Some simple statistical methods application in computer capacity and performance evaluation. As these are simple methods, accuracies are not guaranteed. But at least better than just common sense.

1. CAPACITY & PERFORMANCE EVALUATION (CPE)
METODA ANALISA KINERJA SISTEM
SYSTEM PERFORMANCE ANALYSIS METHODOLOGY
© 2003 Deru Sudibyo
Kinerja Server Tunggal
Single Server Performance
Throughput X Banyaknya transaksi yg dapat diselesaikan dalam selang waktu tertentu
Number of transactions can be completed during certain time interval
System workload N Banyaknya beban (transaksi) yg ada dalam sistem dalam selang waktu tertentu
Total 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 ==> X= 32.34
Try this N= 3.5000 X= 80.0000 ==> R= 0.043750
X= 17.0000 R= 3.092000 ==> N= 52.56
CPU-time TCPU Banyaknya siklus CPU yang digunakan untuk memproses
Number of CPU cycle consumed for certain process
CPU busy U atau Utilisasi - adalah nisbah CPU-time yg dikonsumsi selama selang waktu tertentu
or Utilization - is ratio of consumed CPU-time against calendar time frame
Formula (2): U = T CPU / T
Service time S CPU-time yg diperlukan untuk menyelesaikan satu transaksi
CPU-time needed to complete a transaction
Formula (3): U = S * X Coba ini S= 0.085000 X= 17.0000 ==> U= 144.50%
Try this S= 0.085000 U= 80.00% ==> X= 9.4118

2. X= 17.0000 U= 100.00% ==> S= 0.058824
Kinerja Server Majemuk
Multi Server Performance
Untuk sejumlah c CPU server, formula (1) dapat diturunkan menjadi sebagai berikut
For c number of server CPUs, formula (1) can be derived as follow:
Formula (4) U = N * m * S / (c * R) dimana R response time
where N system workload
m kerapatan page-in selama menyelesaikan sekali transaksi
pagi-in frequency during performing a transaction
S service time
c banyaknya CPU
number of CPUs
U 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 ==> R= 51.597000 sec
m= 234.0000
N= 35.0000 R= 6.100000
S= 0.082500 c= 5 ==> U= 94.67%
m= 10.0000
Model Linier untuk CPU dan I/O Majemuk
Linear Model for Multi CPU and Multi I/O Services
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) U = Min(υ,1) Fungsi min() ini untuk menghindari U > 100% seperti yang mungkin terjadi pada formula (4)

3. Function of min() is to avoid possibility U > 100% as one probably happen with formula (4)
where
υ = k / [c * (1 + S I O /S)]
Coba ini: k= 19 SIO= 3.700000
Try this: S= 0.185600 c= 2 ==> U= 45.38%
Model Exponensial untuk CPU dan I/O Majemuk
Exponential Model for Multi CPU and Multi I/O Services
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
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
dimana d diperoleh dengan perhitungan sebagai berikut:
where d is obtained from the following calculation:
┌ C(n,k) * S/SIO
for n = 1, 2,…, c
│
rn = │
│ n! * C(n,k) * S
└ _____________ for n = c+1, c+2, … k
cn-c * c! * SIO
Coba latihan ini dan bandingkan dengan kalkulator anda
k Try this exercise and compare with your calculator
p0 = 1/[1 + Σ rn]
n=1
pn = rn * p0 for n = 1, 2, .., k S= 0.185600
SIO= 3.700000
c= 5 S/SIO= 0.05
k
Lq = Σ [n - c] * pn k= 49 p0= 0
n=c+1 Lq= 14.8
Tq= 1.68

4. Tq = Lq*[S + SIO] / [k - Lq] d= 8.8
d = k / [Tq + S + SIO] 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 Pengamatan
Capture Ratio
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 Dimana UAPPL merupakan utilisasi yg diukur pada tingkat program aplikasi
is utilization measured at application program level
UOS merupakan utilisasi yg diukur pada tingkat OS
is utilization measured at OS level

5. PENERAPAN CPE UNTUK PERENCANAAN SISTEM
Di lapangan, pada kenyataannya angka-angka utilisasi, response time, throughput dan beban kerja lain sistem tidak perlu dihi
khusus seperti RMF maupun produk-produk program canggih lainnya yang sudah menyediakan angka-angka tersebut secara
angka-angka tersebut lebih teliti karena pengukuran langsung, ketimbang pendugaan dengan rumus-rumus statistik pada she
penting, bagaimana memanfaatkan angka-angka tersebut untuk mengatur dan merencanakan kapasistas sistem anda. Berik
sederhana tentang bagaimana penerapan di lapangan.
1. Angka-angka yang Diperoleh dari Alat-alat Pemantau
Response time, R Waktu yg diperlukan untuk menyelesaikan satu transaksi sejak memasuki sistem hingga selesai.
pemantau biasanya terinci untuk tiap jenis beban. Untuk keperluan pengaturan kinerja, kita bisa p
akan dianalisa. Tetapi untuk keperluan perencanaan, angka ini harus satu, yaitu angka rata-rata
Maka harus dihitung sendiri angka rata-rata R terboboti. Pilih hanya selang waktu yang paling sib
yang paling berkaitan adalah pemakaian CPU time.
Cobalah contoh ini:
R1 R2 R3 R4
t1 t2 t3 t4
n n
Formula (7) R = Σ(ti * Ri) / Σ ti R= ?
i=1 i=1
CPU busy, U Atau utilisasi - adalah nisbah CPU-time yg dikonsumsi selama selang waktu tertentu. Biasanya,
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 seper
pada setiap beban. Maka cara mendapatkannyapun dengan merata-ratakan seperti R di atas.
Coba contoh ini:
X1 X2 X3 X4
t1 t2 t3 t4
n n
Formula (8) X = Σ(ti * Xi) / Σ ti X= ?
i=1 i=1
CPU service time, S Jumlah CPU-time yg dimanfaatkan untuk melayani satu transaksi. Tergantung alatnya, angka in
apa adanya, ada pula yang dilaporkan berupa angka service rate (misal dalam RMF). Karena 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 proses
operasi I/O atau network. Kita sebut saja I/O time, sehingga SIO adalah jumlah I/O-time yg diman
O satu transaksi. Tergantung alatnya, angka ini ada yang dilaporkan apa adanya, ada pula yang
angka service rate (misal dalam RMF, tapi hanya untuk disk). Karena I/O service rate/detik = 1
membalik angka itu saja.

