence SIO can be obtained in the same way as S.

Page-in rate, m Number of paged-out memory content transfered back into memory during serving a transaction. This factor illustrates not all concurrent transaction can be served. Some have to be placed in queue. When memory is not enough, some queued transactions are swapped-out to auxiliary storage. Not every tool reports this information. For IBM mainframe system, however, RMF reports this information.

Interval, tINTV Time interval used by the tool to explore information of system performance. Although interval usually set in the monitor parameter, in fact it could be bias. The fair tools like RMF (in mainframe) always report tINTV information for further custom analysis.

Processor power, PMAX Manucaturer constant of certain model and type of processor regarding processing power. P is a maximum number of service unit (SU) can be delivered during a CPU second. In IBM terminology P is named as SRM constant. If P is not in SU/CPUsec, should be converted first to SU/CPUsec equivalent.

P = 1 / (S * TCPU) PMAX is P when U = 100%, or TCPU = tINTV.

Once a number of accurate tool reports are collected, capacity analysis can be started in 3 stages below. Note that number of colected information must be enough to get all data in statistical normal distribution.

Group the reports into several time periods. Remember that reports must only for peak time. To avoid misleading, online peak and batch peak must be in separated groups. For mainframe OS/390 or z/OS easier because SMF does it automatically.

Below is an example form periodical reports during 12 time period groups. Assume as 12months and each info in the table is weighted average obtained from its group of daily reports according to formula (7) and (8). These are just dummy and modifiable. You can try with either your dummy for excercise or true info for real analysis.

Power PMAX =#CPU c =

tINTV

4 14.9670 2.005321 64.000% 475.40005 14.7840 2.018625 67.500% 491.23406 14.7820 2.051946 70.200% 513.45507 14.3890 2.092395 71.900% 550.45608 14.4782 2.107058 80.000% 601.34569 15.0032 2.187599 82.000% 599.4500

10 14.9780 2.258318 84.000% 613.731011 14.7380 2.428865 87.000% 612.234012 14.8360 2.589000 90.000% 625.4570

Average 14.8229 2.145920 73.300% 541.8227

Stage 2

N = R * X P

1 961.5645 9.02700000 89.77212 943.0782 9.22126000 82.15533 939.1956 9.15061000 82.57694 953.3296 9.57888000 76.01205 991.6170 9.97920000 71.15566 1,053.5817 10.37696400 65.85167 1,151.7714 10.34569100 68.38738 1,267.0699 11.58256000 60.66389 1,311.3560 12.30262400 55.5845

10 1,385.9995 12.58152000 55.426511 1,487.0337 12.82206000 52.589712 1,619.3082 13.35240000 50.1493

Average 1,172.0754 10.86006408 67.5271

Stage 3 (Final)

R S/U

1 2.002300 0.00205667 0.00139934

Calculate necessary statistical values based on the above observation table. The most important statistical values are CPU-time, TCPU = tINTV * U, and processing power consumption (P) according to formula (9). Some others also listed below just a reserved for further analysis if needed.

Period t TCPU = tINTV * U = 1/(S * TCPU)

Main focus in capacity analysis is the most important value for users, which is response time, R. Then determine the closest functional relationship to R.

From formula (4) we get R = (N*m/c) * S/U. Based on formula (6), if R = TQ + S + SIO, then R = (k/c) * S/U. Both show that R = b * (S/U), where b = (k/c) = (N*m/c). Referring formula (9) that S = 1/(P * TCPU), so R can be stated as R = b / (P * TCPU * U). Assuming that 1/(P * TCPU * U) and S/U can be assumed as independent variables, then both functional relationships to R above can be assumed as linear functions. Next is to find resolution for both linear functions, R = a + b * (S/U) + e and R = a + b / (P * TCPU * U) + e using simple linear regression analysis method.

