Modeling of Multi-Component Server Systems

Build and simulate a reliability model for server components using standard lifetime distributions

A data center needs 20 servers (each consisting of a disk, CPU, and RAM), one power supply, one cooling system, and one network connection to work. The power supply has a standby component. The network connection consists of two parallel connections.

Define disk reliability. Each disk system can tolerate one failure out of three:

In[1]:=

ℛhdd=ReliabilityDistributionBooleanCountingFunction[{2,3},{x,y,z}],{{x,WeibullDistribution[4,1.25

]},{y,WeibullDistribution[4,1.25

]},{z,WeibullDistribution[4,1.25

]}};

Define CPU and RAM lifetime distributions:

In[2]:=

cpu=ExponentialDistribution[1/30000];ram=WeibullDistribution[.82,2500];

Model a single server's reliability (works only if all components work):

In[3]:=

ℛServer=ReliabilityDistribution[hdd∧cpu∧ram,{{hdd,ℛhdd},{cpu,cpu},{ram,ram}}];

Model the power supply with

StandbyDistribution

In[4]:=

PowerSupply=StandbyDistribution[ExponentialDistribution[1/5000],{ExponentialDistribution[1/2000]}];

Model network and cooling components:

In[5]:=

Network=ParetoDistribution[1500,10];Cooling=ExponentialDistribution[1/5000];

Define server variables and the data center logical structure:

In[6]:=

servervars=Table[

,{i,20}];serverdists=Table[{i,ℛServer},{i,servervars}];ℛDatacenter=ReliabilityDistribution[(And@@servervars)∧power∧(net1∨net2)∧cooling,Join[serverdists,{{power,PowerSupply},{net1,Network},{net2,Network},{cooling,Cooling}}]];

Calculate the mean time to failure (MTTF):

In[7]:=

NExpectation[t,tℛDatacenter]

Out[7]=

66.8787

Simulate the uptime of the data center:

In[8]:=

Histogram[RandomVariate[ℛDatacenter,100],AxesLabel{"Lifetime (hours)","Frequency"},ChartStyle"Pastel",PlotLabel"Simulated Data Center Lifetimes",ImageSize400]

Out[8]=