6. Mirip S tetapi bukan CPU-time, melainkan cycletime-nya IOP atau I/O channel dan seluruh proses
operasi I/O atau network. Kita sebut saja I/O time, sehingga SIO adalah jumlah I/O-time yg diman
O satu transaksi. Tergantung alatnya, angka ini ada yang dilaporkan apa adanya, ada pula yang
angka service rate (misal dalam RMF, tapi hanya untuk disk). Karena I/O service rate/detik = 1
membalik angka itu saja.
Page-in rate, m Jumlah pemanggilan kembali isi memori yang telah disapu ke penampungan selama melayani sat
mengambarkan bahwa terjadi secara serempak dan tidak semua mendapat pelayanan. Karena m
menampung yang antre, maka disapu ke penampungan (auxiliary storage). Untuk sistem non-m
kebanyakan tidak dilaporkan.
Interval, tINTV Interval atau selang waktu yang digunakan oleh alat pemantau untuk menggali informasi kinerja si
ini ditetapkan dalam parameter alat pemantau, namun pelaksanaannya pasti ada sedikit penyimpa
yang baik pasti melaporkan angka tINTV ini agar laporannya bisa dianalisa lanjut.
2. Angka-angka Pabrikan
Processor power, PMAX Konstanta pabrikan tentang besarnya tenaga prosesor. P adalah maximum banyaknya service u
diberikan dalam setiap detik CPU-time. Dalam terminologi IBM dinamakan SRM constant. Bila
dalam satuan SU/CPUsec, agar dikonversi dulu menjadi angka ini.
Konsumsi processor power untuk sistem dirumuskan sebagai berikut:
Formula (9) P = 1 / (S * TCPU) PMAX adalah P pada saat utilisasi U = 100%, atau TCPU = tINTV.
3. Langkah-langkah Perhitungan Kapasitas
Setelah mendapatkan angka-angka yang cukup akurat dari laporan alat pemantau, perhitungan pe
dimulai.
Langkah 1 Kumpulkan pemantauan kinerja sistem dalam kurun yang cukup panjang. Laporan hanya untuk s
harus dipisahkan antara saat tersibuk online dan tersibuk batch. Untuk mainframe OS/390 atau
karena SMF melakukannya secara otomatis.
Berikut ini contoh hasil pengumpulan laporan pemantauan berkala dalam 12 kurun. Anggap saja
angka setiap bulannya merupakan hasil perhitungan rata-rata terboboti seperti dalam formula (7) d
harian. Silakan dicoba mengganti angka2 contoh ini dengan data anda.
Power PMAX = 335.0000
#CPU c = 6
Kurun Interval Resp.time Utilisasi Thruput
tINTV R U X
1 15.0450 2.002300 60.000% 480.2300
2 14.8730 2.004630 62.000% 470.4500

7. 3 15.0010 2.004986 61.000% 468.4300
4 14.9670 2.005321 64.000% 475.4000
5 14.7840 2.018625 67.500% 491.2340
6 14.7820 2.051946 70.200% 513.4550
7 14.3890 2.092395 71.900% 550.4560
8 14.4782 2.107058 80.000% 601.3456
9 15.0032 2.187599 82.000% 599.4500
10 14.9780 2.258318 84.000% 613.7310
11 14.7380 2.428865 87.000% 612.2340
12 14.8360 2.589000 90.000% 625.4570
Rata-rata 14.8229 2.145920 73.300% 541.8227
Langkah 2 Menghitung angka-angka statistik yang diperlukan berdasarkan masukan data di atas. Yang palin
adalah CPU-time TCPU = tINTV * U, dan pemakaian power (P) merujuk formula (9). Beberapa yang
analisa pelengkap jika diperlukan.
Kurun t N=R*X TCPU P
= tINTV * U = 1/(S * TCPU)
1 961.5645 9.02700000 89.7721
2 943.0782 9.22126000 82.1553
3 939.1956 9.15061000 82.5769
4 953.3296 9.57888000 76.0120
5 991.6170 9.97920000 71.1556
6 1,053.5817 10.37696400 65.8516
7 1,151.7714 10.34569100 68.3873
8 1,267.0699 11.58256000 60.6638
9 1,311.3560 12.30262400 55.5845
10 1,385.9995 12.58152000 55.4265
11 1,487.0337 12.82206000 52.5897
12 1,619.3082 13.35240000 50.1493
Indikator 1 1 1
Rata-rata 1,172.0754 10.86006408 67.5271
Langkah 3 (Akhir) Fokus utama dalam perhitungan kapasitas adalah pada angka yang paling penting bagi penggu
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
ada hubungan fungsi R = β * (S/U), dimana β = (k/c) = (N*m/c). Merujuk formula (9) bahwa S = 1
dapat dinyatakan R = β / (P * TCPU * U). Jika 1/(P * TCPU * U) dan S/U kita anggap sebagai satu pe
hubungannya dengan R bisa dianggap hubungan linier. Selanjutnya kita cari penyelesaian hubun
U) + ε dan R = α + β / (P ∗ TCPU ∗ U) + ε dengan analisis regresi sederhana.