Period t 1/(P * TCPU * U)

2 2.004630 0.00212903 0.001529073 2.004986 0.00216951 0.001521264 2.005321 0.00214597 0.001652655 2.018625 0.00208637 0.001765456 2.051946 0.00208462 0.001907647 2.092395 0.00196579 0.001836918 2.107058 0.00177900 0.002070789 2.187599 0.00178334 0.00226001

10 2.258318 0.00170714 0.0022664511 2.428865 0.00170460 0.0023887112 2.589000 0.00165933 0.00250495

Conclusion 1

1.265756457.1646170.886411 accurate

400.0000

Conclusion 2

3.764354-834.554114-0.861157 accurate

0.00114202Estimated U = 53.354% which originally (average):

hence lowered:

4. Additional Infos

Resolve function (1), R = a + b /(P * TCPU * U) + e and find its correlation factor. Coefficient a is an intercept and b is a slope of the growth. Regression analysis results:

Interceptl, a =Slope, b =

Correlation, r =

If at least correlation factor above indicates fairly accurate (e can be assumed 0), then function (1) can be used to simulate expected response time R according max processor power you entered in New PMAX input field below. Try specify New PMAX to find out the best R for you.

New PMAX = then estimated R =

RAM load, N =

Resolve function (2), R = a + b * S/U + e and find its correlation factor. Coefficient a is an intercept and b is a slope of the growth. Regression analysis results:

Intercept, a =Slope, b =

Correlation, r =

Based on the correlation factor, if function (2) is at least fairly accurate, we can assume U = S * b/(R - a). Referring formula (9), S = 1/(P * TCPU), we get function (3), U = b / [(R - a) * P * TCPU]. This U can be used to estimate utilization of newly processor according your New PMAX input.

Estimated SMIN =

Note

Email

Special notes for OS/390

Accuracy of the above conclusions, very depend on normality of data from collected monitor reports. More data gathered will get closer to normal distribution. The result, of course is more accurate. Actually, accuracy of the above analysis can be easily verified. Just enter new PMAX = old PMAX, then see estimated R and U resulted. If not the same, mean there are improvements or changes, then analisys is inaccurate . The problem, no changes when you type new PMAX = old PMAX, it doesn't mean that analysis is accurate, until you can prove that data you have collected is normal and correlation factor indicates at least fairly accurate. Drop me a message should you have any question or critizise for correction.

Deru Sudibyo

Special consideration for OS/390 and z/OS, that R is reported by RMF monitor I on "WORKLOAD ACTIVITY" report, in the last part, which is whole workload-policy. Info of R is in column TRANS.-TIME item ACTUAL. Usually it quite high since this R is average of whole system workload, including batch jobs and long running STCs. If you only expect R of online interactive application, that's why, batch shift report must be grouped separately. Info of transaction rate, X is item baris END/S of column TRANSACTIONS. Service time is not directly reported, but just calculate TOT - IOC of column SERVICE, then inverse it since it is service rate. S = 1/(servicerate). I/O service time can be obtained from item IOC of column SERVICE, or RESP at column DASD-I/O. Page-in rate is even provided in a separate column. Utilization, U is separated on CPU ACTIVITY report.

1. Information collected from Monitor Tool Reports

FOR SYSTEM PLANNING

In fact, values of utilization, response time, throughput and other system workload indicators, don't need to be calculated any more. There are lots of sophisticated tools that can obtain those values automatically. Even more accurate because they directly measure, instead of estimation using statistical formulas as presented on the previous sheet. The important thing is how to use those values to manage and plan your system capacity.

Amount of time needed to complete a transaction since entered to the system. Usually, monitor tool provides R value in detail for each particular workload. For tuning, R can be selected only from certain workload we concern to. For capacity planning, however, R must represent the whole system. Hence, we need to calculate the weighted average R value of whole system workload Keep in mind that all observation must be within peak time only period. The most relevant

R5 R6 R7

t5 t6 t7

Or - Utilization - is a ratio of consumed CPU-time during certain time interval. A single value of U is usually provided in

Number of transactions completed during certain time interval. As R info, usually X is reported in detail for each particular workload. To get a single info, do the same way as R, calculate weighted average.

X5 X6 X7

t5 t6 t7

Number of CPU-time to serve a single transaction. Some tools report S directly in seconds or milliseconds. Some service rate/sec = 1/S, so S can be easily obtained. For example,

Service time of I/O. The unity is not CPU seconds instead, but cycletime of IOP or I/O channel and all other processors involve during I/O operation whether to I/O or network devices. From the view of device-RAM interaction, it can be considered as I/O response time. Just say I/O time, hence SIO is a number of I/O-time to serve a single I/O operation of a certain transaction. Depend on the tool, some reported in time unity, and some others in rate. Since I/O service

can be obtained in the same way as S.