8. Dari formula (4) diperoleh R = (N*m/c) * S/U. Sedangkan formula (6), jika R = TQ + S + SIO, maka
ada hubungan fungsi R = β * (S/U), dimana β = (k/c) = (N*m/c). Merujuk formula (9) bahwa S = 1
dapat dinyatakan R = β / (P * TCPU * U). Jika 1/(P * TCPU * U) dan S/U kita anggap sebagai satu pe
hubungannya dengan R bisa dianggap hubungan linier. Selanjutnya kita cari penyelesaian hubun
U) + ε dan R = α + β / (P ∗ TCPU ∗ U) + ε dengan analisis regresi sederhana.
Kurun t R S/U 1/(P * TCPU * U)
1 2.002300 0.00205667 0.00139934
2 2.004630 0.00212903 0.00152907
3 2.004986 0.00216951 0.00152126
4 2.005321 0.00214597 0.00165265
5 2.018625 0.00208637 0.00176545
6 2.051946 0.00208462 0.00190764
7 2.092395 0.00196579 0.00183691
8 2.107058 0.00177900 0.00207078
9 2.187599 0.00178334 0.00226001
10 2.258318 0.00170714 0.00226645
11 2.428865 0.00170460 0.00238871
12 2.589000 0.00165933 0.00250495
Penyimpulan 1 Menyelesaikan hubungan fungsi (1), R = α + β /(P ∗ TCPU ∗ U) + ε dan menghitung indikator korelas
merupakan nilai awal dan β laju perkembangannya. Dengan analisa regresi linier diperoleh:
Nilai awal, α = 1.265756
Laju, β = 457.164617
Korelasi, r = 0.886411 akurat
Jika indikasi korelasi yang diperoleh di atas cukup akurat (ε boleh dianggap 0), maka fungsi (1) bis
mensimulasi response time R yang anda kehendaki dengan merubah angka PMAX seolah memilih
Silakan dicoba memilih PMAX.
PMAX baru = 500.0000 maka R baru = 1.83556968
beban RAM, N = 1,002.5658
Penyimpulan 2 Menyelesaikan hubungan hubungan (2), R = α + β ∗ S/U + ε dan menghitung indikator korelasinya
merupakan nilai awal dan β laju perkembangannya. Dengan analisa regresi linier diperoleh:
Nilai awal, α = 3.764354
Laju, β = -834.554114
Korelasi, r = -0.861157 akurat
Jika dari korelasinya, hubungan fungsi (2) akurat, maka U = S ∗ β/(R - α). Merujuk formula (9), S
diperoleh hubungan fungsi (3), U = β / [(R - α) ∗ P ∗ TCPU]. U dalam fungsi ini bisa digunakan untu
prosesor dengan PMAX baru kelak, yaitu:

9. Jika dari korelasinya, hubungan fungsi (2) akurat, maka U = S ∗ β/(R - α). Merujuk formula (9), S
diperoleh hubungan fungsi (3), U = β / [(R - α) ∗ P ∗ TCPU]. U dalam fungsi ini bisa digunakan untu
prosesor dengan PMAX baru kelak, yaitu:
S baru, SMIN = 0.00091362
U baru, U = 39.531% rata-rata semula adalah:
berarti turun sebesar:
4. Tambahan
Catatan Akurasi dari penyimpulan-penyimpulan di atas, sangat tergantung dari normalitas data laporan yan
Tentu, makin banyak data yang dianalisa, makin normal sebarannya. Berarti makin akurat hasilny
bisa menguji seberapa akurat analisa ini dengan cara memasok PMAX baru = PMAX semula dan perh
angka R dan U baru yang diperoleh ada perubahan, berarti analisa tidak akurat. Malahnya, tidak
menjamin analisa akurat, sampai anda buktikan data yang dipasok normal dan koreaslinya mengin
"cukup akurat". Jika ada pertanyaan atau koreksi, silakan email saya.
Email Deru Sudibyo
Khusus untuk OS/390 Pertimbangan khusus untuk OS/390 maupun z/OS, angka R dapat diambil langsung dari laporan R
"WORKLOAD ACTIVITY" di bagian total keseluruhan workload-policy. Info R ada di kolom TRAN
Biasanya angka ini cukup besar karena merupakan rata-rata R untuk seluruh beban termasuk ba
menginginkan R aplikasi interaktif online, harus dipilih loporan pada interval online saja, tapi harus
kepadatan transaksi, X bisa diperoleh dari baris END/S pada kolom TRANSACTIONS. Service t
langsung, tapi tinggal menghitung TOT - IOC pada kolom SERVICE, hasilnya adalah service rate.
O service time bisa menggunakan IOC pada kolom SERVICE, maupun RESP pada kolom DASD-
bahkan tersedia dalam satu kolom terpisah. Utilisasi, U diperoleh dari laporan CPU ACTIVITY.

10. ANAAN SISTEM
an beban kerja lain sistem tidak perlu dihitung lagi. Ada program
enyediakan angka-angka tersebut secara otomatis. Bahkan
n dengan rumus-rumus statistik pada sheet sebelumnya. Yang
ncanakan kapasistas sistem anda. Berikut ini penjelasan
mantau
sejak memasuki sistem hingga selesai. Angka dari alat
k keperluan pengaturan kinerja, kita bisa pilih beban mana yg
ngka ini harus satu, yaitu angka rata-rata keseluruhan sistem.
Pilih hanya selang waktu yang paling sibuk. Faktor pembobot
R5 R6 R7
t5 t6 t7
elama selang waktu tertentu. Biasanya, angka tunggal untuk
u, sehingga tidak perlu dirata-ratakan lagi.
g waktu tertentu. Bisanya angka ini seperti R, menyebar terinci
engan merata-ratakan seperti R di atas.
X5 X6 X7
t5 t6 t7
ransaksi. Tergantung alatnya, angka ini ada yang dilaporkan
vice rate (misal dalam RMF). Karena service rate/detik = 1/S,
IOP atau I/O channel dan seluruh prosesor yang terkait dengan
ngga SIO adalah jumlah I/O-time yg dimanfaatkan untuk melayani I/
ng dilaporkan apa adanya, ada pula yang dilaporkan berupa
disk). Karena I/O service rate/detik = 1/SIO, maka tinggal

11. pu ke penampungan selama melayani satu transaksi. Ini
k semua mendapat pelayanan. Karena memori tidak cukup
(auxiliary storage). Untuk sistem non-mainframe, angka ini
mantau untuk menggali informasi kinerja sistem. Meskipun angka
elaksanaannya pasti ada sedikit penyimpangan. Alat pemantau
ya bisa dianalisa lanjut.
P adalah maximum banyaknya service unit (SU) yang bisa
ogi IBM dinamakan SRM constant. Bila angka pabrikan tidak
angka ini.
bagai berikut:
aat utilisasi U = 100%, atau TCPU = tINTV.
ari laporan alat pemantau, perhitungan pendugaan kapasitas bisa
g cukup panjang. Laporan hanya untuk saat-saat tersibuk, dan
k batch. Untuk mainframe OS/390 atau z/OS lebih mudah
an berkala dalam 12 kurun. Anggap saja selama 12 bulan dan
-rata terboboti seperti dalam formula (7) dan (8) dari laporan
ngan data anda.
Servicetime I/O servicetime Page-in
S SIO m
0.001234 0.237800
0.001320 0.297800

12. 0.001323 0.389700
0.001373 0.352300
0.001408 0.398700
0.001463 0.421000
0.001413 0.498000
0.001423 0.502300
0.001462 0.568930
0.001434 0.600000
0.001483 0.623400
0.001493 1.389324
0.001403 0.523271 0.000000
sarkan masukan data di atas. Yang paling diperlukan disini
P) merujuk formula (9). Beberapa yang lain disertakan untuk
m k TQ
=f*c/N = U*c*(1+SIO/S) =k*S/(c*U)-S-SIO
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 0
5.777798 1,705 0.00000000
angka yang paling penting bagi pengguna, yaitu response
encerminkan fungsi bagi response time.
n formula (6), jika R = TQ + S + SIO, maka R = (k/c) * S/U. Tampak
N*m/c). Merujuk formula (9) bahwa S = 1/(P * TCPU), maka R
* U) dan S/U kita anggap sebagai satu peubah bebas, maka
Selanjutnya kita cari penyelesaian hubungan linier R = a + β ∗ (S/
regresi sederhana.

13. ∗ U) + ε dan menghitung indikator korelasinya. Koefisien α
ngan analisa regresi linier diperoleh:
(ε boleh dianggap 0), maka fungsi (1) bisa digunakan untuk
gan merubah angka PMAX seolah memilih prosesor yang tepat.
yang semula: 2.14592009
perbaikan: 14.46%
yang semula: 1,172.0754
perbaikan: 14.46%
+ ε dan menghitung indikator korelasinya. Koefisien α
ngan analisa regresi linier diperoleh:
U = S ∗ β/(R - α). Merujuk formula (9), S = 1/(P * TCPU), maka
]. U dalam fungsi ini bisa digunakan untuk menduga utilisasi

14. 73.300%
46.070%
rgantung dari normalitas data laporan yang anda kumpulkan.
sebarannya. Berarti makin akurat hasilnya. Secara awam anda
emasok PMAX baru = PMAX semula dan perhatikan hasilnya. Jika
arti analisa tidak akurat. Malahnya, tidak adanya perubahan tidak
g dipasok normal dan koreaslinya mengindikasikan minimal
an email saya.
a R dapat diambil langsung dari laporan RMF monitor I topik
rkload-policy. Info R ada di kolom TRANS.-TIME baris ACTUAL.
-rata R untuk seluruh beban termasuk batch job. Jika hanya
poran pada interval online saja, tapi harus yang paling padat. Info
ada kolom TRANSACTIONS. Service time memang tidak
m SERVICE, hasilnya adalah service rate. S = 1/(servicerate). I/
VICE, maupun RESP pada kolom DASD-I/O. Page-in rate juga
diperoleh dari laporan CPU ACTIVITY.