2. Manufacturer Information

Processor power is formulated as follow:

3. Capacity Analysis Stages

Servicetime I/O servicetime Page-inS m0.001234 0.2378000.001320 0.2978000.001323 0.389700

Service time of I/O. The unity is not CPU seconds instead, but cycletime of IOP or I/O channel and all other processors involve during I/O operation whether to I/O or network devices. From the view of device-RAM interaction, it can be considered as I/O response time. Just say I/O time, hence SIO is a number of I/O-time to serve a single I/O operation of a certain transaction. Depend on the tool, some reported in time unity, and some others in rate. Since I/O service

can be obtained in the same way as S.

Number of paged-out memory content transfered back into memory during serving a transaction. This factor illustrates not all concurrent transaction can be served. Some have to be placed in queue. When memory is not enough, some queued transactions are swapped-out to auxiliary storage. Not every tool reports this information. For IBM mainframe

Time interval used by the tool to explore information of system performance. Although interval usually set in the monitor parameter, in fact it could be bias. The fair tools like RMF (in mainframe) always report tINTV information for further

Manucaturer constant of certain model and type of processor regarding processing power. P is a maximum number of service unit (SU) can be delivered during a CPU second. In IBM terminology P is named as SRM constant. If P is not in SU/CPUsec, should be converted first to SU/CPUsec equivalent.

= 100%, or TCPU = tINTV.

Once a number of accurate tool reports are collected, capacity analysis can be started in 3 stages below. Note that number of colected information must be enough to get all data in statistical normal distribution.

Group the reports into several time periods. Remember that reports must only for peak time. To avoid misleading, online peak and batch peak must be in separated groups. For mainframe OS/390 or z/OS easier because SMF does it

Below is an example form periodical reports during 12 time period groups. Assume as 12months and each info in the table is weighted average obtained from its group of daily reports according to formula (7) and (8). These are just dummy and modifiable. You can try with either your dummy for excercise or true info for real analysis.

SIO

0.001373 0.3523000.001408 0.3987000.001463 0.4210000.001413 0.4980000.001423 0.5023000.001462 0.5689300.001434 0.6000000.001483 0.6234000.001493 1.3893240.001403 0.523271 0.000000

m k

6.074885 697 0.0000000000###5.990396 843 0.0000000000###5.903985 1,081 0.0000000000###5.881237 989 0.0000000000###5.854252 1,151 0.0000000000###5.605611 1,216 0.0000000000###5.544884 1,524 0.0000000000###5.608557 1,699 0.0000000000###5.612596 1,919 0.0000000000###5.726685 2,114 0.0000000000###5.749259 2,200 0.0000000000###5.781229 5,029 0.0000000000###5.777798 1,705 0.00000000

Calculate necessary statistical values based on the above observation table. The most important statistical values are , and processing power consumption (P) according to formula (9). Some others also listed below

TQ = f * c / N = U*c*(1+SIO/S) =k*S/(c*U)-S-SIO

the most important value for users, which is response time, R. Then determine the

. Based on formula (6), if R = TQ + S + SIO, then R = (k/c) * S/U. Both show that . Referring formula (9) that S = 1/(P * TCPU), so R can be stated as R = b / (P *

can be assumed as independent variables, then both functional relationships to R above can be assumed as linear functions. Next is to find resolution for both linear functions, R = a + b

using simple linear regression analysis method.