15. 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 m
sophisticated tools that can obtain those values automatically. Even more accurate because they directly measure, instead of
statistical formulas as presented on the previous sheet. The important thing is how to use those values to manage and plan y
Below is a brief hint how to do it.
1. Information collected from Monitor Tool Reports
Response time, R Amount of time needed to complete a transaction since entered to the system. Usually, monitor t
detail for each particular workload. For tuning, R can be selected only from certain workload we c
planning, however, R must represent the whole system. Hence, we need to calculate the weighte
whole system workload Keep in mind that all observation must be within peak time only period.
weight factor is CPU time.
Try example below:
R1 R2 R3 R4
t1 t2 t3 t4
n n
Formula (7) R = Σ(ti * Ri) / Σ ti R= ?
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
certain monitor tool report.
Throughput, X Number of transactions completed during certain time interval. As R info, usually X is reported in d
workload. To get a single info, do the same way as R, calculate weighted average.
Try example below:
X1 X2 X3 X4
t1 t2 t3 t4
n n
Formula (8) X = Σ(ti * Xi) / Σ ti X= ?
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 mi
are service rate in service units (SU). Since service rate/sec = 1/S, so S can be easily obtained
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 an
involve during I/O operation whether to I/O or network devices. From the view of device-RAM inte
considered as I/O response time. Just say I/O time, hence SIO is a number of I/O-time to serve a
certain transaction. Depend on the tool, some reported in time unity, and some others in rate.
rate/sec = 1/SIO, hence SIO can be obtained in the same way as S.

16. Service time of I/O. The unity is not CPU seconds instead, but cycletime of IOP or I/O channel an
involve during I/O operation whether to I/O or network devices. From the view of device-RAM inte
considered as I/O response time. Just say I/O time, hence SIO is a number of I/O-time to serve a
certain transaction. Depend on the tool, some reported in time unity, and some others in rate.
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.
not all concurrent transaction can be served. Some have to be placed in queue. When memory i
queued transactions are swapped-out to auxiliary storage. Not every tool reports this information.
system, however, RMF reports this information.
Interval, tINTV Time interval used by the tool to explore information of system performance. Although interval us
parameter, in fact it could be bias. The fair tools like RMF (in mainframe) always report tINTV infor
custom analysis.
2. Manufacturer Information
Processor power, PMAX Manucaturer constant of certain model and type of processor regarding processing power. P is a
service unit (SU) can be delivered during a CPU second. In IBM terminology P is named as SRM
SU/CPUsec, should be converted first to SU/CPUsec equivalent.
Processor power is formulated as follow:
Formula (9) P = 1 / (S * TCPU) PMAX is P when U = 100%, or TCPU = tINTV.
3. Capacity Analysis Stages
Once a number of accurate tool reports are collected, capacity analysis can be started in 3 stages
number of colected information must be enough to get all data in statistical normal distribution.
Stage 1 Group the reports into several time periods. Remember that reports must only for peak time. To a
peak and batch peak must be in separated groups. For mainframe OS/390 or z/OS easier becau
automatically.
Below is an example form periodical reports during 12 time period groups. Assume as 12months
table is weighted average obtained from its group of daily reports according to formula (7) and (8).
and modifiable. You can try with either your dummy for excercise or true info for real analysis.
Power PMAX = 335.0000
#CPU c = 6
Period Interval Resp.time Utilization Thruput
tINTV R U X
1 15.0450 2.002300 60.000% 480.2300
2 14.8730 2.004630 62.000% 470.4500

17. 3 15.0010 2.004986 61.000% 468.4300
4 14.9670 2.005321 64.000% 475.4000
5 14.7840 2.018625 67.500% 491.2340
6 14.7820 2.051946 70.200% 513.4550
7 14.3890 2.092395 71.900% 550.4560
8 14.4782 2.107058 80.000% 601.3456
9 15.0032 2.187599 82.000% 599.4500
10 14.9780 2.258318 84.000% 613.7310
11 14.7380 2.428865 87.000% 612.2340
12 14.8360 2.589000 90.000% 625.4570
Average 14.8229 2.145920 73.300% 541.8227
Stage 2 Calculate necessary statistical values based on the above observation table. The most important
CPU-time, TCPU = tINTV * U, and processing power consumption (P) according to formula (9). Some
just a reserved for further analysis if needed.
Period t N=R*X TCPU P
= tINTV * U = 1/(S * TCPU)
1 961.5645 9.02700000 89.7721
2 943.0782 9.22126000 82.1553
3 939.1956 9.15061000 82.5769
4 953.3296 9.57888000 76.0120
5 991.6170 9.97920000 71.1556
6 1,053.5817 10.37696400 65.8516
7 1,151.7714 10.34569100 68.3873
8 1,267.0699 11.58256000 60.6638
9 1,311.3560 12.30262400 55.5845
10 1,385.9995 12.58152000 55.4265
11 1,487.0337 12.82206000 52.5897
12 1,619.3082 13.35240000 50.1493
Average 1,172.0754 10.86006408 67.5271
Stage 3 (Final) Main focus in capacity analysis is the most important value for users, which is response time, R
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/
R = β * (S/U), where β = (k/c) = (N*m/c). Referring formula (9) that S = 1/(P * TCPU), so R can be s
TCPU * U). Assuming that 1/(P * TCPU * U) and S/U can be assumed as independent variables, then
relationships to R above can be assumed as linear functions. Next is to find resolution for both lin
∗ (S/U) + ε and R = α + β / (P ∗ TCPU ∗ U) + ε using simple linear regression analysis method.

18. From formula (4) we get R = (N*m/c) * S/U. Based on formula (6), if R = TQ + S + SIO, then R = (k/
R = β * (S/U), where β = (k/c) = (N*m/c). Referring formula (9) that S = 1/(P * TCPU), so R can be s
TCPU * U). Assuming that 1/(P * TCPU * U) and S/U can be assumed as independent variables, then
relationships to R above can be assumed as linear functions. Next is to find resolution for both lin
∗ (S/U) + ε and R = α + β / (P ∗ TCPU ∗ U) + ε using simple linear regression analysis method.
Period t R S/U 1/(P * TCPU * U)
1 2.002300 0.00205667 0.00139934
2 2.004630 0.00212903 0.00152907
3 2.004986 0.00216951 0.00152126
4 2.005321 0.00214597 0.00165265
5 2.018625 0.00208637 0.00176545
6 2.051946 0.00208462 0.00190764
7 2.092395 0.00196579 0.00183691
8 2.107058 0.00177900 0.00207078
9 2.187599 0.00178334 0.00226001
10 2.258318 0.00170714 0.00226645
11 2.428865 0.00170460 0.00238871
12 2.589000 0.00165933 0.00250495
Conclusion 1 Resolve function (1), R = α + β /(P ∗ TCPU ∗ U) + ε and find its correlation factor. Coefficient α is a
slope of the growth. Regression analysis results:
Interceptl, α = 1.265756
Slope, β = 457.164617
Correlation, r = 0.886411 accurate
If at least correlation factor above indicates fairly accurate (ε can be assumed 0), then function (1)
expected response time R according max processor power you entered in New PMAX input field be
PMAX to find out the best R for you.
New PMAX = 400.0000 then estimated R =
RAM load, N =
Conclusion 2 Resolve function (2), R = α + β ∗ S/U + ε and find its correlation factor. Coefficient α is an interce
growth. Regression analysis results:
Intercept, α = 3.764354
Slope, β = -834.554114
Correlation, r = -0.861157 accurate
Based on the correlation factor, if function (2) is at least fairly accurate, we can assume U = S ∗ β/(
formula (9), S = 1/(P * TCPU), we get function (3), U = β / [(R - α) ∗ P ∗ TCPU]. This U can be used to
newly processor according your New PMAX input.

19. Based on the correlation factor, if function (2) is at least fairly accurate, we can assume U = S ∗ β/(
formula (9), S = 1/(P * TCPU), we get function (3), U = β / [(R - α) ∗ P ∗ TCPU]. This U can be used to
newly processor according your New PMAX input.
Estimated SMIN 0.00114202
Estimated U = 53.354% which originally (average):
hence lowered:
4. Additional Infos
Note Accuracy of the above conclusions, very depend on normality of data from collected monitor repor
will get closer to normal distribution. The result, of course is more accurate. Actually, accuracy of
be easily verified. Just enter new PMAX = old PMAX, then see estimated R and U resulted. If not th
improvements or changes, then analisys is inaccurate . The problem, no changes when you type
doesn't mean that analysis is accurate, until you can prove that data you have collected is normal
indicates at least fairly accurate. Drop me a message should you have any question or critizise f
Email Deru Sudibyo
Special notes for OS/390 Special consideration for OS/390 and z/OS, that R is reported by RMF monitor I on "WORKLOAD
last part, which is whole workload-policy. Info of R is in column TRANS.-TIME item ACTUAL. Us
this R is average of whole system workload, including batch jobs and long running STCs. If you o
interactive application, that's why, batch shift report must be grouped separately. Info of transacti
END/S of column TRANSACTIONS. Service time is not directly reported, but just calculate TOT
SERVICE, then inverse it since it is service rate. S = 1/(servicerate). I/O service time can be ob
column SERVICE, or RESP at column DASD-I/O. Page-in rate is even provided in a separate co
separated on CPU ACTIVITY report.