1.97802321 which originally: 2.14592009improvement: 7.82%

1,080.3722 whch originally: 1,172.0754improvement: 7.82%

73.300%27.211%

4. Additional Infos

and find its correlation factor. Coefficient a is an intercept and b is a

If at least correlation factor above indicates fairly accurate (e can be assumed 0), then function (1) can be used to simulate according max processor power you entered in New PMAX input field below. Try specify New

and find its correlation factor. Coefficient a is an intercept and b is a slope of

Based on the correlation factor, if function (2) is at least fairly accurate, we can assume U = S * b/(R - a). Referring / [(R - a) * P * TCPU]. This U can be used to estimate utilization of

Accuracy of the above conclusions, very depend on normality of data from collected monitor reports. More data gathered will get closer to normal distribution. The result, of course is more accurate. Actually, accuracy of the above analysis can

, then see estimated R and U resulted. If not the same, mean there are improvements or changes, then analisys is inaccurate . The problem, no changes when you type new PMAX = old PMAX, it doesn't mean that analysis is accurate, until you can prove that data you have collected is normal and correlation factor indicates at least fairly accurate. Drop me a message should you have any question or critizise for correction.

Special consideration for OS/390 and z/OS, that R is reported by RMF monitor I on "WORKLOAD ACTIVITY" report, in the last part, which is whole workload-policy. Info of R is in column TRANS.-TIME item ACTUAL. Usually it quite high since this R is average of whole system workload, including batch jobs and long running STCs. If you only expect R of online interactive application, that's why, batch shift report must be grouped separately. Info of transaction rate, X is item baris END/S of column TRANSACTIONS. Service time is not directly reported, but just calculate TOT - IOC of column SERVICE, then inverse it since it is service rate. S = 1/(servicerate). I/O service time can be obtained from item IOC of column SERVICE, or RESP at column DASD-I/O. Page-in rate is even provided in a separate column. Utilization, U is

1. Input Section

Technical specs

Input tablePeriod Interval Resp.time Utilization Thruput

R U X123456789

1011121314151617181920212223242526

CPE SHEET FOR SYSTEM PLANNING

Enter your collected performance information into input table below. All column except the last one (m), are required. Group your collection into 50 periods to avoid normality test. Each period should be weighted average of the group.

Power PMAX =#CPU c =

tINTV

27282930313233343536

3738394041424344454647484950

Average 0.0000 0.000000 0.000% 0.0000

2. Analysis Section0

N = R * X P

1 0.0000 0.00000 0.00002 0.0000 0.00000 0.00003 0.0000 0.00000 0.00004 0.0000 0.00000 0.00005 0.0000 0.00000 0.00006 0.0000 0.00000 0.00007 0.0000 0.00000 0.00008 0.0000 0.00000 0.00009 0.0000 0.00000 0.0000

10 0.0000 0.00000 0.0000

Period t TCPU = tINTV * U = 1/(S * TCPU)

11 0.0000 0.00000 0.000012 0.0000 0.00000 0.000013 0.0000 0.00000 0.000014 0.0000 0.00000 0.000015 0.0000 0.00000 0.000016 0.0000 0.00000 0.000017 0.0000 0.00000 0.000018 0.0000 0.00000 0.000019 0.0000 0.00000 0.000020 0.0000 0.00000 0.000021 0.0000 0.00000 0.000022 0.0000 0.00000 0.000023 0.0000 0.00000 0.000024 0.0000 0.00000 0.000025 0.0000 0.00000 0.000026 0.0000 0.00000 0.000027 0.0000 0.00000 0.000028 0.0000 0.00000 0.000029 0.0000 0.00000 0.000030 0.0000 0.00000 0.000031 0.0000 0.00000 0.000032 0.0000 0.00000 0.000033 0.0000 0.00000 0.000034 0.0000 0.00000 0.000035 0.0000 0.00000 0.000036 0.0000 0.00000 0.000037 0.0000 0.00000 0.000038 0.0000 0.00000 0.000039 0.0000 0.00000 0.000040 0.0000 0.00000 0.000041 0.0000 0.00000 0.000042 0.0000 0.00000 0.000043 0.0000 0.00000 0.000044 0.0000 0.00000 0.000045 0.0000 0.00000 0.000046 0.0000 0.00000 0.000047 0.0000 0.00000 0.000048 0.0000 0.00000 0.000049 0.0000 0.00000 0.000050 0.0000 0.00000 0.0000

Average n/a n/a n/a

R S/U

1 0.000000 0.00000000 0.000000002 0.000000 0.00000000 0.000000003 0.000000 0.00000000 0.000000004 0.000000 0.00000000 0.000000005 0.000000 0.00000000 0.000000006 0.000000 0.00000000 0.000000007 0.000000 0.00000000 0.000000008 0.000000 0.00000000 0.000000009 0.000000 0.00000000 0.00000000