20. M PLANNING
dicators, don't need to be calculated any more. There are lots of
because they directly measure, instead of estimation using
o use those values to manage and plan your system capacity.
s
entered to the system. Usually, monitor tool provides R value in
selected only from certain workload we concern to. For capacity
Hence, we need to calculate the weighted average R value of
n must be within peak time only period. The most relevant
R5 R6 R7
t5 t6 t7
certain time interval. A single value of U is usually provided in
erval. As R info, usually X is reported in detail for each particular
calculate weighted average.
X5 X6 X7
t5 t6 t7
me tools report S directly in seconds or milliseconds. Some others
te/sec = 1/S, so S can be easily obtained. For example, service
ad, but cycletime of IOP or I/O channel and all other processors
vices. From the view of device-RAM interaction, it can be
ce SIO is a number of I/O-time to serve a single I/O operation of a
in time unity, and some others in rate. Since I/O service
way as S.

21. to memory during serving a transaction. This factor illustrates
e to be placed in queue. When memory is not enough, some
e. Not every tool reports this information. For IBM mainframe
ystem performance. Although interval usually set in the monitor
MF (in mainframe) always report tINTV information for further
ssor regarding processing power. P is a maximum number of
In IBM terminology P is named as SRM constant. If P is not in
uivalent.
0%, or TCPU = tINTV.
pacity analysis can be started in 3 stages below. Note that
l data in statistical normal distribution.
that reports must only for peak time. To avoid misleading, online
mainframe OS/390 or z/OS easier because SMF does it
me period groups. Assume as 12months and each info in the
y reports according to formula (7) and (8). These are just dummy
excercise or true info for real analysis.
Servicetime I/O servicetime Page-in
S SIO m
0.001234 0.237800
0.001320 0.297800

22. 0.001323 0.389700
0.001373 0.352300
0.001408 0.398700
0.001463 0.421000
0.001413 0.498000
0.001423 0.502300
0.001462 0.568930
0.001434 0.600000
0.001483 0.623400
0.001493 1.389324
0.001403 0.523271 0.000000
e observation table. The most important statistical values are
mption (P) according to formula (9). Some others also listed below
m k TQ
=f*c/N = U*c*(1+SIO/S) =k*S/(c*U)-S-SIO
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
alue for users, which is response time, R. Then determine the
rmula (6), if R = TQ + S + SIO, then R = (k/c) * S/U. Both show that
ula (9) that S = 1/(P * TCPU), so R can be stated as R = β / (P *
e assumed as independent variables, then both functional
ons. Next is to find resolution for both linear functions, R = a + β
e linear regression analysis method.

23. d its correlation factor. Coefficient α is an intercept and β is a
e (ε can be assumed 0), then function (1) can be used to simulate
er you entered in New PMAX input field below. Try specify New
1.97802321 which originally: 2.14592009
improvement: 7.82%
1,080.3722 whch originally: 1,172.0754
improvement: 7.82%
elation factor. Coefficient α is an intercept and β is a slope of the
airly accurate, we can assume U = S ∗ β/(R - α). Referring
(R - α) ∗ P ∗ TCPU]. This U can be used to estimate utilization of

24. 73.300%
27.211%
mality of data from collected monitor reports. More data gathered
e is more accurate. Actually, accuracy of the above analysis can
see estimated R and U resulted. If not the same, mean there are
The problem, no changes when you type new PMAX = old PMAX, it
ve that data you have collected is normal and correlation factor
hould you have any question or critizise for correction.
orted by RMF monitor I on "WORKLOAD ACTIVITY" report, in the
column TRANS.-TIME item ACTUAL. Usually it quite high since
tch jobs and long running STCs. If you only expect R of online
be grouped separately. Info of transaction rate, X is item baris
t directly reported, but just calculate TOT - IOC of column
servicerate). I/O service time can be obtained from item IOC of
e-in rate is even provided in a separate column. Utilization, U is

25. CPE SHEET FOR SYSTEM PLANNING
1. Input Section
Enter your collected performance information into input table below. All column except the last o
Group your collection into 50 periods to avoid normality test. Each period should be weighted av
Technical specs
Power PMAX =
#CPU c =
Input table
Period Interval Resp.time Utilization Thruput
tINTV R U X
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27

26. 28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
Average 0.0000 0.000000 0.000% 0.0000
2. Analysis Section
0
Period t N=R*X TCPU P
= tINTV * U = 1/(S * TCPU)
1 0.0000 0.00000 0.0000
2 0.0000 0.00000 0.0000
3 0.0000 0.00000 0.0000
4 0.0000 0.00000 0.0000
5 0.0000 0.00000 0.0000
6 0.0000 0.00000 0.0000
7 0.0000 0.00000 0.0000
8 0.0000 0.00000 0.0000
9 0.0000 0.00000 0.0000
10 0.0000 0.00000 0.0000
11 0.0000 0.00000 0.0000