10 0.000000 0.00000000 0.0000000011 0.000000 0.00000000 0.0000000012 0.000000 0.00000000 0.0000000013 0.000000 0.00000000 0.0000000014 0.000000 0.00000000 0.0000000015 0.000000 0.00000000 0.0000000016 0.000000 0.00000000 0.0000000017 0.000000 0.00000000 0.0000000018 0.000000 0.00000000 0.0000000019 0.000000 0.00000000 0.0000000020 0.000000 0.00000000 0.0000000021 0.000000 0.00000000 0.0000000022 0.000000 0.00000000 0.0000000023 0.000000 0.00000000 0.0000000024 0.000000 0.00000000 0.0000000025 0.000000 0.00000000 0.0000000026 0.000000 0.00000000 0.0000000027 0.000000 0.00000000 0.0000000028 0.000000 0.00000000 0.0000000029 0.000000 0.00000000 0.0000000030 0.000000 0.00000000 0.0000000031 0.000000 0.00000000 0.0000000032 0.000000 0.00000000 0.0000000033 0.000000 0.00000000 0.0000000034 0.000000 0.00000000 0.0000000035 0.000000 0.00000000 0.0000000036 0.000000 0.00000000 0.0000000037 0.000000 0.00000000 0.0000000038 0.000000 0.00000000 0.00000000

Period t 1/(P * TCPU * U)

39 0.000000 0.00000000 0.0000000040 0.000000 0.00000000 0.0000000041 0.000000 0.00000000 0.0000000042 0.000000 0.00000000 0.0000000043 0.000000 0.00000000 0.0000000044 0.000000 0.00000000 0.0000000045 0.000000 0.00000000 0.0000000046 0.000000 0.00000000 0.0000000047 0.000000 0.00000000 0.0000000048 0.000000 0.00000000 0.0000000049 0.000000 0.00000000 0.0000000050 0.000000 0.00000000 0.00000000

3. Conclusion Section

Conclusion 1

n/a

Conclusion 2

n/a

Function (1), R = a + b /(P * TCPU * U) + e resolution Coefficient a is an intercept and b is a slope of the growth. Regression analysis results:

Interceptl, a =Slope, b =

Correlation, r =

If at least correlation factor above indicates fairly accurate (e can be assumed 0), then function (1) can be used to simulate expected response time R according max processor power you entered in New PMAX input field below. Enter New PMAX to find out the best R for you.

New PMAX = then estimated R =

RAM load, N =

Function (2), R = a + b * S/U + e resolution. Coefficient a is an intercept and b is a slope of the growth. Regression analysis results:

Intercept, a =Slope, b =

Correlation, r =

Based on the correlation factor, if function (2) is at least fairly accurate, we can assume U = S * b/(R - a). Referring formula (9), S = 1/(P * TCPU), we get function (3), U = b / [(R - a) * P * TCPU]. This U can be used to estimate utilization of newly processor according your New PMAX input.

n/aEstimated U = n/a which originally (average):

Support Email

Estimated SMIN =

Deru Sudibyo

1. Input Section

Servicetime I/O servicetime Page-inS m

SHEET FOR SYSTEM PLANNING

Enter your collected performance information into input table below. All column except the last one (m), are required. Group your collection into 50 periods to avoid normality test. Each period should be weighted average of the group.

SIO

0.000000 0.000000 n/a

2. Analysis Section

m k

0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###

TQ = f * c / N = U*c*(1+SIO/S) =k*S/(c*U)-S-SIO

0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###0.000000 0 0.00000000###

n/a n/a n/a

3. Conclusion Section

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resolution Coefficient a is an intercept and b is a slope of the growth.

If at least correlation factor above indicates fairly accurate (e can be assumed 0), then function (1) can be used to simulate according max processor power you entered in New PMAX input field below. Enter New PMAX to

resolution. Coefficient a is an intercept and b is a slope of the growth. Regression

Based on the correlation factor, if function (2) is at least fairly accurate, we can assume U = S * b/(R - a). Referring / [(R - a) * P * TCPU]. This U can be used to estimate utilization of

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