27. 12 0.0000 0.00000 0.0000
13 0.0000 0.00000 0.0000
14 0.0000 0.00000 0.0000
15 0.0000 0.00000 0.0000
16 0.0000 0.00000 0.0000
17 0.0000 0.00000 0.0000
18 0.0000 0.00000 0.0000
19 0.0000 0.00000 0.0000
20 0.0000 0.00000 0.0000
21 0.0000 0.00000 0.0000
22 0.0000 0.00000 0.0000
23 0.0000 0.00000 0.0000
24 0.0000 0.00000 0.0000
25 0.0000 0.00000 0.0000
26 0.0000 0.00000 0.0000
27 0.0000 0.00000 0.0000
28 0.0000 0.00000 0.0000
29 0.0000 0.00000 0.0000
30 0.0000 0.00000 0.0000
31 0.0000 0.00000 0.0000
32 0.0000 0.00000 0.0000
33 0.0000 0.00000 0.0000
34 0.0000 0.00000 0.0000
35 0.0000 0.00000 0.0000
36 0.0000 0.00000 0.0000
37 0.0000 0.00000 0.0000
38 0.0000 0.00000 0.0000
39 0.0000 0.00000 0.0000
40 0.0000 0.00000 0.0000
41 0.0000 0.00000 0.0000
42 0.0000 0.00000 0.0000
43 0.0000 0.00000 0.0000
44 0.0000 0.00000 0.0000
45 0.0000 0.00000 0.0000
46 0.0000 0.00000 0.0000
47 0.0000 0.00000 0.0000
48 0.0000 0.00000 0.0000
49 0.0000 0.00000 0.0000
50 0.0000 0.00000 0.0000
Average n/a n/a n/a

28. Period t R S/U 1/(P * TCPU * U)
1 0.000000 0.00000000 0.00000000
2 0.000000 0.00000000 0.00000000
3 0.000000 0.00000000 0.00000000
4 0.000000 0.00000000 0.00000000
5 0.000000 0.00000000 0.00000000
6 0.000000 0.00000000 0.00000000
7 0.000000 0.00000000 0.00000000
8 0.000000 0.00000000 0.00000000
9 0.000000 0.00000000 0.00000000
10 0.000000 0.00000000 0.00000000
11 0.000000 0.00000000 0.00000000
12 0.000000 0.00000000 0.00000000
13 0.000000 0.00000000 0.00000000
14 0.000000 0.00000000 0.00000000
15 0.000000 0.00000000 0.00000000
16 0.000000 0.00000000 0.00000000
17 0.000000 0.00000000 0.00000000
18 0.000000 0.00000000 0.00000000
19 0.000000 0.00000000 0.00000000
20 0.000000 0.00000000 0.00000000
21 0.000000 0.00000000 0.00000000
22 0.000000 0.00000000 0.00000000
23 0.000000 0.00000000 0.00000000
24 0.000000 0.00000000 0.00000000
25 0.000000 0.00000000 0.00000000
26 0.000000 0.00000000 0.00000000
27 0.000000 0.00000000 0.00000000
28 0.000000 0.00000000 0.00000000
29 0.000000 0.00000000 0.00000000
30 0.000000 0.00000000 0.00000000
31 0.000000 0.00000000 0.00000000
32 0.000000 0.00000000 0.00000000
33 0.000000 0.00000000 0.00000000
34 0.000000 0.00000000 0.00000000
35 0.000000 0.00000000 0.00000000
36 0.000000 0.00000000 0.00000000
37 0.000000 0.00000000 0.00000000
38 0.000000 0.00000000 0.00000000
39 0.000000 0.00000000 0.00000000

29. 40 0.000000 0.00000000 0.00000000
41 0.000000 0.00000000 0.00000000
42 0.000000 0.00000000 0.00000000
43 0.000000 0.00000000 0.00000000
44 0.000000 0.00000000 0.00000000
45 0.000000 0.00000000 0.00000000
46 0.000000 0.00000000 0.00000000
47 0.000000 0.00000000 0.00000000
48 0.000000 0.00000000 0.00000000
49 0.000000 0.00000000 0.00000000
50 0.000000 0.00000000 0.00000000
3. Conclusion Section
Conclusion 1 Function (1), R = α + β /(P ∗ TCPU ∗ U) + ε resolution Coefficient α is an intercept and β is a slope
Regression analysis results:
Interceptl, α =
Slope, β =
Correlation, r = n/a
If at least correlation factor above indicates fairly accurate (ε can be assumed 0), then function (1)
expected response time R according max processor power you entered in New PMAX input field be
find out the best R for you.
New PMAX = then estimated R =
RAM load, N =
Conclusion 2 Function (2), R = α + β ∗ S/U + ε resolution. Coefficient α is an intercept and β is a slope of the g
analysis results:
Intercept, α =
Slope, β =
Correlation, r = n/a
Based on the correlation factor, if function (2) is at least fairly accurate, we can assume U = S ∗ β/(
formula (9), S = 1/(P * TCPU), we get function (3), U = β / [(R - α) ∗ P ∗ TCPU]. This U can be used to
newly processor according your New PMAX input.
Estimated SMIN n/a
=

30. Estimated U = n/a which originally (average):
Support Email Deru Sudibyo

31. G
able below. All column except the last one (m), are required.
est. Each period should be weighted average of the group.
Servicetime I/O servicetime Page-in
S SIO m

32. 0.000000 0.000000 n/a
m k 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

33. 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

35. oefficient α is an intercept and β is a slope of the growth.
e (ε can be assumed 0), then function (1) can be used to simulate
er you entered in New PMAX input field below. Enter New PMAX to
wrong input!!! which originally: 0.00000000
improvement: n/a
n/a whch originally: n/a
improvement: n/a
α is an intercept and β is a slope of the growth. Regression
airly accurate, we can assume U = S ∗ β/(R - α). Referring
(R - α) ∗ P ∗ TCPU]. This U can be used to estimate utilization of

36. 0.000%
n/a